Patent Publication Number: US-11655498-B2

Title: Systems and methods for genetic identification and analysis

Description:
RELATED APPLICATIONS 
     This application is a national stage filing under 35 U.S.C. § 371 of international PCT application, PCT/US2018/041081, filed Jul. 6, 2018, entitled “SYSTEMS AND METHODS FOR GENETIC IDENTIFICATION AND ANALYSIS,” which claims the benefit of the filing date of U.S. Provisional Application No. 62/529,939, filed on Jul. 7, 2017, entitled “SYSTEMS AND METHODS FOR ALLELE IDENTIFICATION AND ANALYSIS,” and U.S. Provisional Application No. 62/534,590, filed on Jul. 19, 2017, entitled “DNA MIXTURES FROM ONE OR MORE SOURCES AND METHODS OF BUILDING INDIVIDUAL PROFILES THEREFROM.” The contents of these applications are incorporated herein by reference in their entirety. 
    
    
     GOVERNMENT SUPPORT 
     This invention was made with Government support under Contract No. FA8721-05-C-0002 awarded by the U.S. Air Force. The Government has certain rights in the invention. 
    
    
     BACKGROUND 
     Sequence differences in the human genome are a cornerstone in human identification and forensic applications. Genetic fingerprinting is a forensic technique used to identify individuals by characteristics of their genetic information (e.g., RNA, DNA). A genetic fingerprint is a small set of one or more nucleic acid variations that is likely to be different in all unrelated individuals, thereby being as unique to individuals as are fingerprints. 
     Current forensic standards have been developed using unlinked short tandem repeat (STR) polymorphisms. The FBI has defined core STR loci for the Combined DNA Index System (CODIS) database as the current forensic standard in the United States. Current forensic protocols identify STR alleles by length of polymerase chain reaction (PCR) amplicons sized on capillary electrophoresis (CE) instruments. 
     Criminal justice DNA forensics provides for identification based on characterization of sets of short tandem repeats (STRs) found in DNA samples. For example, a sample taken from a suspect can be compared to an independent sample (e.g., from a crime scene) to determine a match. Conventional methodologies rely upon identifying the length of repeat patterns, (sizing of number of repeat units and any partial repeat units) of STR loci (specific known positions and sequences of DNA) in DNA amplified by the polymerase chain reaction (PCR). The amplified DNA is used to measure PCR product sizes with capillary electrophoresis (CE). The obtained sizes are compared to known standards to determine specific alleles (e.g., STR loci). 
     SUMMARY 
     Advances in DNA sequencing technologies now enable the sequencing of both STRs and single nucleotide polymorphisms (SNPs) for better identification. Sequencing STR loci enables distinguishing between STR with the same length but different allele sequences. Additionally, sequencing SNPs enables prediction of externally visible traits (EVTs), biogeographic ancestry, improved analysis of complex forensic samples originating from multiple individuals, characterization of trace DNA samples, etc. 
     It is appreciated that there are issues of PCR relating to the DNA polymerases used in preparing samples. Specifically, the DNA polymerases for PCR have an increased error rate specific to short tandemly repeated DNA sequences (STRs) and their respective length. The longer the length of the repeat sequence, the higher the probability that the polymerase will delete an entire repeat unit or create an extra copy of a repeat unit (i.e., stutter alleles). A deletion of a repeat unit is referred to as a −1 allele and an addition of a repeat unit as a +1 allele. Deletions are more likely to occur than additions. For each cycle of PCR, errors can impact errors yielding higher errors rates of −2, −3, and +2 stutter alleles over multiple cycles. The appearance of −2, −3, and +2 stutter alleles are typically proportional to the −1/+1 stutter error rate applied to stutter sequences generated in earlier cycles of PCR amplification (e.g., the ratio of −2 to −1 counts of sequences is typically slightly less than the ratio of −1 to real allele counts of sequences). DNA polymerases also have an error rate (typically less than 1%) of introducing random DNA base errors. This creates sequence variants of all of the PCR products being amplified at a lower rate than the stutter error rate. 
     Although the sources of PCR artifacts or errors can usually be ignored for samples from a single individual, it is realized that distinguishing real alleles from artifacts in mixtures of multiple individuals presents a new challenge area for DNA forensics. Accordingly, there is a need for improved systems and methods of analysis for handling multiple contributors, as well as systems and methods that model not only individual error rates per locus but factor in amplification of errors induced through PCR cycles. In some embodiments, modeling of error rates can be applied in multi-contributor settings to more accurately establish real alleles from artifacts. Other aspects involve application of sequencing in error modeling. For example, sequencing of the dominant stutter in the −1 allele for each locus (and/or amplification agent) enables increased identification accuracy (e.g., allele calling accuracy), and further enhances accuracy in analysis of multiple contributor samples. Other embodiments can also estimate a number of contributors within a sample based on differences in PCR amplification strength for different STR loci. Improvements based on resolving amplification strength result in greater increases in identification accuracy. For example, estimates of a number of contributors to a given sample enables greater precision in the application of error profiles—not to mention the implication for criminal investigation and knowing a specific number of contributors. 
     Still other aspects relate to implementing STR sequencing to improve matching of individuals to sample mixtures over conventional approaches. For example, conventional implementations match individuals to sample mixtures based on STR names and allele length matching. Various embodiments extend multi-contributor analysis further, via integration of machine learning approaches to predict the numbers of contributors in a sample based on one or both of STR and SNP profiles. 
     According to one aspect, a DNA analysis system is provided. The system comprising at least one processor operatively connected to a memory, a receiver component configured to receive DNA analysis information including locus and allele read information generated from PCR amplification of DNA in a DNA sample, an analysis component, executed by the at least one processor, configured to: identify a first error profile associated with a first DNA locus and evaluate the locus and allele read information against the first error profile to determine an adjusted read threshold, confirm presence of the first locus and allele in the DNA sample, responsive to the confirmed presence of the first locus and allele information adjust error analysis of at least a second allele or at least a second locus to account for amplification error reads of the confirmed first locus and allele in the DNA sample, and determine for each respective locus and allele associated with read data obtained from the DNA sample whether a total number of reads from the DNA sample exceeds an error profile adjusted threshold, and for each confirmation or exclusion of read data adjust the threshold based on the confirmation or exclusion. 
     According to one embodiment, the analysis component is further configured to generate, by the least one processor, an identification profile for at least one individual within the DNA sample comprising each confirmed locus and alleles for the at least one individual. 
     According to one embodiment, the receiver component further comprises a physical DNA sample receiver and PCR analysis element for generating read information for respective loci and alleles. According to one embodiment, the error profile for the first locus and allele includes calculations of different threshold adjustments according to PCR amplification cycles executed on the sample. According to one embodiment, the error profile includes calculations for a number of reads associated with at least −1 stutter allele, a +1 stutter allele, and a −2 stutter allele, wherein the calculations are adjusted by the analysis component to a number of PCR amplification cycles. 
     According to one embodiment, the analysis component is further configured to determine whether the total number of reads from the sample exceeds the error profile adjusted threshold based on a combined error read count derived from stutter alleles from at least a first and second allele. According to one embodiment, the analysis component is further configured to determine the total number of reads from the sample exceeds the error profile adjusted threshold based on a combined error read count derived from stutter alleles from at least a first, second, and third allele. According to one embodiment, the analysis component is further configured to identify PCR products from the sample for sequencing. According to one embodiment, the analysis component is further configured to evaluate confirmed alleles to determine information on a respective dominant −1 stutter allele and identify PCR products from the sample from sequencing based on the properties of the respective dominant −1 stutter allele. According to one embodiment, the analysis component is further configured to update confirmed allele information responsive to reducing reads counts for each dominant −1 stutter allele identified based on sequencing. 
     According to one aspect, a computer implemented method for DNA analysis is provided. The method comprises receiving, by at least one processor, DNA analysis information including locus and allele read information generated from PCR amplification of DNA in a DNA sample, identifying, by the at least one processor, a first error profile associated with a first DNA locus and evaluating, by the at least one processor, the locus and allele read information against the first error profile to determine an adjusted read threshold, confirming, by the at least one processor, a presence of the first locus and allele in the DNA sample, responsive to the confirmed presence of the first locus and allele information adjusting, by the at least one processor, error analysis of at least a second allele or at least a second locus to account for amplification error reads of the confirmed first locus and allele in the DNA sample, and determining, by the at least one processor, for each respective locus and allele associated with read data obtained from the DNA sample whether a total number of reads from the DNA sample exceeds an error profile adjusted threshold, and for each confirmation or exclusion of read data adjusting, by the at least processor, the threshold based on the confirmation or exclusion. 
     According to one embodiment, the method further comprises generating, by the least one processor, an identification profile for at least one individual within the DNA sample comprising each confirmed locus and allele for the at least one individual. According to one embodiment, receiving includes receiving information from a physical DNA sample receiver and PCR analysis element for generating read information for respective loci and alleles. According to one embodiment, wherein the error profile for the first locus and allele includes calculations of different threshold adjustments according to PCR amplification cycles executed on the sample. 
     According to one embodiment, wherein the error profile includes calculations for a number of reads associated with at least −1 stutter allele, a +1 stutter allele, and a −2 stutter allele, wherein the calculations are adjusted by the analysis component to a number of PCR amplification cycles. 
     According to one embodiment, the method further comprises determining whether the total number of reads from the sample exceeds the error profile adjusted threshold based on a combined error read count derived from stutter alleles from at least a first and second allele. According to one embodiment, the method further comprises determining the total number of reads from the sample exceeds the error profile adjusted threshold based on a combined error read count derived from stutter alleles from at least a first, second, and third allele. According to one embodiment, the method further comprises identifying PCR products from the sample for sequencing. According to one embodiment, the method further comprises evaluating confirmed alleles to determine information on a respective dominant −1 stutter allele and identify PCR products from the sample from sequencing based on the properties of the respective dominant −1 stutter allele. 
     According to one embodiment, the method further comprises updating confirmed allele information responsive to reducing reads counts for each dominant −1 stutter allele identified based on sequencing. 
     According to one aspect, a DNA analysis system is provided. The system comprises at least one processor operatively connected to a memory, a receiver component configured to receive DNA analysis information including locus and allele read information generated from PCR amplification analysis of DNA in a DNA sample, an analysis component, executed by the at least one processor, configured to evaluate a dominant stutter allele associated with at least a first DNA locus and allele of the first DNA locus based on DNA sequencing of at a least a portion of the DNA sample, confirm the read information matches the dominant −1 stutter allele for a first contributor based on matching the dominant −1 stutter allele sequence to sequence information obtained from the DNA sample, eliminate the read information associated with the dominant−1 stutter allele, confirm presence of the first locus and allele in the DNA sample based on the read information with the dominant stutter allele removed, determine for each respective locus and allele associated with read data from the sample whether a total number of reads from the sample exceeds a threshold, and generate, by the least one processor, an identification profile for at least one individual within the DNA sample comprising each confirmed locus and allele for the at least one individual. 
     According to one embodiment, the analysis component is further configured to identify a first error profile associated with a first DNA locus and evaluate the locus and allele read information against the first error profile to determine an adjusted read threshold; and confirm presence of the first locus and allele in the sample based on the adjusted threshold and any dominant stutter allele reads removed. According to one embodiment, the analysis component is further configured to: adjust error analysis of at least a second allele or at least a second locus to account for amplification error reads of the confirmed first locus and allele in the sample responsive to the confirmed presence of the first locus and allele information, determine for each respective locus and allele associated with read data from the sample whether a total number of reads from the sample exceeds an error profile adjusted threshold, and for each confirmation or exclusion of read data adjust the threshold based on the confirmation or exclusion; and generate, by the least one processor, an identification profile for at least one individual within the DNA sample comprising each confirmed locus and allele for the at least one individual. 
     According to one embodiment, the analysis component is further configured to adjust error analysis of at least a second allele or at least a second locus to account for amplification error reads of the confirmed first locus and allele in the sample responsive to the confirmed presence of the first locus and allele information. 
     According to one aspect, a computer implemented method for DNA analysis is provided. The method comprises receiving, by at least one processor, DNA analysis information including locus and allele read information generated from PCR amplification analysis of DNA in a DNA sample, evaluating, by the at least one processor, a dominant stutter allele associated with at least a first DNA locus and allele of the first DNA locus based on DNA sequencing of at a least a portion of the DNA sample, confirming, by the at least one processor, the read information matches the dominant −1 stutter allele for a first contributor based on matching the dominant −1 stutter allele sequence to sequence information obtained from the DNA sample, eliminating, by the at least one processor, the read information associated with the dominant −1 stutter allele, confirming, by the at least processor, presence of the first locus and allele in the DNA sample based on the read information with the dominant stutter allele removed, determining, by the at least one processor, for each respective locus and allele associated with read data from the sample whether a total number of reads from the sample exceeds a threshold, and generating, by the least one processor, an identification profile for at least one individual within the DNA sample comprising each confirmed locus and allele for the at least one individual. 
     According to one embodiment, the method further comprises identifying a first error profile associated with a first DNA locus and evaluate the locus and allele read information against the first error profile to determine an adjusted read threshold; and confirming presence of the first locus and allele in the sample based on the adjusted threshold and any dominant stutter allele reads removed. According to one embodiment, the method further comprises adjusting error analysis of at least a second allele or at least a second locus to account for amplification error reads of the confirmed first locus and allele in the sample responsive to the confirmed presence of the first locus and allele information, determining for each respective locus and allele associated with read data from the sample whether a total number of reads from the sample exceeds an error profile adjusted threshold, and for each confirmation or exclusion of read data adjust the threshold based on the confirmation or exclusion; and generating, by the least one processor, an identification profile for at least one individual within the DNA sample comprising each confirmed locus and allele for the at least one individual. 
     According to one embodiment, the method further comprises adjusting error analysis of at least a second allele or at least a second locus to account for amplification error reads of the confirmed first locus and allele in the sample responsive to the confirmed presence of the first locus and allele information. 
     According to one aspect, a DNA analysis system is provided. The system comprising at least one processor operatively connected to a memory, a receiver component configured to receive DNA analysis information including locus and allele read information generated from PCR amplification of DNA in a multiple DNA contributor sample, an analysis component, executed by the at least one processor, configured to: compare a first contributor DNA sample to the multiple DNA contributor sample, determine absence or presence of the first contributor DNA sample in the multiple DNA contributor sample, and apply an amplification strength model to improve determination accuracy for the absence or presence of the first contributor DNA sample within the multiple contributor sample. 
     According to one embodiment, the analysis component is further configured match a plurality of strongest amplification strength alleles to determine possible presence of the first contributor. According to one embodiment, the analysis component is further configured exclude a plurality of weakest amplification strength alleles to determine possible presence of the first contributor. According to one embodiment, the analysis component is further configured to determine an absence of a plurality of strongest amplification strength alleles to determine the absence of the first contributor in the multiple DNA contributor sample. 
     According to one aspect, a computer implemented DNA analysis method is provided. The method comprises receiving, by at least one processor, DNA analysis information including locus and allele read information generated from PCR amplification of DNA in a multiple DNA contributor sample, comparing, by the at least one processor, a first contributor DNA sample to the multiple DNA contributor sample, determining, by the at least one processor, absence or presence of the first contributor DNA sample in the multiple DNA contributor sample, and applying, by the at least one processor, an amplification strength model to improve determination accuracy for the absence or presence of the first contributor DNA sample within the multiple contributor sample. 
     According to one embodiment, the method further comprises matching, by the at least one processor, a plurality of strongest amplification strength alleles to determine possible presence of the first contributor. According to one embodiment, the method further comprises excluding a plurality of weakest amplification strength alleles to determine possible presence of the first contributor. According to one embodiment, the method further comprises determining an absence of a plurality of strongest amplification strength alleles to determine the absence of the first contributor in the multiple DNA contributor sample. 
     Some aspects provide for methods comprising using at least one computer hardware processor to perform: receiving sequence information obtained from a nucleic acid sample, wherein the sequence information comprises a plurality of genetic loci, the plurality of genetic loci including a first genetic locus; generating, based on the received sequence information, an encoding for the nucleic acid sample at least in part by encoding the first genetic locus using a first value when the first genetic locus is homozygous for a major allele and using a second value different from the first value when the first genetic locus is not homozygous for the major allele; comparing the generated encoding of the nucleic acid sample with a plurality of previously-generated encodings for a respective plurality of nucleic acid samples; and when it is determined that, as a result of the comparing, the generated encoding of the nucleic acid sample matches at least one encoding in the plurality of previously-generated encodings, the at least one encoding being associated with at least one person, providing an indication that the nucleic acid sample is consistent with the at least one person. 
     In some embodiments, generating the encoding comprises generating a lossy encoding. In some embodiments, generating the encoding comprises generating a binary encoding. In some embodiments, the first value is a binary value. In some embodiments, the first value consists of a first bit and the second value consists of a second bit different from the first bit. In some embodiments, the first bit is zero. 
     In some embodiments, the received sequence information obtained from the nucleic acid sample consists of sequence information for only one person. In some embodiments, the received sequence information obtained from the nucleic acid sample consists of sequence information for more than one person. 
     In some embodiments, when the generated encoding of the nucleic acid sample matches two different encodings in the plurality of previously-generated encodings, the two different encodings being associated with two different people, the method further comprises providing an indication that the nucleic acid sample is consistent with the two different people. 
     In some embodiments, generating the encoding comprises using the second value when the first genetic locus is homozygous for a minor allele or the first genetic locus is heterozygous. In some embodiments, the presence of the second value in the generated encoding indicates a presence of a single nucleotide polymorphism (SNP) at the first genetic locus. In some embodiments, the generating further comprises encoding each of the plurality of genetic loci using the first value or the second value. In some embodiments, the comparing is performed using bitwise instructions native to the at least one computer hardware processor executing the method. 
     Some aspects provide for a system comprising: at least one database storing a plurality of encodings for a respective plurality of nucleic acid samples; at least one computer hardware processor; at least one non-transitory computer-readable storage medium storing processor-executable instructions that, when executed by the at least one computer hardware processor, cause the at least one computer hardware processor to perform: receiving sequence information obtained from a nucleic acid sample, wherein the sequence information comprises a plurality of genetic loci, the plurality of genetic loci including a first genetic locus; generating, based on the received sequence information, an encoding for the nucleic acid sample at least in part by encoding the first genetic locus using a first value when the first genetic locus is homozygous for a major allele and using a second value different from the first value when the first genetic locus is not homozygous for the major allele; comparing the generated encoding of the nucleic acid sample with the plurality of encodings stored in the at least one database; and when it is determined that, as a result of the comparing, the generated encoding of the nucleic acid sample matches at least one encoding in the plurality of encodings stored in the at least one database, the at least one encoding being associated with at least one person, providing an indication that the nucleic acid sample is consistent with the at least one person. 
     In some embodiments, the at least one computer hardware processor is configured to perform a plurality of native bitwise instructions. In some embodiments, native bitwise instructions include a population count bitwise instruction, an “XOR” bitwise instruction, and an “AND” bitwise instruction. Additionally or alternatively, native bitwise instructions include a bitwise OR instruction, a bitwise NAND instruction, a bitwise NOT instruction, an arithmetic shift instruction, a logical shift instruction, a circular shift instruction, and/or any other suitable bitwise instructions that the at least one computer hardware processor is configured to execute, as aspects of the technology described herein are not limited in this respect. 
     Some aspects provide for methods comprising using at least one computer hardware processor to perform: receiving sequence information obtained from a nucleic acid sample, wherein the sequence information comprises at least one short tandem repeat (STR) locus, the at least one STR locus comprising a unit of nucleotides repeated a number of times; generating, based on the received sequence information, an encoding for the nucleic acid sample at least in part by encoding the at least one STR locus using a value that corresponds to the number of times the unit of nucleotides is repeated; comparing the generated encoding of the nucleic acid sample with a plurality of previously-generated encodings for a respective plurality of nucleic acid samples; and when it is determined that, as a result of the comparing, the generated encoding of the nucleic acid sample matches at least one encoding in the plurality of previously-generated encodings, the at least one encoding being associated with at least one person, providing an indication that the nucleic acid sample is consistent with the at least one person. 
     In some embodiments, the encoding comprises generating a lossy encoding. In some embodiments, the encoding comprises generating a binary encoding. In some embodiments, the value is a binary value. In some embodiments, the value consists of 1 bit, between 1-3 bits, between 2-4 bits, between 3-5 bits, between 4-6 bits, between 5-7 bits, between 6-8 bits, between 7-9 bits, between 8-10 bits, 10 bits, or more than 10 bits. In some embodiments, the value consists of 5 bits. In some embodiments, the value directly corresponds to the absolute number of times the unit of nucleotides is repeated. In some embodiments, the value is one of between 2-30 possible values. In some embodiments, the value is one of between 5-25 possible values. In some embodiments, the value is one of around 20 possible values. 
     In some embodiments, the received sequence information obtained from the nucleic acid sample consists of sequence information for only one person. In some embodiments, the received sequence information obtained from the nucleic acid sample consists of sequence information for more than one person. In some embodiments, when the generated encoding of the nucleic acid sample matches two different encodings in the plurality of previously-generated encodings, the two different encodings being associated with two different people, the method further comprises providing an indication that the nucleic acid sample is consistent with the two different people. 
     In some embodiments, the generating comprises encoding at least two STR loci. In some embodiments, the at least one STR locus is selected from D3S1358, vWA, FGA, D8S1179, D21S11, D18S51, D5S818, D13S317, D7S820, D16S539, THO1, TPDX, CSF1PO, AMEL, D1S1656, D2S441, D2S1338, D 10S1248, D125391, D19S433. D22S1045, or any other STR loci In some embodiments, the comparing is performed using bitwise instructions native to the at least one computer hardware processor executing the method. 
     Some aspects provide for a system comprising: at least one database storing a plurality of encodings for a respective plurality of nucleic acid samples; at least one computer hardware processor; at least one non-transitory computer-readable storage medium storing processor-executable instructions that, when executed by the at least one computer hardware processor, cause the at least one computer hardware processor to perform: receiving sequence information obtained from a nucleic acid sample, wherein the sequence information comprises at least one short tandem repeat (STR) locus, the at least one STR locus comprising a unit of nucleotides repeated a number of times; generating, based on the received sequence information, an encoding for the nucleic acid sample at least in part by encoding the at least one STR locus using a value that corresponds to the number of times the unit of nucleotides is repeated; comparing the generated encoding of the nucleic acid sample with a plurality of previously-generated encodings for a respective plurality of nucleic acid samples; and when it is determined that, as a result of the comparing, the generated encoding of the nucleic acid sample matches at least one encoding in the plurality of previously-generated encodings, the at least one encoding being associated with at least one person, providing an indication that the nucleic acid sample is consistent with the at least one person. 
     In some embodiments, the at least one computer hardware processor is configured to perform a plurality of native bitwise instructions. In some embodiments, native bitwise instructions include a population count bitwise instruction, an “XOR” bitwise instruction, and an “AND” bitwise instruction. Additionally or alternatively, native bitwise instructions include a bitwise OR instruction, a bitwise NAND instruction, a bitwise NOT instruction, an arithmetic shift instruction, a logical shift instruction, a circular shift instruction, and/or any other suitable bitwise instructions that the at least one computer hardware processor is configured to execute, as aspects of the technology described herein are not limited in this respect. 
     In some aspects, techniques described herein can be used to determine kinship of one or more samples. 
     Further, other aspects relate to determining individuals from complex mixtures. As discussed, DNA forensics is a common tool used within law enforcement and US intelligence agencies to identify unknown suspects and to accurately link crime scene evidence to criminal perpetrators. Crime scene evidence often contains DNA from multiple people however, confounding current DNA analysis techniques. 
     At present, the forensics community uniquely identifies individual DNA samples through extraction of short tandem repeats (STRs) and determination of mitochondrial DNA (mtDNA) sequences. Capillary electrophoresis is often used to quantify SIR lengths and mtDNA sequences. This methodology has been proven accurate for individual profile identification. However, if a given reference DNA profile is contained within a complex DNA mixture, identifying an individual profile is difficult and sometimes impossible using this methodology. 
     Thus, the ability to build individual profiles from a complex mixture and the direct deconvolution of a mixture into candidate and/or individual component DNA signatures are unmet needs. 
     To address these unmet needs, the methods of the disclosure provide a system to confirm the co-occurrence of individual DNA profiles from unknown individuals in one or more complex mixtures of DNA signatures and to build individual DNA profiles for unknown individuals from analysis of one or more complex DNA mixtures. By using a panel of between several hundred to tens of thousands of genetic markers, e.g. Single Nucleotide Polymorphism (SNPs), the methods of the disclosure may be used to build an individual profile. Moreover, by finding the intersection, or overlapping population, of genetic markers across multiple DNA mixtures, the methods of the disclosure produce a DNA SNP profile unique to the common contributors to the mixtures. The preferred genetic markers used in the methods of the disclosure include SNPs. 
     Methods of the disclosure provide superior properties over the existing methods of building and deconvoluting DNA profiles in a forensic setting, however, applications for the methods described herein are not confined to the context of a forensic or crime scene investigation. For example, the methods of the disclosure may be used for medical diagnosis and/or prognosis. In the field of cancer, biopsy samples often contain many cell types, of which a small proportion may form any part of a tumor. Consequently, DNA obtained from tumor biopsies is another form of complex DNA mixture. Moreover, within a tumor, the multitude of cells may be molecularly distinct with respect to the expression of factors indicating or facilitating, for example, vascularization and/or metastasis. A DNA mixture obtained from a tumor sample may also form a complex DNA mixture of the disclosure. In both of these non-limiting examples, the methods of the disclosure may be used to build individual profiles for each cell or cell type that contributes to the complex DNA mixture. Moreover, the methods of the disclosure may be used to deconvolute contributors to a complex DNA mixture. For instance, a complex DNA mixture obtained from a breast cancer tumor biopsy may be used to build an individual profile of the malignant cells. In the same patient, a brain cancer tumor biopsy, this individual profile may be used to deconvolute the contributors to the complex DNA mixture obtained from the brain cancer tumor biopsy to determine, for instance, if a malignant breast cancer cell from that subject metastasized to the brain to form a secondary tumor. This method would resolve a question as to whether the tumors arose independently, or, on the other hand, if these tumors are related. 
     Of significance to the methods to the disclosure, the ability of these methods to either build an individual DNA profile or to deconvolute complex DNA mixtures into component profiles does not require any prior knowledge of the components. For example, the methods described herein are effective to either build an individual DNA profile or to deconvolute complex DNA mixtures into component profiles without any knowledge of genetic markers or DNA sequences belonging to any individual or component that contributes to any one of the complex DNA mixtures. Thus, one of the superior properties of the methods of the disclosure is that the methods do not require any prior knowledge or data regarding individual profiles, contributors, or components of a complex DNA mixture. 
     The disclosure provides a SNP panel comprising one, two, or more loci of a single-nucleotide polymorphism (SNP) having at least one of: (a) a low fixation index (FST); (b) a low minor allele frequency (mAF) value or a low average heterozygosity value; and (c) a minimal distance between loci (e.g., a minimum recommended distance of at least 100,000 nucleic acid bases) when present within a single chromosome. In certain embodiments of the SNP panels of the disclosure, a low FST may indicate that the minor allele of the SNP has no statistically significant correlation with ancestry. In certain embodiments, a low FST is less than 0.06. In certain embodiments of the SNP panels of the disclosure, a low mAF and/or a low average heterozygosity value may indicate that the minor allele is rare in a population. In certain embodiments, a low mAF is a value between 0.01 and 0.3 or between 0.03 and 0.07 or between 0.01 and 0.06, inclusive of the endpoints for each range. A value of average heterozygosity may be calculated or derived from information provided by the Short Genetic Variations database (dbSNP)(also referred to herein as dbSNP), a publicly-available, free resource overseen by the National Center for Biotechnology Information (NCBI), a division of the National Institutes of Health (NIH). dbSNP may be accessed at www.ncbi.mnlm.nih.gov. Other sources may be used, such as the 1,000 genomes project. Links to heterozygosity from the dbSNP page provide detailed methods for the computation of average heterozygosity from variation data submitted for SNPs by members (sec, for example, www.ncbi.nlm.nih.gov/SNP/Hetfreq.html). In certain embodiments of the SNP panels and methods of the disclosure, a value of average heterozygosity may either be obtained from public databases (e.g. dbSNP) or independently calculated from the raw data provided by this database or other sources of SNP information. In certain embodiments of the SNP panels of the disclosure, the value of average heterozygosity may be between 0.058 and 0.13, inclusive of the endpoints. In certain embodiments of the SNP panels of the disclosure, the minimal distance between loci is, in one example implementation, at least 500,000 nucleic acid bases when present within a single chromosome. 
     In certain embodiments, the disclosure provides a SNP panel comprising one, two, or more loci of a single-nucleotide polymorphism (SNP) having at least two of: (a) a low fixation index (FST); (b) a low minor allele frequency (mAF) value or a low average heterozygosity value; and (c) a minimal distance between loci of at least 100,000 nucleic acid bases (or as close as 50,000 nucleic acid bases) when present within a single chromosome. 
     In certain embodiments, the disclosure provides a SNP panel comprising one, two, or more loci of a single-nucleotide polymorphisms (SNPs) having: (a) a low fixation index (FST); (b) a low minor allele frequency (mAF) value or a low average heterozygosity value; and (c) a minimal distance between loci of at least 100,000 nucleic acid bases when present within a single chromosome. 
     The disclosure also provides a SNP panel comprising one, two, or more loci of a single-nucleotide polymorphisms (SNPs) selected according to any method of the disclosure. 
     The disclosure provides methods for selecting one, two, or more loci of a single-nucleotide polymorphisms (SNPs) for inclusion in a SNP panel comprising selecting one, two, or more loci having at least one of: (a) no statistically significant correlation of a minor allele of the SNP with ancestry; (b) a low minor allele frequency (mAF) value or a low average heterozygosity value; and (c) a minimal distance between loci of at least 100,000 nucleic acid bases when present within a single chromosome; and eliminating one or more loci that: (d) generate data from only one strand of DNA; (e) produce a result that contradicts a relationship from a known family tree; and/or (f) have a minor allele ratio outside of expected values from a known reference sample. In certain embodiments, the method may further comprise eliminating one or more loci that produce results that could not be verified when compared to a known family tree. In certain embodiments of this method, loci are chosen that produce data that are strongly indicative of an individual&#39;s genotype, with minor allele ratios from an individual reference samples of approximately 0, 0.5, or 1.0. For example, for the OptMix panel used herein, ambiguous was defined as mAF&gt;0.0025 and &lt;0.4 (or 0.6-&gt;0.9975). In addition, a locus preferably is not selected for (or is eliminated from) a panel if the locus gives few reads (&lt;10% of average total number of calls); gives impossible calls (conflicting with homozygous parents); produces biased data from one DNA strand (&gt;9:1 ratio); or is a locus for which the major allele is never observed. Other analytical thresholds can be used to classify major, major:minor, and minor:minor alleles in reference samples and DNA mixtures. 
     As used in the context of the expected value of a minor allele ratio from a known reference sample, the term approximately includes the expected value of 0, 0.5, or 1.0 with a range below or above these expected values to account for variability (e.g. statistical noise) within the data and/or statistical analysis. 
     In certain embodiments, this method may further comprise calculating a fixation index (FST) for each locus, wherein a low FST indicates that the minor allele of the SNP correlates poorly with ancestry. In certain embodiments, a low FST is less than 0.06. The FST may be determined by any number of methods, including, for example. utilizing the ALlele FREquency Database (ALFRED). In certain embodiments, this method may further comprise calculating a minor allele frequency (mAF) for each locus, wherein a low mAF indicates that the minor allele is rare in a population. In certain embodiments, a low mAF is a value between 0.01 and 0.3 or between 0.03 and 0.07 or between 0.01 and 0.06, inclusive of the endpoints for each range. In certain embodiments, this method may further comprise calculating a value of average heterozygosity for each locus, wherein a low average heterozygosity value indicates that the minor allele of the SNP is rare in a population. In certain embodiments, the value of average heterozygosity may be calculated or derived from information provided by dbSNP. In certain embodiments, the value of average heterozygosity may be between 0.058 and 0.13, inclusive of the endpoints. In certain embodiments of this method, the minimal distance between loci is at least 500,000 nucleic acid bases when present within a single chromosome. In certain embodiments, a locus may contain more than one SNP. 
     The disclosure provides methods for selecting one, two, or more loci having at least two of: (a) a poor correlation of the SNP allele with ancestry; (b) a low minor allele frequency (mAF) value or a low average heterozygosity value; and (c) a minimal distance between loci of at least 100,000 nucleic acid bases when present within a single chromosome. 
     The disclosure provides methods for selecting one, two, or more loci having: (a) a poor correlation of a minor allele of the SNP with ancestry; (b) a low minor allele frequency (mAF) value or a low average heterozygosity value; and (c) a minimal distance between loci of at least 100,000 nucleic acid bases when present within a single chromosome. 
     The disclosure provides methods for building an individual DNA profile from one, two, or more complex DNA mixtures comprising the steps of: (a) determining the presence of at least one minor SNP allele from a SNP panel in a first complex DNA mixture; (b) determining the presence of at least one minor SNP allele in a second complex DNA mixture; (c) identifying a common set of minor alleles present in the first and second complex mixtures, wherein the occurrence of a common set of minor alleles indicates the presence of a common individual contributor or subset of contributors to each of the first and the second complex mixtures; and (d) assembling all common minor alleles identified in (c) to generate an individual DNA profile, thereby building an individual DNA profile of a shared contributor or contributors to one, two, or more complex DNA mixtures. In certain embodiments of this method, the method involves building an individual genetic profile from one, two, or more samples containing complex DNA mixtures comprising the steps of: (a) determining the presence of at least one minor SNP allele from the SNP panel of the disclosure in a first complex DNA mixture, represented by the numeric value 1 at the position for that SNP in a vector over all loci; (b) determining the presence of at least one minor SNP allele in a second complex DNA mixture, represented by the numeric value 1 at the position for that SNP in a vector over all loci and 0 for major alleles; (c) identifying any common minor alleles present in the first and second complex mixtures represented by the numeric value 1 in a vector for each mixture, wherein the occurrence of a common minor allele indicates the presence of a common individual contributor to each of the first and the second complex mixtures and; (d) assembling all common minor alleles identified in (c) to generate an individual DNA profile via a multiplication of the two vectors in (a) and (b); thereby building an individual DNA profile from one, two, or more complex DNA mixtures, represented by the vector of 1 over all loci. Optionally, this embodiment may further comprise (e) isolating the summed DNA profiles from non-common contributors from the original samples by subtracting the derived profile generated in (d) from the samples in (a) and (b). In certain embodiments, the one, two, or more complex DNA mixtures are at least 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163,1 64, 165,1 66, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, or more complex DNA mixtures, up to and including millions of complex DNA mixtures. In theory and in practice, there is no maximum or limit on the number of complex DNA mixtures that this method can use to build an individual DNA profile or the DNA profile of a group of individuals. Importantly, the accuracy and/or specificity of the individual DNA profile or the DNA profile of a group of individuals increases as the number of complex mixtures increases. In certain embodiments of this method, one, two, or more complex DNA mixtures are obtained from a crime and/or forensic kit and/or laboratory. In certain embodiments of this method, one, two, or more complex DNA mixtures are obtained from a medical or biological sample or a genetically heterogeneous medical or biological sample. The SNP panel used for this method, as well as any method of the disclosure, may be any SNP panel described by the disclosure. For example, the SNP panel comprises one, two, or more loci of a single-nucleotide polymorphism (SNP) having at least one of: (a) a low fixation index (FST); (b) a low minor allele frequency (mAF) value or a low average heterozygosity value; and (c) a minimal distance between loci of at least 100,000 nucleic acid bases when present within a single chromosome, wherein the one, two, or more loci of a SNP are selected for those loci that predict or correlate with the occurrence and/or development of a biological condition or disease. Alternatively, or in addition, SNP panels of the disclosure, including those used for this method, may include SNPs from established panels and those SNPs that predict a biological disease or condition. Moreover, the SNP panels of the disclosure, including those used for this method, may include SNPs that are particularly enriched in a particular population due to any number of factors including shared geographic and/or cultural proximity and/or isolation. 
     The disclosure provides a method for resolving a DNA profile for a major and/or a minor contributor from a complex DNA mixture comprising the steps of: (a) amplifying a sequence containing at least one minor SNP allele from a SNP panel of the disclosure in the complex DNA mixture using a quantitative amplification method; (b) optionally, contacting the resultant amplification product with a detectable label, wherein each sequence containing a distinct minor SNP allele contacts a distinct detectable label; (c) detecting a signal from each of the resultant amplification products; (d) comparing the signal amplitude between amplification products, wherein the signal amplitude of a minor-allele-containing sequence provided by a major contributor is greater than the signal amplitude of a minor-allele-containing sequence provided by a minor contributor, and (e) assembling the minor allele sequences having a low signal amplitude into a DNA profile to identify a minor contributor to the complex DNA mixture, and/or (f) assembling the sequences having a high signal amplitude into a second DNA profile to identify a major contributor to the complex DNA mixture, thereby resolving separate DNA profiles for a major and/or a minor contributor from a single analysis of a non-equimolar DNA mixture. As an alternative, resolving a DNA profile for a major and/or a minor contributor from a complex DNA mixture comprises the steps of: sequencing the DNA, and counting the number of sequence reads for each allele. 
     In certain embodiments of the methods of the disclosure, the single multi-contributor DNA mixture may be obtained from a laboratory or forensic laboratory. In certain embodiments, the major or minor contributor is a victim of a crime. Alternatively, or in addition, the major or minor contributor is a perpetrator of a crime. 
     In certain embodiments of the methods of the disclosure, the complex DNA mixture may be obtained from a biopsy, a medical examination or a medical laboratory. In certain embodiments of the methods of the disclosure, the complex DNA mixture may analyzed to resolve the major and/or minor contributors to the mixture in the context of any biological condition or disease. For example, when used to resolve contributors to a biopsy sample obtained from a cancer patient, the major or minor contributor may a benign cell or tissue. Alternatively, or in addition, the major or minor contributor is a cancerous cell or tissue. 
     In certain embodiments of the methods of the disclosure, the percentage of DNA in the complex DNA mixture provided by a minor contributor may be between 0.001 (and lower) and 49.9 percent of total DNA. Importantly, this method can resolve a DNA profile of a minor contributor to a complex DNA mixture when the percentage of DNA attributable to that minor contributor is as minimal as between &gt;0 and 1 percent of total DNA. As the number of contributors to a complex DNA mixture increases, the resolution of the method of deconvoluting the individual contributors decreases. Thus, this method may be use to resolve a DNA profile of an individual contributor to a complex DNA mixture when the percentage of DNA attributable to that individual contributor is less than 0.001 percent of the total DNA. In certain aspects of this method, the accuracy or efficacy of the method increases as (a) an amount of total DNA contained in the complex DNA mixture increases; and/or (b) a greater number of loci from a SNP panel of the disclosure are analyzed and/or (c) the accuracy of the ability to measure DNA improves. 
     In certain embodiments of the SNP panels and methods of the disclosure, contemplated populations may comprise or consist of a plurality of individuals and/or data obtained from a database. The individuals of these populations may share common features, including, but not limited to, age, gender, race, ethnicity, geography, medical condition or predisposition, inherited or novel genetic traits, and/or circumstance. For example, the individuals of these populations may share the common feature of having been diagnosed or having survived cancer. In other embodiments, the individuals of these populations may have been involved in the same event (e.g. crime and/or present at a crime scene) or be associated with that event through physical proximity and/or social/familial relationship. 
     Various embodiments relate, either alone or in combination with other embodiments which include: 
     Resolving Individual Contributions to Complex DNA Mixtures 
     A Venn method is provided which can be used to determine individual contributors&#39; DNP profiles from direct comparison of complex DNA mixtures without a known reference sample. There are no known methods for directly deconvolving a DNA SNP mixture into individual profiles or sub-profiles without reference profiles. The Venn method identifies individual sub-profiles my identifying common major and minor alleles across two or more DNA mixtures.
 
The Venn method can resolve the identity of individual contributors to DNA mixtures when the DNA profile is not known by intersecting the observed SNP profiles of two or more DNA mixtures using Venn logic on SNP alleles.
 
Plateau Method
 
A plateau method is provided to build individual sub-profiles directly from complex mixtures without known reference profiles. In some embodiments, a Plateau method is provided for directly deconvolving a single mixture into individual sub-profiles by leveraging differences in DNA concentrations of contributors to DNA mixtures. The Plateau method identifies individual sub-profiles directly from complex mixtures without known reference profiles by leveraging differences in DNA concentrations of individuals (e.g., direct mixture deconvolution) using SNP allele minor allele ratios (mAR) or minor allele counts (mAC) to assign minor alleles to different DNA contributors to the mixture.
 
Forensic DNA Sample and Mixture Comparison Methods
 
In some embodiments, Fast Identification and Mixture Analysis for SNP or STR profiles is provided using bit encode alleles combined with hardware XOR, AND, and population count instructions—FastID &amp; FastSTR. In some implementations, high performance parallelization is possible on graphics processing units (GPUs). As the number of STR and SNP loci increases, the time complexity of searching large databases of reference profiles and mixtures also increases. Scaling up from 20 loci to 20,000 loci is 1,000 times more comparisons. The FastID and TachysSTR methods enable high performance comparison of SNP or STR profiles for reference profiles or mixture profiles against a very large set of millions of reference profiles using bit encoding of alleles and hardware XOR, AND, and population count instructions. Millions of profile comparisons can be done in seconds using a single computational thread on modern computers. Parallelization of comparisons is possible for large volume comparisons using graphical processing units (GPUs).
 
STRs Analysis Methods
 
In some embodiments, new STR analysis methods are provided including:
         Novel STR allele identification versus stutter artifacts leveraging comparison on STR sequences to identify STR alleles that are not stutter artifacts of nearby alleles   Learning STR stutter sequences to classify HTS STR data—create database of observed (−1) and (+1) stutter sequences from reference profiles   STR mixture analysis leveraging loci amplification levels—higher precision of results if exclude weakly amplifying STR loci   Estimating relative contributions of DNA in STR mixtures—proportion of DNA contributed to mixture for each individual   STR allele matching versus matching on size or name—mixture analysis results are improved if STR allele sequences are used rather than STR allele sizes or names   Estimating number of contributors to STR mixtures with machine learning methods   Estimating number of contributors to SNP mixtures with machine learning methods
 
A method of analyzing sequence data from a biological sample that contains DNA comprised of the steps:
   Sample identification by optional DNA barcode enabling demultiplexing of multiple samples within a sequence dataset;   Identification of source genome source locus by using flanking sequences of short tandem repeats (STRs);
           Determining the correct flanking sequences of STR alleles with DNA sequence reads is essential for correct allele identification;   
           Identification of SNP and STR variants in flanking sequences can differentiate between individuals and enables higher precision matching of allele contributions to DNA mixtures with two or more individual contributors;   Tallying observed variants for multiple STR loci for multiplexed samples with variants in flanking sequences for individual reference samples and DNA mixtures with contributions from two or more individuals;   Identification of imbalances in DNA sequence reads for each DNA strand, known as strand bias, can be optionally used in data filtering of results;   Identification of DNA polymerase stutter alleles from reference samples to identify dominant −1 and +1 stutter alleles to create a library or database of likely stutter allele sequences;
           Prediction of −2, −3, and +2 stutter alleles by recursively applying the −1 and +1 stutter losses or gain of STR unit to the observed STR stutter sequence;   Prediction of −1, −2, −3, +1, and +2 stutter alleles by incrementally decreasing of increasing the largest subscript in a STR sequence—e.g., a (ATAT) 2 (ATAG) 10  STR allele would have a predicted −1 stutter allele of (ATAT) 2 (ATAG) 9 , etc.   
           Identification of contributed STR alleles to DNA mixtures as observed STR allele sequences that are inconsistent with being likely stutter alleles of other contributed STR alleles with unit differences in STR unit lengths that can obscure contributed STR alleles with possible stutter alleles;
           Example, if a STR allele is observed with high number of read counts with two or more candidate STR alleles consistent with being −1 stutter alleles, then only one of the −1 alleles is likely, the stutter allele (and not two or more) with the remaining STR alleles having a high probability of deriving from individual contributors;   
           STR alleles with read counts larger than expected proportional STR stutter allele rate have a high probability of being STR alleles contributed by an individual and not stutter artifacts (e.g., if the −2 allele count is higher than the −1 allele count at a locus, then the −2 allele has a high probability of being an allele from an individual;   Poorly amplifying STR amplicons are a primary source of dropped alleles for contributors to DNA mixtures; a priori elimination of poorly amplifying STR loci prior to mixture analysis reduces dropped alleles for DNA contributors to DNA mixtures and reduces the probability of incorrect exclusion of DNA contributors;   Higher fidelity of STR mixture analysis is achieved by matching STR allele sequences rather than STR allele names or STR allele sizes due to the increased precision of STR alleles with different allele sequences but identical allele lengths;   Higher fidelity of STR mixture analysis is achieved by matching STR allele sequences and adjacent polymorphisms in flanking sequences between reference profiles and DNA mixtures; two contributed identical STR allele sequences can be differentiated by variant differences in flanking sequences;   The read counts of contributed STR alleles for an individual are proportional to the amount of DNA contributed to DNA mixtures; the percentage of contributed DNA for each known contributor to a mixture and unknown contributors can be used to estimate proportion of DNA contributed to DNA mixtures;   Machine learning methods can predict the number of individual contributors to STR mixtures;   Machine learning methods can predict the number of individual contributors to STR mixtures;
 
GrigoraSNPs
   Fast SNP and STR sequence analysis with read lookup table to identify locus for HTS reads   Higher accuracy SNP allele calling leveraging SNP flanking sequences
 
A method of analyzing sequence data from a biological sample that contains DNA comprised of one or more of the following steps:
   Sample identification by optional DNA barcode enabling demultiplexing of multiple samples within a sequence dataset;   Identification of source genome source locus by using subset(s) of the sequence (e.g., DNA tag sequence lookup table(s) mapping tag sequences to candidate loci);
           Locus lookup tables enables high performance analysis of DNA sequence datasets   
           Identification of target SNP base by verification of matching flanking sequences on one or two sides of the target SNP base;
           Higher accuracy of SNP allele calling is achieved by leveraging SNP flanking sequences to ensure correct identification of SNP with DNA sequence read   
           Identification of one or more SNP and variant polymorphisms in a single sequence read; multiple sequence variants in a single DNA sequence read represent the variants from one source chromosome (from an individual) representing a phased microhaplotype;   Optional quality filtering of SNP bases by associated quality scores (Q20 is a frequently selected quality filter cutoff for bases in DNA sequence reads);   Tallying observed variants for multiple SNP loci for multiplexed samples with optional quality filtering;   Identification of imbalances in DNA sequence reads for each DNA strand, known as strand bias, can be optionally used in data filtering of results;   Multiple tools exist for SNP allele calling. A novel tool. named GrigoraSNPs, is described that is roughly 20 times faster than the closest tool (SAMtools) and avoids assignment of 50% of sequence reads for Y chromosome pseudoautosomal region incorrectly to the X chromosome (as seen from SAMtools results). GrigoraSNPs leverages a novel sequence tag lookup approach to rapidly identify SNP loci to match against for each HTS sequence read. High precision SNP allele calling is achieved by matching flanking sequences immediately adjacent to target SNP bases. GrigoraSNPs can automatically identify multiplexed barcodes and demultiplex reads for multiple samples to tally results. GrigoraSNPs includes an optional SNP quality base filter (frequently used Q20) for filtering identified SNP
 
Venn Matrix Method
 
A Venn Matrix method is provided to identify known and unknown mixture contributors. The method includes first identifying knowns, remove known profiles from mixtures, apply the Venn Method, and then analyze residues profiles to identify unknown individuals and smaller mixtures with multiple contributors (fewer than the original mixtures).
 
DNA Mixture-to-Mixture Analysis
 
In some embodiments, a visualization of overlap is provided between contributors to multiple complex mixtures. This provides overview in a glance across multiple complex mixtures/crime scenes for identification in a more expeditious manner. Further, it is appreciated that untangling overlaps between different mixtures or crime scenes can require a considerable amount of analyst time. Mixture-to-mixture visualization provides an immediate view of overlapping contributors common across multiple mixtures.
 
Detecting Unknowns in DNA Forensic Samples
 
There are no available methods to identify unknown individuals in SNP mixture samples. Four approaches are described to identify profiles for unknown individuals. First, identify contributors to mixtures can be subtracted leaving profiles for one or more unknowns (Subtraction method). Second, individual profiles common to two or more mixtures can be isolated with Venn logic by intersecting the mixtures together (Venn method). Third, some profiles can be directly derived from individual mixtures be leveraging differences in contributed DNA concentrations to that mixture (Plateau method). Fourth, the FastID method can be used to identify contributors to mixtures and sub-mixtures derived from the Subtraction method can be overlapped with the Venn method to identify common contributors (Venn Matrix method).
   Identification of unknowns in DNA forensic samples
           Subtraction of knowns   Venn method   Plateau method   Venn matrix method
 
Advanced DNA Forensics Software Platform
 
According to various embodiments, an integrated Forensics platform for SNPs and STR forensic analysis is provided. In some implementations, a unified forensic analysis system is provided with all data processing and analysis modules integrated.
   
           A method of combining multiple SNP and STR sequence analysis tools to provide an integrated DNA forensic system with capabilities for one or more of:
           Identification   Mixture analysis   Mixture deconvolution   Saturated mixture analysis   Identification of contributors of trace profiles   Detection of unknown contributors   Estimating number of contributors to SNP or STR mixtures   Prediction of externally visible traits (EVTs) or phenotypes
               Flair color, eye color, hair texture, skin color, facial features, etc.   
               Medical genetics predictions   Kinship prediction   Biogeographic ancestry prediction   Analysis of contributes to multiple mixtures   Etc.   
               

     An integrated platform for SNPs and STR forensic analysis does not exist. A novel integration of multiple forensic analysis tools is presented that enable the fully automated analysis of raw high throughput sequences (HTS) directly from the sequencer, demultiplexing of sequence datasets to individual samples with DNA barcodes, allele calling of individual sequence reads, tallying results, and data quality filtering to create reference and mixture profiles. These sample profiles are automatically loaded into the platform database and searched against all known reference profiles using FastID or TachysSTR. Mixtures are automatically deconvoluted with the Plateau method to identify individual sub-profiles for individuals with no reference profiles, trace profiles and identified and characterized against reference trace exemplar profiles, saturated mixtures are automatically desaturated, etc. Reference profiles are characterized to predict individual gender, phenotype traits (hair color, hair texture, eye color, etc.), biogeographic ancestry, kinship relationships to other reference profiles, etc. The platform is designed with fully automated sample analysis requiring no input from an expert. Results are displayed graphically with interactive features like the Venn mixture deconvolution method, etc. This platform is designed to be extensible, web based, secure with user authentication, encypted passwords, etc. The platform includes a database to manage system data on panels and DNA profiles (references and mixtures). In short, everything described in this patent disclosure is integrated into a single system, named IdPrism. 
     Estimating Individual Contributions to DNA Mixtures 
     No methods exist for estimating the amount of DNA contributed to SNP mixtures by individuals. Three novel methods are described that enable estimation of contributed DNA by identified contributors and remaining unknown contributor(s). The first two methods take the average or median value of the major:minor SNPs attributed to an individual to proportional estimate the contributions for each contributor. The third method leverages the mathematical slope intercept to estimate individual contributions to mixtures.
         Provided are three (3) methods for estimating amount contributed to mixtures by individuals
           Median   Average   Slope intercept
 
Fast P(RMNE) High Precision
 
Statistical calculations for identification and mixture analysis encounter calculation precision errors as the number of loci increases. A novel reformulation of the random person (man) not excluded, P(RMNE), enables high precision calculations with high performance on a single computational thread. This method out performs standard high precision libraries and approximation methods (Taylor series approximations, Big Decimal library, etc.).
 
High Performance Kinship Comparisons
 
A novel method of encoding SNP alleles is provided to enable high performance kinship comparisons across reference profiles. Relatives share 0, 1, or 2 SNP alleles depending upon kinship relationship. This encoding enables fast comparisons of SNP loci and tallying of the number of SNPs with 0, 1, or 2 shared alleles. A parent and a child share at least one allele at all autosomal SNP loci. A grandparent and grandchild share half of these alleles in contiguous chromosomal blocks broken up by chromosomal cross-over events. Two siblings are expected to have roughly 25% of SNP loci with 2 shared alleles, 50% with 1 shared allele, and 25% with 0 shared alleles by chance.
 
Some features may include:
   
           Encoding and method for high performance kinship analysis encoding all SNP alleles using 8 bits [ACGT][ACGT]   A high-performance method for kinship analysis by encoding all SNP alleles using 8 bits
 
Saturated Mixture Analysis
 
In some embodiments, a saturated mixture analysis approach is provided that includes a desaturation of saturated mixture to identify contributors to saturated mixtures.
 
A SNP panel can be designed with multiple SNPs with an average minor allele frequency (mAF) for identifying multiple individuals in DNA mixtures. A panel with a population average mAF of 0.05 results in individuals with minor alleles at roughly 0.10 (2 times 0.05 times 0.95 or 2pq with p+q=1 and q=0.05) for autosomal SNP loci. These SNP panels will approach saturation of SNP loci in mixtures as the number of contributors approaches or exceeds 1/mAF (or 1/0.1 or 10 in this example). The ability to identify individual contributors to saturated mixtures diminishes as the total number of SNP loci for the mixture saturates with observed minor alleles. A novel method for desaturating saturated mixtures is proposed that enables identification of a subset of individual contributors to saturated mixtures. The SNP loci for the saturated mixture are sorted by increasing mAR and a subset of the saturated mixture SNPs with observed mAR are treated as major alleles for the subset of SNPs with the lowest mAR values; this enables the identification of higher DNA concentration contributors to saturated mixtures.
 
Trace Profile Detection
 
It is appreciated that there exists no methods to identify individuals who contribute trace profiles to SNP mixtures. A new method is proposed that leverages a subset of a reference profile with the highest minor allele ratios to match against trace profiles identified in SNP mixtures to identify trace contributes to SNP mixtures. In one implementation, a trace profile mixture analysis includes novel methods for identifying trace profile contributors to complex mixtures.
 
Minor Allele Count Method
 
One focus of SNP mixture analysis methods described herein use the minor allele ratio (mAR) in the classification of SNP alleles as major, major:minor, and minor:minor for reference profiles and mixture profiles. Analytical thresholds are used to differentiate between only major alleles present as a SNP loci (mAR approximately 0), a mixture of major and minor alleles (0&lt;mAR&lt;1), or only minor alleles present (mAR approximately 1). The minor allele count (mAC) provides an equivalent approach as an alternative to only using the mAR. SNP loci with low minor allele counts are more likely to be derived by polymerase or sequencer errors than low concentration contributed minor alleles. As provided herein, one minor allele count (mAC) approach includes an alternative data analysis approach that compliments the minor allele ratio (mAR) approach.
       

     Still other aspects, embodiments, and advantages of these exemplary aspects and embodiments, are discussed in detail below. Any embodiment disclosed herein may be combined with any other embodiment in any manner consistent with at least one of the objects, aims, and needs disclosed herein, and references to “an embodiment,” “some embodiments,” “an alternate embodiment,” “various embodiments,” “one embodiment” or the like are not necessarily mutually exclusive and are intended to indicate that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment. The appearances of such terms herein are not necessarily all referring to the same embodiment. The accompanying drawings are included to provide illustration and a further understanding of the various aspects and embodiments, and are incorporated in and constitute a part of this specification. The drawings, together with the remainder of the specification, serve to explain principles and operations of the described and claimed aspects and embodiments. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various aspects of at least one embodiment are discussed herein with reference to the accompanying figures, which are not intended to be drawn to scale. The figures are included to provide illustration and a further understanding of the various aspects and embodiments, and are incorporated in and constitute a part of this specification, but are not intended as a definition of the limits of the invention. Where technical features in the figures, detailed description or any claim are followed by reference signs, the reference signs have been included for the sole purpose of increasing the intelligibility of the figures, detailed description, and/or claims. Accordingly, neither the reference signs nor their absence are intended to have any limiting effect on the scope of any claim elements. In the figures, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every figure. 
       In the figures: 
         FIG.  1    illustrates a block diagram of a sample analysis system, according to one embodiment. 
         FIG.  2    illustrates an example process for building an error profile per locus, according to one embodiment. 
         FIG.  3    illustrates an example process for eliminating read error, according to one embodiment. 
         FIG.  4    illustrates an example process for defining a dominant stutter allele sequence, according to one embodiment. 
         FIG.  5    is an example process for eliminating error induced by PCR amplification, according to one embodiment. 
         FIG.  6    is an example boxplot of STR allele PCR amplification strength, according to one embodiment. 
         FIG.  7    is an example process for identifying a contributor in a sample, according to one embodiment. 
         FIG.  8    illustrates mixture composition estimates, according to one embodiment. 
         FIG.  9    illustrates actual mixture composition, according to one embodiment. 
         FIG.  10    illustrates a plot of the average number of alleles by locus for one to five contributors to STR mixture, according to one embodiment. 
         FIG.  11    is a block diagram of an example distributed database system in which various aspects of the present invention can be practiced. 
         FIGS.  12 A and  12 B  are diagrams illustrating identifying an individual from a nucleic acid sample containing genetic material from multiple individuals, in accordance with some embodiments of the technology described herein. 
         FIG.  13    depicts an illustrative environment in which embodiments of the present technology may operate. 
         FIGS.  14 A and  14 B  are flow charts of illustrative processes for encoding sequence information obtained from a nucleic acid sample and comparing the resultant encoding with encodings of other nucleic acid samples, in accordance with some embodiments of the technology described herein. 
         FIG.  15    depicts experimental results of a kinship analysis, in accordance with some embodiments of the technology described herein. 
         FIG.  16 A  depicts an illustrative chart showing a comparison between an individual versus four generations of relatives and an individual versus 1 million unrelated individuals using 12,456 SNPs with mAF 0.01 to 0.2 (note: height of data not to scale), in accordance with some embodiments of the technology described herein. 
         FIG.  16 B  depicts an illustrative comparison of the individual in  FIG.  5 A  versus four generations of relatives (e.g., descendants) using 12,456 SNPs with mAF 0.01-0.2 (note: height of data not to scale), in accordance with some embodiments of the technology described herein. 
         FIG.  17 A  depicts a chart illustrating a kernel density estimation (KDE) for 12,456 SNPs with a mAF between 0.01 and 0.2, in accordance with some embodiments of the technology described herein. 
         FIG.  17 B  depicts a chart illustrating the KDE for 3,453 SNPs with a mAF between 0.01 and 0.1, in accordance with some embodiments of the technology described herein. 
         FIG.  18    is a diagram illustrating the identification of individuals by comparing mixtures. I 1 , I 2 , I 3 , and I 4  represent individuals common between the different overlaps in the three mixtures, in accordance with some embodiments of the technology described herein. 
         FIG.  19    is a schematic depiction of a DNA profile or barcode based upon a 1,000 SNP panel for a given individual (referred to as subject 1) in which the location of a black line indicates the presence of a minor allele SNP at that locus. 
         FIG.  20    is a schematic depiction of a DNA profile or barcode based upon a 1,000 SNP panel for a mixture of 5 peoples&#39; DNA, including subject 1. 
         FIG.  21    is a schematic depiction of a DNA profile or barcode reproduced using the methods of the disclosure to compare five 5-person DNA mixtures with one common contributor across them. Subject 1&#39;s  127  SNP profile can be reliably reproduced to within 11 SNPs (compared to the DNA profile for subject 1 shown in  FIG.  12   ). 
         FIG.  22    is a graph depicting, an analysis of mAR of a two-person mixture, sequenced using a panel of 975 SNP loci. The minor and major contributor&#39;s allele signatures are immediately apparent. Expected genotypes mARs are labeled as mm (homozygous minor), mM (heterozygous) and MM (homozygous major) on the right. P(RMNE) has been calculated using the major allele profiles as 6.07E-16. 
         FIG.  23    is a pair of graphs depicting a theoretical match of a suspect&#39;s SNP profile in two mixtures. Major allele (orange, bottom arrow) and Minor allele (blue, top arrow) SNP profiles are extracted and compared across mixtures. Partially matching sub-profiles are circled. A collection of matching sub-profiles can be added in union to provide a larger DNA profile. 
         FIG.  24    is a schematic depiction of the probability of a Random Man Not Excluded P(RMNE) as exemplified in a graph plotting the probability of a false match against SNP frequency of a mixture containing DNA from 8 individuals and a SNP panel having either 500 or 1000 SNPs. 
         FIG.  25    is a graph depicting individual reference data from a SNP panel and a depiction of the same data as an individual SNP “barcode”. 
         FIG.  26    is a graph depicting the determination of the threshold for calling a minor allele using the ratio of the minor allele calls to the total number of reads at a locus. In this example, a subject is determined to have a minor allele at a locus if the ratio of the minor allele calls to total calls exceeds 0.25. There are ratios with intermediate values that can make it difficult to clearly distinguish homozygous major from heterozygous genotypes, and heterozygous from homozygous minor genotypes. These intermediate values may result from amplification error, sequence error, or copy number variants, and may be corrected by optimization of the analysis algorithm or use of alternate loci. 
         FIG.  27    is a graph depicting results from a mixture analysis using 468 SNPs with a minor allele frequency of approximately 0.05. Mixtures containing equal amounts of DNA from 8, 5, 3, 10 and 15 individuals were amplified using Fluidigm multiplexed PCR technology and sequenced on Ion Torrent PGM. 
         FIG.  28    is a graph depicting the effect of mismatches on receiver operating characteristic (ROC) Curve using 480 loci with minor allele frequencies of approximately 0.05. Calculations of probability of detection vs. P(RMNE) demonstrate that a P(RMNE) of less than 10-9 can be achieved in a 3-5 person mixture with minimal detriment to the probability of detection (Pd). 
         FIG.  29    is a diagram depicting results from a mixture analysis using 975 SNPs with a minor allele frequency of approximately 0.05. Mixtures containing equal amounts of DNA from 8, 10, 15, and 20 individuals were amplified using Ampliseq multiplexed PCR technology and sequenced on Ion Torrent PGM. 
         FIG.  30    is a diagram depicting the effect of mismatches on ROC Curve using 975 loci with minor allele frequencies of approximately 0.05. Calculations of probability of detection vs. P(RMNE) demonstrate that a P(RMNE) of less than 10-9 can be achieved in a 8-10 person mixture with a Pd of 1. 
         FIG.  31    shows an advanced DNA forensics system modules and example architecture. 
         FIG.  32    shows and example sample characterization pipeline according to various embodiments. 
         FIG.  33    shows one example of an STR mixture analysis of mixtures of 3, 4, 5, and 12 individual contributors. 
         FIG.  34    shows an example Plateau mixture deconvolution method according to various embodiments. 
         FIG.  35    shows an example Venn mixture deconvolution method according to various embodiments. 
         FIG.  36    shows an example mixture-to-mixture analysis method according to various embodiments. 
         FIG.  37    shows a process for predicting the number of individuals in mixtures with SNP panels. 
         FIG.  38    shows a process for predicting the number of individuals in mixtures with STR panels. 
         FIG.  39    shows estimating the relative contributions of individuals to DNA STR mixtures. 
         FIG.  40    shows a BGA for an individual using Google maps. 
         FIGS.  41 A- 41 C  show database tables that may be used to implement an advanced DNA forensics system. 
         FIG.  42    shows the distribution of the minor allele loci of four high contributors in a mixture. 
         FIG.  43    shows the distribution of minor allele loci of two minor contributors in a mixture. 
         FIG.  44    illustrates that two unrelated are likely to share a set of alleles in common by chance alone. 
         FIG.  45 A  shows an example mixture  41  plot of minor allele ratios. 
         FIG.  45 B  shows an example mixture  41  FastID search results against references and mixtures. 
         FIG.  45 C  shows an example reference  83  plot of minor allele ratios. 
         FIG.  45 D  shows an example mix 41  Mixture-to-Mixture results. 
         FIG.  46    shows an example SNP Panel with 2,655 loci example profile for an individual. 
         FIG.  47    shows an example SNP Panel with 14,933 loci example profile for an individual. 
         FIG.  48    shows an example mixture profile with known reference and partial profile for an unknown contributor. 
         FIG.  49    shows example mixture alleles for Unknown Contributor shown with Known Contributor. The allele signature for the unknown contributor shown with the corresponding alleles from the known contributor from the mixture profile in  FIG.  48   . 
         FIG.  50    shows an example Venn method for mixture deconvolution. 
         FIG.  51    shows an example Plateau method for mixture deconvolution. 
         FIG.  52    shows an example Venn Matrix Method for identification of unknowns. 
         FIG.  53   . shows an example two person dilution series for DNA ratios 75:25, 90:10, 99:1, 200:1, and 400:1 plus the detection of unknown trace profile in 90:10 dilution mixture. 
         FIG.  54    shows an example touch mixture with six DNA contributors with touch order by individuals: 7, 7, 7, 8, 5, 7, 3, 7, 3, 7, 7, 3, and 4. 
         FIG.  55    shows example P(RMNE) calculation methods for 1,000 SNPs. 
         FIG.  56    shows example P(RMNE) calculations for 2,000 SNPs. 
         FIG.  57    shows example P(RMNE) calculations for 3,000 SNPs. 
         FIG.  58    shows example P(RMNE) calculations for 4,000 SNPs. 
         FIG.  59    shows example runtimes for P(RMNE) methods. 
         FIG.  60    shows reference mAR profiles of high and low contributors in the 1:400 defined mixture. 
         FIG.  61    shows a mAR plot of the 1:400 Defined Mixture experiment without any modifications on the left. 
         FIG.  62    shows an minor allele count (mAC) and minor allele ratio (mAR) plots of the 1:400 Defined Mixture experiment without any modifications on the left. 
         FIG.  63    shows plots of 1:99 two person defined mixture using the mAC on the left and mAR on the right. 
         FIG.  64    shows plots of 10:90 two person defined mixture using the mAC on the left and mAC Frequency Filter on the right. 
         FIG.  65    shows an example reference 1 chromosome 22 loci minor allele ratios. 
         FIG.  66    shows example sorted minor allele ratios for references 1 and 2. 
         FIG.  67    shows example two-person Dilution Series with DNA ratios of 25:75, 10:90, 1:99, and 1:200. 
         FIG.  68    shows example sorted two-person dilution series. 
         FIG.  69    shows an example of Plateau mixture deconvolution for three-person mixture with DNA concentrations 5%:20%:75%. 
         FIG.  70    shows an example of Plateau mixture deconvolution for four-person mixture with DNA concentrations 2%:17%:32%:47%. 
         FIG.  71    shows example HIS DNA Sequence Components. 
         FIG.  72    shows example GrigoraSNPs runtimes. 
         FIG.  73    shows a reference family tree. 
         FIG.  74    shows differences separated by degree of relationship for 39k SNP panel. 
         FIG.  75    shows differences separated by degree of relationship for 20k SNP panel. 
         FIG.  76    shows differences separated by degree of relationship for 2k SNP panel. 
         FIG.  77    shows allele call (i.e., allele identification based on allele sizing) errors that result from conventional sequencing and analysis. 
     
    
    
     DETAILED DESCRIPTION 
     Systems and methods are provided for distinguishing STR (short tandem repeat) alleles from DNA polymerase artifacts created by DNA amplification when using PCR (polymerase chain reaction) techniques. Various embodiments of the systems and methods characterize the observed DNA polymerase errors on individual references per each locus to generate an error profile specific to each locus. Embodiments of the systems and methods analyze samples against the error profiles to distinguish real alleles from artifacts in individual reference samples and, in other examples, to distinguish real alleles from artifacts in samples that include mixtures of multiple individuals. 
     In some embodiments, the error profiling is configured to include tracking of −3, −2, −1, 0, +1, +2, and +3 allele length stutters, a respective rate of error for each polymerase and loci, as well as identifying a dominant −1 stutter sequence generated by the DNA polymerase for each loci (as error rates vary by locus and/or selected polymerase). Each integer for identifying allele length error (e.g., −1, −2, −3) represents introduction or deletion of a repeat sequence of length of 1 repeat unit. The 0 length allele stutters are individual base errors that randomly occur within the STR allele during PCR amplification. Discussed in greater detail below, results from methods and systems implementing various aspects demonstrate superior allele calls (i.e., identification of STRs) for individuals and mixture samples over conventional systems. Further embodiments extend the error profiles based on deeper sequencing depth (higher sequence counts) and incorporate, for example, −4, +4, etc., stutter artifacts. 
     Other aspects incorporate PCR amplification strength for different loci into sample analysis, improving accuracy over conventional identification approaches. In various embodiments, amplification strength modelling can be combined with other aspects to further increase accuracy. For example, estimating relative contributions of DNA of individuals in a DNA mixture can be enhanced based on estimates of relative proportions (e.g., normalized relative proportions) of STR allele strengths of individuals within the mixture. In another example, matching STR sequences rather than matching names based on allele length improves STR allele matching. In yet another embodiment, machine learning models on actual or in silico mixtures of individuals (e.g., from 2 to 30 contributors) enhances accuracy in predicting numbers of contributors. The machine learning models can be based on, trained on, or extrapolated from individual or combinations of STR and SNP profiles. Any of the embodiments and aspects can be combined to achieve increases in identification accuracy or improve estimates. 
     Examples of the methods, devices, and systems discussed herein are not limited in application to the details of construction and the arrangement of components set forth in the following description or illustrated in the accompanying drawings. The methods and systems are capable of implementation in other embodiments and of being practiced or of being carried out in various ways. Examples of specific implementations are provided herein for illustrative purposes only and are not intended to be limiting. In particular, acts, components, elements and features discussed in connection with any one or more examples are not intended to be excluded from a similar role in any other examples. 
     Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. Any references to examples, embodiments, components, elements or acts of the systems and methods herein referred to in the singular may also embrace embodiments including a plurality, and any references in plural to any embodiment, component, element or act herein may also embrace embodiments including only a singularity. References in the singular or plural form are not intended to limit the presently disclosed systems or methods, their components, acts, or elements. The use herein of “including,” “comprising,” “having,” “containing,” “involving,” and variations thereof is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. References to “or” may be construed as inclusive so that any terms described using “or” may indicate any of a single, more than one, and all of the described terms. 
       FIG.  1    is an example of a sample analysis system  100 . The sample analysis system  100  illustrates a sequencing device in which a DNA sample can be introduced and analyzed. For example, the system  100  can be used in conjunction with PCR amplification for sequencing of PCR products (e.g., STRs and SNPs), sizing of PCR products, etc. System  100  can be configured as a standalone device, or as a multi-component system (e.g., with a sample amplification and sequencing component and a separate or integrated analysis component). According to various embodiments, sample or analysis kits  102  can be provided for users to capture biological samples and/or process samples through pre-analysis stages. The pre-analysis stages can include adding adapters, primers, polymerases, heating, and cooling, and any other known steps and approaches for PCR amplification/tagging of alleles in the samples. The kits can employ specific polymerases and the analysis of the resulting PCR products can include error profiles tailored to the agents employed (e.g., adapters, primers, polymerases, combinations of each, etc.) and respective loci being analyzed. 
     The FBI recently expanded its combined DNA index system (CODIS) from 13 loci (STR alleles) to 20 loci to better align with forensics used in Europe. Other systems may be used that analyze even greater numbers of loci. These various loci are identified and known by name as well as their genomic position and respective length in base pairs. Tables 1A-1B (collectively, Table 1) below shows observed polymerase errors rates for some loci. According to one embodiment, characterization of the PCR amplification artifacts observed across multiple individuals can be used to build profiles of expected artifacts specific to each locus (e.g., and each polymerase and PCR primer pairs). The analysis component shown at block  104  can be programmed with the error profiles for any number of agents used in PCR (or other amplification technique) and resolve allele identification based on leveraging the error profiles to distinguish real STR alleles from artifacts. 
     According to various embodiments, the analysis component shown at  104  can include any one or more of the illustrated analysis approaches. Further, the analysis component  104  can be integrated into a sequencing device  100  or can be executed by one or more separate systems. In some embodiments, each of the internal blocks  104 A,  104 B,  104 C,  104 D, and  104 E can be executed on different systems. In various embodiments, the different systems can communicate respective results to other components/systems to improve accuracy. According to one embodiment, a DNA sequencing device or DNA analysis system can be enhanced to include allele error profiling by locus. In one example, each locus for analysis (e.g., CODIS loci, as well as additional loci) is modeled to establish an error profile. The modeling is executed based on comparing sequences established through PCR techniques against known or previously sequenced DNA. According to one embodiment, the deviations between the PCR established sequences and the known sequence provide an error model that the system (and e.g., component  104 A) applies to unknown samples. 
     According to another embodiment, the analysis performed by block  104 A relies on building error profiles for each locus based on multiple reference samples. For the multiple reference samples, the relevant portions (e.g., loci of interest) can be completely sequenced to provide an accurate baseline for evaluating any observed errors stemming from PCR amplification. 
     Building Per Locus Error Profiles 
     According to one embodiment, characterization of PCR amplification artifacts observed in multiple individuals enables the profiling of expected artifacts by STR locus (and/or agents used in PCR). For example, the system can be configured to model the observed patterns of STR stutter alleles. In one embodiment, the observed errors pattern can be shown to be dependent upon the number of PCR amplification cycles during sample preparation. Thus, the error profile per locus can also be applied to account for any number of amplification cycles. For example, the error profile can store error rate data associated with a data value for a number PCR cycles to which the error rate is associated. 
     Generally stated, the value in establishing an error profile for each locus (i.e., improving allele identification accuracy) can be observed in Table 1. For example, an error profile may be determined that is broken down into two components, the average error, and the variability of the error. Table 1a shows the mean locus error across samples, while Table 1b shows the standard deviation of the locus error across samples. Taking one convention system and resulting data, stutter alleles for −3, −2, −1, +1, +2, and +3 lengths were observed for some of the STR loci. Also 0 length allele variants were also observed for random DNA single nucleotide errors (at lower rate of error than deletions and additions). 
     One embodiment uses the observed errors across multiple reference samples to characterize errors by STR locus to generate per locus error profiles. The STR loci can be selected based on variations in DNA sequences between individuals (e.g., polymorphisms) that can be used in DNA analysis (e.g., in forensics cases) to determine identity. Table 1 A provides examples of observed error rates for 15 of the 20 STR loci that are used in conjunction with the FBI&#39;s CODIS database to identify individuals. Discussed in greater detail below, for both individual samples and mixture samples, distinguishing between real STR alleles and polymerase artifacts is accomplished by leveraging error profiles to distinguish real STR alleles from artifacts. Various embodiments improve the accuracy of distinguishing real STR alleles from artifacts—which can be key for DNA mixtures. And importantly improves the accuracy of DNA identification over conventional approaches. 
     
       
         
           
               
             
               
                 TABLE 1A 
               
             
            
               
                   
               
               
                 Mean Error Characterization 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 −3 
                 −2 
                 −1 
                 +0 
                 +1 
                 +2 
                 +3 
               
               
                 Locus 
                 Stut 
                 Stut 
                 Stut 
                 Error 
                 Stut 
                 Stut 
                 Stut 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 D13S317 
                 0.0035% 
                 0.108% 
                 3.29% 
                 2.37% 
                 1.04% 
                 0.011% 
                 0.00011% 
               
               
                 D6S1043 
                 0.046% 
                 0.595% 
                 7.71% 
                 0.66% 
                 1.42% 
                 2.7% 
                 0.0003% 
               
               
                 CSF1PO 
                 0.0088% 
                 2.35% 
                 4.44% 
                 1.74% 
                 1.73% 
                 0.03% 
                 0.0005% 
               
               
                 D7S820 
                 0.017% 
                 0.312% 
                 5.58% 
                 0.884% 
                 1.46% 
                 0.021% 
                 0.0003% 
               
               
                 vWA 
                 0.11% 
                 1.07% 
                 10.36% 
                 9.94% 
                 19.11% 
                 3.65% 
                 0.70% 
               
               
                 D10S1248 
                 0.13% 
                 1.21% 
                 11.00% 
                 0.592% 
                 0.512% 
                 0.003% 
                 0.00001% 
               
               
                 D17S1301 
                 0.33% 
                 2.02% 
                 14.84% 
                 2.27% 
                 1.28% 
                 0.02% 
                 0.0002% 
               
               
                 TH01 
                 0.2% 
                 0.433% 
                 6.58% 
                 0.520% 
                 0.363% 
                 0.001% 
                 0.000005% 
               
               
                 FGA 
                 1.5% 
                 2.50% 
                 15.80% 
                 1.17% 
                 1.42% 
                 0.02% 
                 0.5% 
               
               
                 D19S433 
                 0.05% 
                 0.603% 
                 7.77% 
                 1.14% 
                 0.538% 
                 0.003% 
                 0.00002% 
               
               
                 D20S482 
                 0.13% 
                 1.21% 
                 11.02% 
                 0.669% 
                 2.12% 
                 0.04% 
                 0.001% 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 1B 
               
             
            
               
                   
               
               
                 Standard Deviation Error Characterization 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 −3 
                 −2 
                 −1 
                 +0 
                 +1 
                 +2 
                 +3 
               
               
                 Locus 
                 Stut 
                 Stut 
                 Stut 
                 Error 
                 Stut 
                 Stut 
                 Stut 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 D13S317 
                 0.002% 
                 0.058% 
                 1.21% 
                 1.73% 
                 0.596% 
                 0.0095% 
                 0.00013% 
               
               
                 D6S1043 
                 0.0421% 
                 0.422% 
                 3.66% 
                 1.73% 
                 0.596% 
                 0.195% 
                 0.00022% 
               
               
                 CSF1PO 
                 0.0097% 
                 0.166% 
                 2.46% 
                 1.73% 
                 0.861% 
                 0.0222% 
                 0.00050% 
               
               
                   
               
            
           
         
       
     
     Various embodiments leverage the observed DNA polymerase error rates shown in Table 1 to build error profiles that can filter out such errors identifying unknown samples. For example, the error rate when viewed on a locus by locus basis shows the error rate (e.g., −1 &amp; −2) is proportional when reduced to specific STR alleles. For example, the −2 is roughly the square of the −1 error rate. In some implementations, for example, where there is insufficient data to directly capture the −2 error rate, algorithm optimizations can be used to establish a −2 error rate (e.g., square a −1 error rate and use the square as the −2 error rate). 
     According to one modeling approach, the system  100  can be configured to establish and apply expected error profiles per analyzed loci. In further examples, the error profiles can be tailored or have database entries for an error rate per loci that are also specific to the agents used in processing (e.g., polymerase, tagging agent, adapter, etc.).  FIG.  77    illustrates allele call (i.e., allele identification based on allele sizing) errors that result from conventional sequencing and analysis. Various embodiments of the present system identify and resolve such calling error by applying respective error profiles. According to one embodiment, the error profiles are applied by setting a threshold equal to the error rate plus a predefined number of standard deviations beyond the error rate. This is done to prevent edge cases from being falsely included. Allowing the number of standard deviations to be system defined (e.g., set by an administrative user) allows for setting the stringency of excluding false calls—and further allows users to dynamically tailor the precision based on the analysis being performed. 
     In some embodiments, the system can be configured to automatically assess various thresholds, for example, by perturbing the standard deviation setting and evaluating accuracy based on local minima analysis. 
     In  FIG.  77   , Illumina STR Peak calling errors for individual profiles (e.g., I 6 , I 9 , and I 10 ) are shown. For example, allele name  15  (italics) is a false read for individual  6  (I 6 ). Using error profiles of the +1 error for allele  14  and −1 for allele  16 , the number of reads  379  are within an expected error profile, and should not result in calling of allele  15  for D20S482. Various embodiments, are configured to amply combination errors analysis to determine accurate results and reduce errors generated by prior art systems. After application of the combined error profile, the genotype for 16 is 14, 16 and not 14, 15, 16 as identified under conventional approaches. 
     Additional errors generated by conventional approaches include calling of allele  19  for D6S1043. Because the genomic sequences being analyzed via PCR and naming are known, the errors are readily apparent based on comparing results of the PCR and naming against the known sequences. Seen in again for I 6 , a combination error (+1 of allele  18  and −1 of allele  20 ) generated a false call for allele  19 . 236 reads of allele  19  in the sample are within the combined error rate determined by the analysis system  100  (and/or analysis component  104 A). For I 9 , allele  14  is also false call. As is allele  14  for I 10 , based on the 63 reads in the analyzed sample. The error rate for allele  14  is set at the average −1 error for CSF1PO plus three standard deviations from the error. This creates a combined error rate of 12%, which allele  14  falls within the boundary of. According to one embodiment, for each read output generated by the analysis system, the system evaluates the read output to determine whether the value could be generated as a result of error from other alleles. In some examples, the number of PCR cycles executed on a given sample is known, thus error profiles matching the number of cycles can be used. In other embodiments, increasing the number of PCR cycles increases the number of PCR artifacts, thus if a value for the number of reads does not exceed the expected rate of error for a single PCR cycle—the detected peak is determined to be an artifact and not an actual allele. Additionally, combination errors must be accounted for so as any allele is identified (e.g., number of reads for that allele is over an expected error number) the system is configured to account for error contributions for each of the identified alleles. 
       FIG.  2    illustrates an example process  200  for building an error profile per locus. Process  200  begins at  202  with preparation of a sample for PCR analysis. For example, the sample is amplified, tagging agents are added, and read data is generated for loci in the sample, for example, based on capillary electrophoresis (CE). Each appearance of an allele is identified—typically based on a florescent signal obtained as the allele is eluted. Each appearance for an allele on each locus is recorded as a read, for example, captured at  204 . The read data (e.g., peaks) is evaluated against known reference sequences for each locus to determine which reads are correct and which reads are the result of a PCR artifact (e.g., stutter) at  206 . The rate of error is generated as part of profiling the error characteristics on each locus, for example at  208 . 
     In some embodiments, the specific agents used during PCR (e.g., tags, polymerase, etc.) are captured in conjunction with the read data, for example at optional step  210 . In some embodiments, the act of profiling error characteristics can include associating specific PCR primers with observed error patterns. Process  200  is executed repeatedly against number of reference samples to build error profile models. For example, confidence evaluations and fitting analysis can be used to determine accuracy of the models, and ensure that the error model meets a confidence threshold. In further embodiments, the error profile models can be refined over time based on incorporation/evaluation of new reference samples. The larger the number of reference samples analyzed, the greater the confidence value for the error profile that is developed. 
     Table 1 illustrates example error rates determined per locus, and each error rate per locus can be used to filter read data to separate stutter alleles from actual alleles. Multiple error profiles can be generated per locus, for example, to include difference agents and/or different numbers of PCR cycles. According to one embodiment, an analysis system can execute processed for eliminating error via locus based error profiles. The error profiles can be matched for specific analysis, for example, based on PC R primers being used and/or a number of PCR cycles executed on a given sample. 
     In one example, a DNA sequencing and/or analysis system can execute a process  300  ( FIG.  3   ) to eliminate read error. According to one embodiment, process  300  filters allele reads (e.g., indicator of a specific allele locus) based on error profile information for each detected locus in a sample, and further can be configured to apply the error profile against reads based on respective instances of alleles for a given locus. In various examples, application of multiple error profiles or conditions can be used to eliminate combination read errors. For example, as shown in Table 1A, for I 6  locus D20s482, allele name  14  is associated with a +1 error and allele name  16  is associated with a −1 error. In combination, the errors triggers a false call on the 15 Allele. 
     According to one embodiment, process  300  can be executed on data collected from analysis of a DNA sample to improve allele calling within the sample. With given read data for respective loci, process  300  can begin at  302  with identification of potential allele names within a given locus based on the read data. At  304 , respective values for a number of reads are evaluated, for example, to determine if they are over a threshold number associated with the Allele name and locus. If the number of reads is over an initial threshold value  304  (YES), the number of reads can be tested against an adjusted threshold (e.g., adjust threshold at  308  and test again at  304 ). For example, at  306 , additional alleles can be identified in the sample which may impact the threshold value used to confirm an artifact (e.g.,  310 ) or confirm an allele (e.g.,  312 ). For example, the threshold value can be adjusted or determined based on the presence of other named alleles (e.g., within a given locus). 
     In other implementations, the presence of read data on all potential alleles/allele names can be used to determine and/or generate a threshold that accounts for the presence of all the potential alleles, and a single evaluation may be used to confirm the presence of an allele versus an artifact, rather than cyclic or recursive analysis. In still other embodiments, confirmation of an artifact can also be used to tailor threshold values, by eliminating any error contribution that the actual presence of the allele would have required. 
     Referencing to  FIG.  77   , Allele name  14  and  16  are identified as being over a threshold value (even when assuming Allele name  15  is properly identified and thresholds increased based on potential error rates for each of  14 ,  15 , and  16 ). In some examples, step  308  can include multiple adjustments and then tests of those threshold values. In further examples, step  308  can also include establishing threshold criteria for unambiguous thresholds where if exceed the named allele must be in the sample (e.g., assume all reads are real, incorporate errors for each read into the thresholds, and identify peaks that pass the adjusted threshold value). Process  300  can then re-evaluate any read data (e.g., via multiple adjustments to threshold values) that did not meet the unambiguous threshold by only considering error values from the named alleles that did pass the unambiguous threshold. In one embodiment, steps  304 - 308  are executed recursively to identify alleles and refine threshold values for determining a named allele is actually present in the sample. The logic for the allele calling is presented in the below pseudo-code example: 
                                LOAD naming_dictionary       FOR locus in unique_loc        SORT reads selected from locus        FOR read in selected_reads        IF number reads greater than minimum threshold AND no previous calls          Call read          Name Read        ELSE          Accumulate expected stutter from alleles within 3 units of distance          IF reads greater than expected stutter reads           Call read           Name Read          END IF        END IF        END FOR       END FOR                    
It should be appreciated that various embodiments of the example logic described above may be used, and the logic may be expressed in one or more programming languages, may include more or less steps, and/or may use a different structure.
 
Build Stutter Allele Sequence Profile
 
     According to another embodiment, the system  100  can also be configured to learn (e.g., model) the dominant −1 stutter allele sequence for each allele within a locus to facilitate STR allele identification in mixtures (e.g., multi-contributor samples). According to one aspect, it is appreciated that learning the dominant −1 stutter allele sequence for each locus enables identification of the −1 stutter allele and enables the system to distinguish the dominant −1 stutter allele from STR alleles from other individuals (e.g., that have STR allele(s) with the same length and similar counts to −1 stutter alleles). When evaluating a mixture, if an allele has a reduced number of reads, one might assume that it is the stutter of a separate allele. However, if the allele in question does not fit the expected stutter pattern, it can be included as a sample present allele. In Table 3 below, both 32 alleles and the 33 allele plus others are distinct by sequence and are very unlikely stutter sequences and are called by this method. Various embodiments implement either of these approaches (e.g., error profiling and stutter allele sequencing) and/or combine these approaches to create novel tools for more accurate: (1) error profiling and (2) allele calling for samples (when analyzing both individual reference and DNA mixtures (multiple contributors). 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Enhanced STR Allele Calling Example 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 Allele 
                 Typed 
                   
                 MITLL 
                 MITLL 
               
               
                   
                 Locus 
                 Name 
                 Allele? 
                 Reads 
                 Name 
                 Called 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 D21S11 
                 29 
                 Yes 
                 680 
                 29      
                 Yes 
               
               
                   
                 
                   D21S11 
                 
                 
                   30 
                 
                 
                   Yes 
                 
                 
                   381 
                 
                 30″ 
                 Yes 
               
               
                   
                 D21S11 
                 30 
                 Yes 
                 519 
                 30′     
                 Yes 
               
               
                   
                 
                   D21S11 
                 
                 
                   31 
                 
                 
                   No 
                 
                 
                   13 
                 
                 31_NC 
                 No 
               
               
                   
                 D21S11 
                 31 
                 
                   No 
                 
                 75 
                 31      
                 Yes 
               
               
                   
                 
                   D21S11 
                 
                 
                   31.2 
                 
                 
                   
                 
                 
                   131 
                 
                 31.2_1 
                 Yes 
               
               
                   
                 D21S11 
                 31.2 
                 No 
                 15 
                 31.2_NC 
                 No 
               
               
                   
                 
                   D21S11 
                 
                 
                   32 
                 
                 
                   
                 
                 
                   95 
                 
                 32_2 
                 Yes 
               
               
                   
                 D21S11 
                 32 
                 
                   No 
                 
                 88 
                 32_1 
                 Yes 
               
               
                   
                 
                   D21S11 
                 
                 
                   32.2 
                 
                 
                   Yes 
                 
                 
                   381 
                 
                 32.2 
                 Yes 
               
               
                   
                 D21S11 
                 33 
                 
                   No 
                 
                 16 
                 33_1 
                 Yes 
               
               
                   
                   
               
            
           
         
       
     
       FIG.  4    is an example process  400  for defining a dominant −1 stutter allele sequence. Process  400  begins at  402  with sequencing PCR products as discussed above. The sequenced PCR products can be compared to known sequences (e.g., on a reference sample having a known genomic sequence) at  404 . For example, sequences of alleles having the same base pair length are compared to determine if the alleles match the references. Errors are reviewed and at  406 , a dominant −1 stutter allele (e.g., a PCR artifact) can be identified for each real allele. For example, a −1 stutter reflects a single deletion of a STR for a specific allele name and locus. The deletion may also be accompanied by individual base pair errors. Regardless of the changes introduced during PCR, the most numerous error is identified at  406  by genomic sequence, and the sequence for each dominant −1 stutter is recorded at  408  for each allele and locus. In some embodiments, the data is recorded in conjunction with specific PCR primers, as different primers can generate different −1 dominant stutter sequences. Further embodiments include the dominant −1 stutter sequence produced by a first PCR primer and respective loci, a second PCR primer and respective loci, a third PCR primer and respective loci, and so on, to capture commonly used PCR primers and effect on the dominant −1 stutter allele for each allele and loci. 
     According to another embodiment, an analysis system (e.g. system  100 ) and/or an analysis component (e.g.,  104  and/or  104 B) is configured to identify a dominant sequence for each −1 allele at each locus. In additional embodiments, the analysis system (e.g., system  100 ) and/or analysis component  104  (e.g.,  104  and/or  104 B) is configured to match the dominant −1 stutter against an analyzed sample to remove for each allele at each locus data reads on the dominant −1 stutter. Various embodiments limit the error resolution to dominant −1 stutter alleles to improve processing over more invasive sequencing approaches. Limiting the analysis to the dominant −1 stutter, in some embodiments, significantly reduces the computational burden associated with matching, for example, more than one or all of the −1 stutter sequences. Further embodiments can be configured to address specific PCR primers, or accept as an input specification of PCR primers used during sample amplification. The dominant −1 stutter sequences are then employed by the system, if the PCR agents match. 
     According to various embodiments, execution of error profiling and/or dominant stutter sequencing resolves miscalled peaks observed in conventional allele calling for D20S482, D6S1043, CSF1PO, and D22S1045 shown in  FIG.  77    and failed identifications/miscalled alleles in Table 4 (see e.g., Mix  1 —THO01 8_NC; Mix—3 D2S1338 16_NC; Mix—3 D5S818 13_NC; and Mix—3 D8S1179 12 NC). Table 4 below presents a series of mixtures (Mix—1—Mix—3) where different mixtures contain a varied number of individuals contributing DNA at different concentrations. 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Enhancements in STR allele calling for DNA Mixture samples 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                 Allele 
                 Current 
                   
                   
                   
                   
               
               
                 Sample 
                 Locus 
                 Name 
                 Test 
                 Reads 
                 Old name 
                 Old Way 
                 Notes 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Mix---1 
                 
                   D12S391 
                 
                   25 _0 
                 
                   Yes 
                 
                 
                   84 
                 
                 
                   25 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---1 
                 
                   D13S317 
                 
                   12 _0 
                 
                   Yes 
                 
                 
                   108 
                 
                 
                   12 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---1 
                 D18S51 
                 13_0 
                 Yes 
                 3740 
                 13 
                 Yes 
                 Reference 
               
               
                 Mix---1 
                 
                   D18S51 
                 
                   13.2 _0 
                 
                   Yes 
                 
                 
                   201 
                 
                 
                   13.2 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---1 
                 D2S441 
                 14_0 
                 Yes 
                 2077 
                 14 
                 Yes 
                 Reference 
               
               
                 Mix---1 
                 D2S441 
                 15_NC 
                 No 
                 22 
                 15 
                 No 
                 Reference 
               
               
                 Mix---1 
                 
                   D2S441 
                 
                   16 _0 
                 
                   Yes 
                 
                 
                   201 
                 
                 
                   16 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---1 
                 FGA 
                 22 
                 Yes 
                 1566 
                 22 
                 Yes 
                 Reference 
               
               
                 Mix---1 
                 FGA 
                 23_NC 
                 No 
                 34 
                 23 
                 No 
                 Reference 
               
               
                 Mix---1 
                 
                   FGA 
                 
                 
                   24 
                 
                 
                   Yes 
                 
                 
                   140 
                 
                 
                   24 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---1 
                 TH01 
                    8 _NC 
                 
                   No 
                 
                 
                   557 
                 
                 
                   8 
                 
                 
                   Yes 
                 
                 −1 stutter of 9 allele 
               
               
                 Mix---1 
                 TH01 
                  9 
                 Yes 
                 3975 
                 9 
                 Yes 
                 Reference 
               
               
                 Mix---2 
                 
                   D12S391 
                 
                   16 _0 
                 
                   Yes 
                 
                 
                   40 
                 
                 
                   16 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---2 
                 D12S391 
                 18_0 
                 Yes 
                 137 
                 18 
                 Yes 
                 Reference 
               
               
                 Mix---2 
                 
                   D13S317 
                 
                   12 _0 
                 
                   Yes 
                 
                 
                   52 
                 
                 
                   12 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---2 
                 D18S51 
                 13_0 
                 Yes 
                 1747 
                 13 
                 Yes 
                 Reference 
               
               
                 Mix---2 
                 
                   D18S51 
                 
                   13.2 _0 
                 
                   Yes 
                 
                 
                   78 
                 
                 
                   13.2 
                 
                 
                   No 
                 
                 13.2 not stutter of 13 
               
               
                   
                   
                   
                   
                   
                   
                   
                 allele 
               
               
                 Mix---2 
                 
                   D18S51 
                 
                   15 _0 
                 
                   Yes 
                 
                 
                   52 
                 
                 
                   15 
                 
                 
                   No 
                 
                 not likely +2 stutter 
               
               
                   
                   
                   
                   
                   
                   
                   
                 allele 
               
               
                 Mix---2 
                 
                   D2S1338 
                 
                   22 _0 
                 
                   Yes 
                 
                 
                   140 
                 
                 
                   22 
                 
                 
                   No 
                 
                 22_novel not likely −1 
               
               
                   
                   
                   
                   
                   
                   
                   
                 stutter 
               
               
                 Mix---2 
                 
                   D2S1338 
                 
                 
                   23′ 
                 
                 
                   Yes 
                 
                 
                   331 
                 
                 
                   23 
                 
                 
                   Yes 
                 
                 Reference 
               
               
                 Mix---2 
                 
                   D6S1043 
                 
                   18 _0 
                 
                   Yes 
                 
                 
                   139 
                 
                 
                   18 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---2 
                 
                   D6S1043 
                 
                   19 _0 
                 
                   Yes 
                 
                 
                   65 
                 
                 
                   19 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---3 
                 
                   D16S539 
                 
                 
                    8 
                 
                 
                   Yes 
                 
                 
                   124 
                 
                 
                   8 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---3 
                 
                   D1S1656 
                 
                   16.3 _0 
                 
                   Yes 
                 
                 
                   46 
                 
                 
                   16.3 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---3 
                 
                   D21S11 
                 
                 
                   28|28.2 
                 
                 
                   Yes 
                 
                 
                   82 
                 
                 
                   28 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---3 
                 
                   D21S11 
                 
                 
                   30″ 
                 
                 
                   Yes 
                 
                 
                   101 
                 
                 
                   30 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---3 
                 
                   D2S1338 
                 
                   16 _NC 
                 
                   No 
                 
                 
                   315 
                 
                 
                   16 
                 
                 
                   Yes 
                 
                 −1 stutter of 17 allele 
               
               
                 Mix---3 
                 
                   D2S1338 
                 
                 
                   17 
                 
                 
                   Yes 
                 
                 
                   1539 
                 
                 
                   17 
                 
                 
                   Yes 
                 
                 Reference 
               
               
                 Mix---3 
                 
                   D2S1338 
                 
                   22 _0 
                 
                   Yes 
                 
                 
                   410 
                 
                 
                   22 
                 
                 
                   Yes 
                 
                 Reference 
               
               
                 Mix---3 
                 
                   D2S1338 
                 
                   22 _1 
                 
                   Yes 
                 
                 
                   80 
                 
                 
                   22 
                 
                 
                   No 
                 
                 False Negative 
               
               
                 Mix---3 
                 
                   D5S818 
                 
                   12 _0 
                 
                   Yes 
                 
                 
                   342 
                 
                 
                   12 
                 
                 
                   Yes 
                 
                 Reference 
               
               
                 Mix---3 
                 
                   D5S818 
                 
                   13 _NC 
                 
                   No 
                 
                 
                   71 
                 
                 
                   13 
                 
                 
                   Yes 
                 
                 +1 stutter of 12 allele 
               
               
                 Mix---3 
                 
                   D5S818 
                 
                   13 _NC 
                 
                   No 
                 
                 
                   35 
                 
                 
                   13 
                 
                 
                   Yes 
                 
                 +1 stutter of 12 allele 
               
               
                 Mix---3 
                 
                   D8S1179 
                 
                   12 _NC 
                 
                   No 
                 
                 
                   672 
                 
                 
                   12 
                 
                 
                   Yes 
                 
                 −1 stutter of 13 allele 
               
               
                 Mix---3 
                 
                   D8S1179 
                 
                 
                   13 
                 
                 
                   Yes 
                 
                 
                   3975 
                 
                 
                   13 
                 
                 
                   Yes 
                 
                 Reference 
               
               
                   
               
            
           
         
       
     
     Shown in table 4 above, the STR sequence for the 22 allele is different from the 23′ allele. A −1 alleles for the 23′ allele should be a 22′ allele. The 23′ alleles has the third to the last repeat unit mutated from TTCC to GTCC where the 22 allele has a TTCC for the third to the last repeat unit. 
     Various embodiments implement mixture analysis based on comparing allele calling for both references and mixture samples and/or comparing the STR allele sequences from references with sequences present in the mixture sample. 
       FIG.  5    is an example process  500  for eliminating error induced by PCR amplification. Process  500  can be executed by an analysis system (e.g.  100 ), an analysis component (e.g.,  104 ), and/or an subcomponent (e.g.,  104 B) to improve accuracy in allele calling and ultimately identification. Process  500  begins at  502  with sequencing of PCR products as discussed above. Based on the results of the sequencing each read for a specific allele can be evaluated against dominant −1 stutter allele sequences at  504 . In some examples, the dominant −1 stutter allele sequences are selected based on specific PCR primers used to process a sample under analysis. In other embodiments, the dominant −1 stutter sequence is retrieved from database records without need for determining the PCR primers used (e.g., agent agnostic sequence data or system is configured with dominant −1 stutter sequence using the same agents under analysis). If a match to a dominant −1 sequence is identified  506  (YES), then the data associated with that sequence can be confirmed as a stutter (i.e., not a genuine allele) and any data associated with the stutter can be excluded or discounted in confirming real alleles. For example, if the sequence obtained at  504  is evaluated and does not match  506  (NO), then process  500  can confirm it as a real allele at  510  or step  510  can include operations to confirm that the sequenced PCR product is a real allele. In one example, the  510  can include analysis of read data on the sequenced product to determine that the sequence is not within an error range (e.g., established by error profiles of other alleles). 
     Generate Allele Amplification Pattern 
     According to another aspect, analysis systems can be configured to leverage the strength of PCR amplification. PCR amplification strength varies by locus and is specific to the PCR primers used and other amplification condition factors. By determining and factoring strength of PCR amplification, various embodiments can be configured to improve identification accuracy. For example, the system can be configured to use PCR amplification strength to establish inclusion/exclusion criteria, where the inclusion/exclusion criteria is implemented on the system to establish an individual as a contributor to a DNA sample. 
     Shown in  FIG.  6    are the median percentage of reads against the maximum number of reads ( 602 ) for appearance of specific loci ( 604 ) detected in reference samples. For each locus a distribution bar is shown to illustrate variance in percent appearance across a reference sample population (e.g., at  606 —showing the interquartile range of the distribution (1 st  to 3 rd  quartile)). The maximum and minimum of the distributions for each loci are shown above and below the bar (e.g., at  608 ) indicating variability outside the upper and lower quartiles. The solid line within each bar (e.g.,  610 ) illustrates a median value for each locus—which can be used in some embodiments as representative of an amplification strength (for example, other embodiments may use a mean value). In various embodiments, the strongest STR alleles (strongest by amplification strength) can be leveraged for inclusion/exclusion criteria for considering an individual as a candidate for having their DNA in an unknown mixture sample. 
     Under various sample conditions, the weakest STR alleles may not be observed in DNA mixtures for individuals. For example, if a contributor has a lower concentration of DNA in a sample, it is likely that STRs that have the weakest amplification will not even appear when analyzed for that individual. Various embodiments of the system employ this imbalance between STR loci as part of the analysis of DNA mixtures to improve identification accuracy over conventional systems. For example, under multiple contributor conditions the system can be configured to exclude the last three loci shown in  FIG.  6    (e.g., at  612 ) from analysis—filtering the data being analyzed at this stage can also lead to computational efficiency over conventional implementation. It is realized that a high probability exists that low concentration contributors will not have some or all values for these loci, and rather than evaluate loci that will have no match because of low concentration (e.g. and lead to an improper conclusion that the individual is not a contributor), the system eliminates the low amplification strength loci, and performs a contributor analysis base on the remaining loci. The threshold and/or selection of loci to include or exclude can be dynamic, based on input into the system on specific PCR primers used and/or other amplification condition factors input into the system or as established by default settings. 
     According to another embodiment, exclusion of a potential contributor can be optimized based on the strongest amplification loci. For example, if a contributor does not have or match on the strongest amplification loci (e.g., shown in  FIG.  6    at  614 ), then that contributor can be eliminated without further analysis. 
       FIG.  7    is an example process  700  for identifying (to a degree of probability) a contributor in a sample. Process  700  begins at  702  with building a profile for matching, for example, against a contributor reference. The profile for matching can be generated using any of the preceding technique to specifically identify alleles by name or sequence, and can execute one or more of the discussed approaches for improving accuracy. The results of the allele calling and/or allele sequencing can be analyzed to determine if all expected loci are present in the sample. If for example, a contributor&#39;s presence in the sample occurs at low concentration various low strength loci may not be detected. If the concentration is high in the sample, all the analyzed loci are more likely to be present  704  YES and analysis of contributor&#39;s profile can be made at  706 . The analysis can be executed against a contributor reference or other profile. In some examples, a sample may be taken from a suspect to generate a contributor reference (via sequencing or allele naming) and perform the analysis at  706 . 
     Where a contributor concentration is low, all loci may not be present, e.g., at  704  NO. Process  700  may then proceed with an exclusion operation to remove the candidate contributor from consideration at  708  based on whether the strongest loci are even present in the sample at  710 . If the strongest amplification strength loci that should be present for a specific contributor are not present  708  NO, then that contributor can be eliminated from consideration at  710 . In some embodiments, the exclusion execution can be a fast filter that achieves a negative result faster than and with fewer computation cycles than some conventional approaches. In other embodiments, the strongest loci analysis can be executed even before the all loci analysis at  704 . In some examples, based on analysis of the strongest amplification loci, potential contributors can be eliminated as a first step of analyzing sample data and analysis only proceeds on potential contributors having at least the strongest amplification strength loci (e.g., and alleles) that are found in the sample under analysis. 
     If the strongest loci are present (and/or match alleles within the strongest loci) at  708  YES, process  700  can proceed with completing the genomic profile of the sample up to any established threshold at  712 . The threshold can be tailored (e.g., by an administrator on the system, set by default, etc.) to exclude low amplification strength loci. In some examples, the process can be executed to determine that a number of loci do not appear at all or in significant quantity to establish the threshold (e.g., detect the bottom three amplification strength loci are not present, or detect sixth, fifth, and fourth lower strength loci are not present—and stop further analysis of weaker loci). This may occur as part of analysis at  706 . In further embodiments, the process may process all potential loci in conjunction with a lowest amplification strength loci excluded profile and present analysis of both options. In a low concentration contributors example, side by side analysis can be provided that shows an exclusion in one setting and a match in another (e.g., using all loci—result: exclude contributor (based on not matching weak amplification strength loci); using threshold loci (exclude weak loci)—result: match and potentially provide the associated degree of probability of the match). 
     Analysis of the profile at  706  can continue with determination of a match (or probability of a match) at  714 . If there is not a match  714  a potential contributor can be excluded at  716 . If there is a match between the sample and a reference  714  YES, the contributor can be identified at  718  (e.g., identified to a degree of probability). Various analysis systems (e.g.,  100 ) can execute process  700 , for example, on samples to identify potential contributors. In further embodiments, process  700  can be executed by contribution analysis component (e.g.,  104 D) or other analysis systems to improved identification accuracy. 
     Analyze DNA Mixture with STR Sequences 
     According to another aspect, rather than comparing called allele names, an analysis system can be configured to match sequences of called STR alleles for individuals to a set of STR sequences found in DNA mixtures. Exact sequence matching can be used to match each called allele for respective individuals and respective sequences in DNA mixtures. According to one example, this is done by identifying the sequences corresponding to called alleles in a reference sample, and querying the mixture to determine if those same sequences are present in the sequenced DNA. If a sequence exactly matching the reference is present, it is considered a positive identification. 
     According to one embodiment, called STR alleles are sequenced for each individual contributor appearing in a DNA mixture. With known sequences the efficacy of prior art approaches can be tested and evaluated against various embodiments disclosed herein. 
     Shown in Table 4 below is a heat map organization of the results of conventional approaches for calling STR loci—the table shows the number of unmatched called alleles of the individual contributors (e.g., when called alleles for each individual of a group of individuals are separately analyzed) when compared in mixture under conventional approaches. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
             
            
               
                 Mix-1 
                 18 
                 26 
                 25 
                 22 
                 19 
                 28 
                 26 
                 4 
                 0 
                 22 
                 25 
                 29 
               
               
                 Mix-2 
                 16 
                 0 
                 15 
                 0 
                 18 
                 20 
                 21 
                 15 
                 20 
                 1 
                 3 
                 20 
               
               
                 Mix-3 
                 7 
                 9 
                 6 
                 5 
                 4 
                 9 
                 4 
                 3 
                 8 
                 7 
                 9 
                 6 
               
               
                   
                 I1 
                 I2 
                 I3 
                 I4 
                 I5 
                 I6 
                 I7 
                 I8 
                 I9 
                 I10 
                 I11 
                 I12 
               
               
                   
               
               
                 Mix-1 is a two-person mixture where I9 has 9x greater DNA concentration than I8. 
               
               
                 Mix-2 is a four-person mixture where I10 and I11 are present at 2:3 the concentration of I2 and I4. Mix-3 is an equimolar mixture composed of all individuals. 
               
               
                 Shown above the colors are a scaled representation of the number of mismatches between a reference individual (x-axis) and a mixture (y-axis). A lighter color represents fewer mismatches while a darker color represents a greater number of mismatches. 
               
            
           
         
       
         
         
           
             Mix- 1  is a two-person mixture where I 9  has 9× greater DNA concentration than 18. 
             Mix- 2  is a four-person mixture where I 10  and I 11  are present at 2:3 the concentration of I 2  and I 4 . Mix- 3  is an equimolar mixture composed of all individuals. 
             Shown above the colors are a scaled representation of the number of mismatches between a reference individual (x-axis) and a mixture (y-axis). A lighter color represents fewer mismatches while a darker color represents a greater number of mismatches. 
           
         
       
    
     According to various embodiments, any reduction in the number of unmatched called alleles represents an increase in identification accuracy. Shown in  FIG.  9    is the intended makeup of the mixtures  1 ,  2 , and  3 . Mixture  1  designed concentrations are 10% I 1 , 20% I 8 , and 70% I 9 . Mixture  2  designed concentrations are 20% I 11 , 30% I 10 , 20% I 4 , and 30% I 2 . Mixture  3  was designed to have equal proportions of each individual (e.g.,  1 - 12 ). 
     Implementation Examples 
     In one embodiment, error patterning by loci is implemented within a python script (e.g., “STR_Noise Profiles Tool”) that when executed is configured to characterize error patterns observed in high throughput sequencing (HTS) STR profiles. In an example execution, STR stutter alleles are observed for −3, −2, −1, +1, +2, and +3 STR allele lengths. It is observed that the higher the read counts for a specific locus, the higher the probability of observing the −2 and sometimes the −3 STR stutter peaks. Polymerase single base calling errors were also observed for the +0 STR allele lengths (see Table 5 below). Various embodiments characterizes these error patterns to create characterization profiles by locus that are used by analysis systems to improve accuracy of STR peak allele calling. For  FIG.  77   , miscalled peaks were observed in conventional allele calling for D20S482, D6S1043, CSF1PO, and D22S1045. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Example STR alleles with +0 stutter alleles 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                   
                 Typed 
                   
               
               
                   
                 Locus 
                 Allele Name 
                 Allele? 
                 Reads 
               
               
                   
                   
               
               
                   
                 D12S391 
                 19 
                 Yes 
                 980 
               
               
                   
                 D12S391 
                 19 
                 No 
                  30 
               
               
                   
                 D12S391 
                 20 
                 Yes 
                 825 
               
               
                   
                 D12S391 
                 20 
                 No 
                  11 
               
               
                   
                   
               
            
           
         
       
     
     According to another embodiment, additional methods can be implemented to improve matching alleles calls for both individuals and mixtures profiles. Table 4 shows the number of unmatched called alleles of individuals compared to mixtures for conventional allele calls in a heatmap. Table 6 shows the improved matching for alleles called by STR_Alleles—through implementation and execution of per loci error profiling. Table 7 illustrates further improvements in accuracy based on excluding the three weakest STR loci (i.e., weakest amplification strength loci) attributable based on amplification profiling of PCR agents and amplification conditions. 
     
       
         
           
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 Error Profiling Results for all autosomal STR loci 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Mix-1 
                 11 
                 23 
                 24 
                 22 
                 19 
                 26 
                 23 
                 3 
                 0 
                 21 
                 24 
                 28 
               
               
                 Mix-2 
                 15 
                 0 
                 15 
                 0 
                 18 
                 19 
                 20 
                 15 
                 20 
                 0 
                 2 
                 20 
               
               
                 Mix-3 
                 2 
                 1 
                 1 
                 1 
                 2 
                 2 
                 2 
                 0 
                 1 
                 4 
                 1 
                 3 
               
               
                   
                 I1 
                 I2 
                 I3 
                 I4 
                 I5 
                 I6 
                 I7 
                 I8 
                 I9 
                 I10 
                 I11 
                 I12 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7 
               
               
                   
               
               
                 Error Profiling Results with removal of three weakest STR loci 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Mix-1 
                 6 
                 19 
                 20 
                 18 
                 15 
                 21 
                 17 
                 0 
                 0 
                 18 
                 22 
                 24 
               
               
                 Mix-2 
                 12 
                 0 
                 13 
                 0 
                 16 
                 15 
                 15 
                 13 
                 17 
                 0 
                 2 
                 19 
               
               
                 Mix-3 
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 4 
                 0 
                 2 
               
               
                   
                 I1 
                 I2 
                 I3 
                 I4 
                 I5 
                 I6 
                 I7 
                 I8 
                 I9 
                 I10 
                 I11 
                 I12 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8 
               
               
                   
               
               
                 STR sequence matching results (without three weakest STR loci) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Mix-1 
                 0 
                 10 
                 14 
                 12 
                 8 
                 14 
                 11 
                 0 
                 0 
                 9 
                 16 
                 17 
               
               
                 Mix-2 
                 8 
                 0 
                 8 
                 0 
                 8 
                 9 
                 10 
                 6 
                 6 
                 0 
                 0 
                 14 
               
               
                 Mix-3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 I1 
                 I2 
                 I3 
                 I4 
                 I5 
                 I6 
                 I7 
                 I8 
                 I9 
                 I10 
                 I11 
                 I12 
               
               
                   
               
            
           
         
       
     
     According to some embodiments, the cells shown in Tables 6 and 7 appear without background fill where the match to the individual is sufficient for a high probability identification (e.g., sufficient for conviction). The improvement over Table 4 is readily apparent based on increase in the number of sufficient to identify cells. Further improvements are shown between Tables 6 and 7 in the reduction in the numbers of unmatched called alleles. Shown in Table 8, direct sequencing analysis (with three weakest loci removed) according to one embodiment provides the best alignment of called alleles with sequences in the DNA mixtures. 
     To establish relevance of various embodiments, standard mixture statistics are calculated. These statistics include the probability that a random man would not be excluded (PRMNE) from being identified as present in the mixture, and the likelihood ratio (LR) that the evidence supports a guilty verdict as opposed to an innocent one. Table 9 below shows the PRMNE and LR for Mix- 1 , Mix- 2 , and Mix- 3 . 
                     TABLE 9                  Forensic Statistics                         Mix   PRMNE   LR                                 Mix-1   3.087 × 10 −6     323,932       Mix-2    1.78 × 10 −3     562.17       Mix-3   3.854 × 10 −2     25.95                    
Generating DNA Concentration Estimates for Individuals in Mixtures
 
     According to another aspect, various analysis systems can be configured to leverage the amplification strength profiles of STFR alleles (see  FIG.  6   ) to estimate the relative concentration of DNA contributions by individuals in a mixture. Given a mixture sample, the distributions of loci and alleles that appear in the sample can be generated. The identified loci and STR alleles can be compared to amplification strength profiles to estimate a relative concentration for a number of individuals in a mixture. Generally, for alleles that are unique to specific contributors—the number of reads on those unique alleles can be used to indicate a concentration of that contributor. More specifically, the replication strength profile for all or a group of the alleles can be used to determine expected numbers of reads for each allele in a sample, and the expected number of reads can be extrapolated into an expected number of reads for two contributors, three contributors, four contributors, to upwards of 30 contributors modeled over various concentrations. 
     Each set of loci/allele combinations can be modeled such that for multiple contributor sample read distributions can be matched to an estimated concentration for each contributor. Other properties of the amplification strength allow for the strength profile to be modeled and then applied in a comparison to an unknown sample. For example, for loci and alleles in common between a number of contributors these reads tend to aggregate (although in some examples they may show a smaller normalized number of reads than a single contributor sample), but the reads on alleles that are not found in common generate a unique signature for that sample that reflects relative concentration of the contributors. If a single individual provides the alleles (not in common to all the contributors) the strength profile provides an estimate of the number of reads that should be detected. Where the number is lower than that estimate—multiple contributors are indicated and relative concentrations can be determined. Each variation in the expected number of reads can be evaluated together to derive an estimate of relative concentration. 
     In further embodiments, called alleles not matched to individuals can also be leveraged to estimate the amount of DNA from unknown contributors. For example, an analysis system (e.g.,  100 ) and/or a an analysis component (e.g.,  104 E) can be configured to analyze a normalized ratio of the observed STR allele counts across STR loci to generate a relative estimate of original DNA concentrations, including estimation of an unknown portion of a sample. Shown in  FIG.  8    are mixture composition estimated across twelve known individuals and an unknown. The system and/or analysis component estimates that Mix- 1  is made up of three contributors having relative concentrations shown by the y-axis of  FIG.  8   . Shown in  FIG.  8   , the estimate for the original DNA concentration for individual  18  is actually higher than expected ( FIG.  9   —reflecting actual mixture elements). Observation of the differences between  FIGS.  8  and  9    includes a reproducible increase that is observed for individual I 8  in both Mix- 1  and Mix- 3 . Thus refinement of the model can be used to eliminate the overestimate. 
     Generate Prediction of Number of Contributors 
     According to another aspect, an analysis system can be configured to calculate a predictive value for a number of contributors in a DNA sample. In one embodiment, the analysis system (e.g.,  100 ) and/or an analysis component (e.g.,  104 E) is configured to leverage profiles of individuals to estimate a number of contributors appearing in a sample. For example, profiles of different STR loci reflect the different complexities of alleles represented for respective individuals and, for example, include significant allele sharing at some loci (e.g., TPDX—shown in  FIG.  10   ). According to one embodiment, multiple in silico mixtures were created for mixtures of 2, 3, 4, 5, and so on up to 20 individuals. The various combination of the read values for different STR loci and different complexities of alleles are illustrated in part in  FIG.  10   . The different combinations of individuals and respective plots for number of alleles by locus that result are used to train a machine learning algorithm and build a tool (e.g., comparison model) for predicting the number of individuals in a mixture using the STR data obtained from analysis any mixture. The model creates a statistical separation based on features characterizing the number of unique alleles present across loci. These features are incorporated into a statistical model that separates unseen data based on these features. In one embodiment, a model is used to reflect the relationship between average number of STR alleles detected by locus (e.g., via a profile of STR Alleles detected by locus over set of loci) and the number of individuals appearing in the modeled data. The model can then be used by the system to evaluate unknown samples having unknown numbers of contributors to predict a number of individuals within the sample. 
     Tables 10A-B illustrates (for a known group of 20 individuals) predictions of a number of contributors for in silico generated mixtures of individual profiles (i.e., known individual STR allele profiles). 
     
       
         
           
               
             
               
                 TABLE 10A 
               
             
            
               
                   
               
               
                 Predictions of individuals in STR mixtures 
               
            
           
           
               
               
            
               
                   
                 Predicted number of individuals 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Truth 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 
                   100.0% 
                 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 2 
                   
                 
                   100.0% 
                 
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 3 
                   
                   
                 
                   99.5% 
                 
                 
                    0.5% 
                 
                   
                   
                   
                   
                   
                   
                   
               
               
                 4 
                   
                   
                 
                    0.2% 
                 
                 
                   97.2% 
                 
                 
                    2.5% 
                 
                   
                   
                   
                   
                   
                   
               
               
                 5 
                   
                   
                   
                 
                    1.6% 
                 
                 
                   96.7% 
                 
                 
                    1.8% 
                 
                   
                   
                   
                   
                   
               
               
                 6 
                   
                   
                   
                   
                 
                    2.2% 
                 
                 
                   92.6% 
                 
                 
                    5.2% 
                 
                   
                   
                   
                   
               
               
                 7 
                   
                   
                   
                   
                   
                 
                    6.2% 
                 
                 
                   90.0% 
                 
                 
                    3.7% 
                 
                   
                   
                   
               
               
                 8 
                   
                   
                   
                   
                   
                   
                 
                    2.6% 
                 
                 
                   94.5% 
                 
                 
                    2.8% 
                 
                  0.0% 
                   
               
               
                 9 
                   
                   
                   
                   
                   
                   
                   
                 
                    3.8% 
                 
                 
                   88.9% 
                 
                 
                    7.3% 
                 
                  0.1% 
               
               
                 10 
                   
                   
                   
                   
                   
                   
                   
                   
                 
                    5.9% 
                 
                 
                   84.1% 
                 
                 
                   10.0% 
                 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 10B 
               
             
            
               
                   
               
               
                 Continued Predictions of individuals in STR mixtures 
               
            
           
           
               
               
            
               
                   
                 Predicted number of individuals 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Truth 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
               
               
                   
               
               
                 11 
                 
                   9.4% 
                 
                 
                   80.6% 
                 
                 
                   10.0% 
                 
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 12 
                 0.0% 
                 
                    9.4% 
                 
                 
                   80.0% 
                 
                 
                   10.6% 
                 
                   
                   
                   
                   
                   
                   
                   
               
               
                 13 
                   
                  0.0% 
                 
                   10.2% 
                 
                 
                   78.8% 
                 
                 
                   11.0% 
                 
                  0.0% 
                   
                   
                   
                   
                   
               
               
                 14 
                   
                   
                  0.0% 
                 
                    9.5% 
                 
                 
                   81.7% 
                 
                 
                    8.8% 
                 
                   
                   
                   
                   
                   
               
               
                 15 
                   
                   
                   
                  0.0% 
                 
                    9.9% 
                 
                 
                   79.6% 
                 
                 
                   10.2% 
                 
                  0.3% 
                   
                   
                   
               
               
                 16 
                   
                   
                   
                   
                  0.1% 
                 
                   10.9% 
                 
                 
                   79.1% 
                 
                 
                    9.9% 
                 
                   
                   
                   
               
               
                 17 
                   
                   
                   
                   
                   
                  0.3% 
                 
                   10.8% 
                 
                 
                   76.7% 
                 
                 
                   11.8% 
                 
                  0.4% 
                   
               
               
                 18 
                   
                   
                   
                   
                   
                   
                  0.1% 
                 
                   15.1% 
                 
                 
                   69.3% 
                 
                 
                   15.3% 
                 
                  0.1% 
               
               
                 19 
                   
                   
                   
                   
                   
                   
                   
                  0.9% 
                 
                   14.7% 
                 
                 
                   68.0% 
                 
                 
                   16.0% 
                 
               
               
                 20 
                   
                   
                   
                   
                   
                   
                   
                   
                  0.3% 
                 
                   17.9% 
                 
                 
                   62.7% 
                 
               
               
                   
               
            
           
         
       
     
     According to one embodiment, an analysis system is configured to apply the STR based prediction model to samples. Example data was captured from executing the prediction model on the mixture samples described above in  FIG.  9   . Table 11 illustrates the performance of the model. For example, Table 11 shows the results of contributor predictions based on a comparison of the model applied to allele profiles generated under conventional analysis approaches (e.g., ForenSeq) and when applied to called STR alleles by embodiments discussed herein (e.g., New Alleles). As shown in Table 11, algorithm performance is significantly more accurate when based on allele profiles generated with embodiments discussed herein, rather than under conventional approaches. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 11 
               
               
                   
               
               
                   
                 ForenSeq 
                 New 
                   
               
               
                 Mixture 
                 Alleles 
                 Alleles 
                 Truth 
               
               
                   
               
             
            
               
                 Mix-1 
                 2 
                  3 
                  3 
               
               
                 Mix-2 
                 4 
                  4 
                  4 
               
               
                 Mix-3 
                 6 
                 11 
                 12 
               
               
                   
               
            
           
         
       
     
     Further embodiments extend prediction modeling (prediction of number of contributors) into additional information based on SNP sequencing. According to various embodiments, analysis systems (e.g.,  100 ) and/or analysis components (e.g.,  104 E) are configured to leverage profiles of individuals with sequenced SNPs to estimate a number of contributors in a sample based on SNP analysis. For example, multiple in silico mixtures were created for mixtures of 2, 3, 4, 5, 7, 8, 9 and 10 individuals. Sequencing of the SNPs in the sample was executed and the pattern of shared minor alleles was represented in a reduced dimensional space. Principal component analysis (PCA) was used to map the data along the dimensions of greatest variance. In place of using all dimensions, the number of dimensions was set such that the selected number of dimensions explains a predefined percentage of the variance in the data. The pattern was used to train a machine learning algorithm representative of the pattern. Various embodiments, implement the machine learning algorithm as an executable tool that predicts the number of individuals in a mixture responsive to analyzing sequenced SNPs of the sample. According to some embodiments, as there is less variance in individual SNPs, a larger number of sequenced loci are required to obtain similar performance (confidence values) to STR analysis discussed above. Table 12 illustrates the percent confidences in the predicted determination generated by embodiments executing the SNP based prediction tool based on sequencing 1500 SNPs within the mixture. 
                         TABLE 12                      Predicted number of individuals                                                     Truth   2   3   4   5   6   7   8   9   10                                                             2   97.6%    2.4%    0.0%    1.0%    0.0%    0.0%    0.0%    0.0%    0.0%       3    0.9%   97.3%    1.7%    0.0%    0.0%    0.0%    0.0%    0.0%    0.0%       4    0.0%    1.0%   98.2%    0.0%    0.0%    0.0%    0.0%    0.0%    0.0%       5    0.0%    0.0%    2.1%   97.1%    0.8%    0.0%    0.0%    0.0%    0.0%       6    0.0%    0.0%    0.0%    3.9%   93.7%    2.4%    0.0%    0.0%    0.0%       7    0.0%    0.0%    0.0%    0.0%    7.4%   88.5%    4.0%    0.0%    0.0%       8    0.0%    0.0%    0.0%    0.0%    0.2%    9.7%   83.7%    6.4%    0.0%       9    0.0%    0.0%    0.0%    0.0%    0.0%    0.2%   11.8%   77.7%   10.3%       10    0.0%    0.0%    0.0%    0.0%    0.0%    0.0%    0.4%   13.9%   85.7%                    
Further embodiments combine the underlying models of the SNP based prediction tool modeling and the STR based prediction tool to achieve greater accuracy and in some examples to reduce the number of SNPs required to achieve similar confidence levels.
 
Example Computer Systems
 
     Various aspects and functions described herein may be implemented as specialized hardware or software components executing in one or more specialized computer systems. There are many examples of computer systems that are currently in use that could be specially programmed or specially configured. These examples include, among others, network appliances, personal computers, workstations, mainframes, networked clients, servers, media servers, application servers, database servers, and web servers. Other examples of computer systems may include mobile computing devices (e.g., smart phones, tablet computers, and personal digital assistants) and network equipment (e.g., load balancers, routers, and switches). Examples of particular models of mobile computing devices include iPhones, iPads, and iPod Touches running iOS operating systems available from Apple, Android devices like Samsung Galaxy Series, LG Nexus, and Motorola Droid X, Blackberry devices available from Blackberry Limited, and Windows Phone devices. Further, aspects may be located on a single computer system or may be distributed among a plurality of computer systems connected to one or more communications networks. 
     For example, various aspects, functions, and processes including read error correction, dominant allele error sequencing and profiling, building and evaluating per locus error profiles, concentration estimation based on amplification strength profiling and evaluation, number of contributor predictions based on amplification strength evaluation, etc., may be distributed among one or more computer systems configured to provide a service to one or more client computers, or to perform an overall task as part of a distributed system, such as the distributed computer system  1100  shown in  FIG.  11   . Additionally, aspects may be performed on a client-server or multi-tier system that includes components distributed among one or more server systems that perform various functions. Consequently, embodiments are not limited to executing on any particular system or group of systems. Further, aspects, functions, and processes may be implemented in software, hardware or firmware, or any combination thereof. Thus, aspects, functions, and processes may be implemented within methods, acts, systems, system elements and components using a variety of hardware and software configurations, and examples are not limited to any particular distributed architecture, network, or communication protocol. 
     Referring to  FIG.  11   , there is illustrated a block diagram of a distributed computer system  1100 , in which various aspects and functions are practiced. As shown, the distributed computer system  1100  includes one or more computer systems that exchange information. More specifically, the distributed computer system  1100  includes computer systems  1102 ,  1104 , and  1106 . As shown, the computer systems  1102 ,  1104 , and  1106  are interconnected by, and may exchange data through, a communication network  1108 . The network  1108  may include any communication network through which computer systems may exchange data. To exchange data using the network  1108 , the computer systems  1102 ,  1104 , and  1106  and the network  1108  may use various methods, protocols and standards, including, among others, Fiber Channel, Token Ring, Ethernet, Wireless Ethernet, Bluetooth, IP, IPV6, TCP/IP, UDP, DTN, HTTP, FTP, SNMP, SMS, MMS, SS7, JSON, SOAP, CORBA, REST, and Web Services. To ensure data transfer is secure, the computer systems  1102 ,  1104 , and  1106  may transmit data via the network  1108  using a variety of security measures including, for example, SSL or VPN technologies. While the distributed computer system  1100  illustrates three networked computer systems, the distributed computer system  1100  is not so limited and may include any number of computer systems and computing devices, networked using any medium and communication protocol. 
     As illustrated in  FIG.  11   , the computer system  1102  includes a processor  1110 , a memory  1112 , an interconnection element  1114 , an interface  1116  and data storage element  1118 . To implement at least some of the aspects, functions, and processes disclosed herein, the processor  1110  performs a series of instructions that result in manipulated data. The processor  1110  may be any type of processor, multiprocessor or controller. Example processors may include a commercially available processor such as an Intel Xeon, Itanium, Core, Celeron, or Pentium processor; an AMD Opteron processor; an Apple A4 or A5 processor; a Sun UltraSPARC processor; an IBM Power5+ processor; an IBM mainframe chip; or a quantum computer. The processor  1110  is connected to other system components, including one or more memory devices  1112 , by the interconnection element  1114 . 
     The memory  1112  stores programs (e.g., sequences of instructions coded to be executable by the processor  1110 ) and data during operation of the computer system  1102 . Thus, the memory  1112  may be a relatively high performance, volatile, random access memory such as a dynamic random access memory (“DRAM”) or static memory (“SRAM”). However, the memory  1112  may include any device for storing data, such as a disk drive or other nonvolatile storage device. Various examples may organize the memory  1112  into particularized and, in some cases, unique structures to perform the functions disclosed herein. These data structures may be sized and organized to store values for particular data and types of data. 
     Components of the computer system  1102  are coupled by an interconnection element such as the interconnection element  1114 . The interconnection element  1114  may include any communication coupling between system components such as one or more physical busses in conformance with specialized or standard computing bus technologies such as IDE, SCSI, PCI and InfiniBand. The interconnection element  1114  enables communications, including instructions and data, to be exchanged between system components of the computer system  1102 . 
     The computer system  1102  also includes one or more interface devices  1116  such as input devices, output devices and combination input/output devices. Interface devices may receive input or provide output. More particularly, output devices may render information for external presentation. Input devices may accept information from external sources. Examples of interface devices include keyboards, mouse devices, trackballs, microphones, touch screens, printing devices, display screens, speakers, network interface cards, etc. Interface devices allow the computer system  1102  to exchange information and to communicate with external entities, such as users and other systems. 
     The data storage element  1118  includes a computer readable and writeable nonvolatile, or non-transitory, data storage medium in which instructions are stored that define a program or other object that is executed by the processor  1110 . The data storage element  1118  also may include information that is recorded, on or in, the medium, and that is processed by the processor  1110  during execution of the program. More specifically, the information may be stored in one or more data structures specifically configured to conserve storage space or increase data exchange performance. The instructions may be persistently stored as encoded signals, and the instructions may cause the processor  1110  to perform any of the functions described herein. The medium may, for example, be optical disk, magnetic disk or flash memory, among others. In operation, the processor  1110  or some other controller causes data to be read from the nonvolatile recording medium into another memory, such as the memory  1112 , that allows for faster access to the information by the processor  1110  than does the storage medium included in the data storage element  1118 . The memory may be located in the data storage element  1118  or in the memory  1112 , however, the processor  1110  manipulates the data within the memory, and then copies the data to the storage medium associated with the data storage element  1118  after processing is completed. A variety of components may manage data movement between the storage medium and other memory elements and examples are not limited to particular data management components. Further, examples are not limited to a particular memory system or data storage system. 
     Although the computer system  1102  is shown by way of example as one type of computer system which may be specially configured and upon which various aspects and functions may be practiced, aspects and functions are not limited to being implemented on the computer system  1102  as shown in  FIG.  11   . Various aspects and functions may be practiced on one or more specially configured computers and having a different architectures or components than that shown in  FIG.  11   . For instance, the computer system  1102  may include specially programmed, special-purpose hardware, such as an application-specific integrated circuit (“ASIC”) tailored to perform a particular operation disclosed herein. While another example may perform the same function using a grid of several general-purpose computing devices running MAC OS System X with Motorola PowerPC processors and several specialized computing devices running proprietary hardware and operating systems. 
     The computer system  1102  may be a computer system including an operating system that manages at least a portion of the hardware elements included in the computer system  1102 . In some examples, a processor or controller, such as the processor  1110 , executes an operating system. Examples of a particular operating system that may be executed include a Windows-based operating system, such as, Windows NT, Windows 2000 (Windows ME), Windows XP, Windows Vista or Windows 7, 8, or 10 operating systems, available from the Microsoft Corporation, a MAC OS System X operating system or an iOS operating system available from Apple Computer, one of many Linux-based operating system distributions, for example, the Enterprise Linux operating system available from Red Hat Inc., a Solaris operating system available from Oracle Corporation. or a UNIX operating systems available from various sources. Many other operating systems may be used, and examples are not limited to any particular operating system. 
     The processor  1110  and operating system together define a computer platform for which application programs in high-level programming languages are written. These component applications may be executable, intermediate, bytecode or interpreted code which communicates over a communication network, for example, the Internet, using a communication protocol, for example, TCP/IP. Similarly, aspects may be implemented using an object-oriented programming language, such as .Net, SmallTalk, Java, C++, Ada, C# (C-Sharp), Python, or JavaScript. Other object-oriented programming languages may also be used. Alternatively, functional, scripting, or logical programming languages may be used. 
     Additionally, various aspects and functions may be implemented in a non-programmed environment. For example, documents created in HTML, XML or other formats, when viewed in a window of a browser program, can render aspects of a graphical-user interface or perform other functions. Further, various examples may be implemented as programmed or non-programmed elements, or any combination thereof. For example, a web page may be implemented using HTML while a data object called from within the web page may be written in C++. Thus, the examples are not limited to a specific programming language and any suitable programming language could be used. Accordingly, the functional components disclosed herein may include a wide variety of elements (e.g., specialized hardware, executable code, data structures or objects) that are configured to perform the functions described herein. 
     In some examples, the components disclosed herein may read parameters that affect the functions performed by the components. These parameters may be physically stored in any form of suitable memory including volatile memory (such as RAM) or nonvolatile memory (such as a magnetic hard drive). In addition, the parameters may be logically stored in a propriety data structure (such as a database or file defined by a user space application) or in a commonly shared data structure (such as an application registry that is defined by an operating system). In addition, some examples provide for both system and user interfaces that allow external entities to modify the parameters and thereby configure the behavior of the components. 
     Improved Computer Systems and Algorithms 
     In the United States of America, the Federal Bureau of Investigation has a database of over 15 million DNA samples in the National DNA Index System (NDIS). Conventional forensic techniques involve comparing STR profiles between samples and individuals whose samples are in the NDIS. The inventor has appreciated that samples with more than one contributor are difficult or impossible to analyze using only STR profiles. The inventor has further appreciated that conventional protocols for searching the NDIS are time consuming, expensive, and often require manual evaluation of the results. Accordingly, the inventor has developed techniques to address these shortcomings of conventional forensic identification techniques. For example, the techniques described herein may be scaled to enable comparisons of large numbers of samples (hundreds of thousands to millions) against databases of tens of millions of samples with performance improvements on the order of 100 to 1000 times faster than traditional approaches. 
     In some embodiments, techniques described herein provide faster implementations for database comparisons in nucleic acid analysis by encoding one or more features of a nucleic acid sequence using a lossy encoding developed by the inventor, which retains information that may be used to identify one or more individuals while eliminating extraneous information. Encoding a nucleic acid sequence using such a lossy encoding facilitates rapid comparison of the encoded sequence with DNA samples in the NDIS or similar database. As a result, the techniques described herein may be used to rapidly compare multiple samples (each of which may include genetic information from multiple contributors) to information stored in the NDIS database. 
     In some embodiments, techniques described herein provide for faster implementations due to the reduction of nucleic acid sequence information to a binary encoding. The binary encoding can be rapidly compared to a database of previously generated binary encodings using native bitwise instructions (e.g., XOR, AND, NAND, NOT, OR, population count instruction, etc.) For example, in some aspects, these techniques can be used in single nucleotide polymorphism (SNP, pronounced “snip”) analysis. In some embodiments, by implementing the coding scheme set forth in Table 13 below, any occurrence of a minor allele in a nucleic acid sequence may be encoded as a “1” bit. 
     
       
         
           
               
             
               
                 TABLE 13 
               
             
            
               
                   
               
               
                 Binary Encoding of SNP Alleles 
               
            
           
           
               
               
            
               
                 Alleles 
                 Binary Encoding 
               
               
                   
               
               
                 MM 
                 0 
               
               
                 Mm 
                 1 
               
               
                 mM 
                 1 
               
               
                 mm 
                 1 
               
               
                   
               
            
           
         
       
     
     In some embodiments, techniques described herein may be used to compare an individual sample to another individual sample. For example, in some embodiments, a first individual sample may contain nucleic acid sequence information for a first individual who is homozygous for a minor allele at a specific genetic locus, indicating the presence of a SNP. As described in the above, a homozygous minor allele (“mm”) may be encoded as a “1” bit. In some embodiments, the encoding of the SNP of the first individual may be compared to one or more encodings of individual samples. In some embodiments, a comparison of the first individual encoding to another individual encoding is executed using an “XOR” instruction. 
     In some embodiments, the comparison using the XOR instruction results in an indication of whether the two individual samples differ in the occurrence of the SNP. For example, in some embodiments, the XOR between the first individual (“1”) and an individual who has a SNP at the same specific genetic locus (“1”) would produce a “0” bit. In some embodiments, the XOR between the first individual (“1”) and an individual who does not have a SNP at the same specific genetic locus (“0”) would produce a “1” bit. In some embodiments, a population count instruction may be used to tally the “1” bits resulting from the XOR instruction. Thus, in some embodiments, a greater value resulting from the population count instruction may provide a greater confidence that the individuals being compared are different. 
     In some embodiments, techniques described herein may be used to compare an individual sample to a mixture of samples. In some embodiments, the comparison of the individual to the mixture is performed using an XOR instruction as described above. In some embodiments, the result of the XOR instruction is “anded” to the individual sample using an “AND” instruction. In some embodiments, the AND instruction results in an indication of whether the mixture does not have the same SNP as the individual. For example, in some embodiments, an XOR result of “1” indicates that the individual and the mixture differ with respect to the presence of a SNP. However, in some embodiments, the individual might not have a SNP while the mixture does have a SNP. In such embodiments, the occurrence of the SNP in the mixture could be the result of a contributor other than the individual. Thus. in some embodiments, the AND instruction allows for an indication of when the individual has a SNP and the mixture does not. In some embodiments, a population count instruction can be used to tally the “1” bits resulting from the AND instruction. 
     In some embodiments, techniques described herein provide advantages over STR analysis in the profiling of a nucleic acid sample by implementing SNP analysis. Such a SNP analysis may be useful for comparisons of sequence information obtained from a nucleic acid sample having more than one contributor against a database of samples. 
     Some embodiments are directed to a method comprising using at least one computer hardware processor to perform: receiving sequence information obtained from a nucleic acid sample, wherein the sequence information comprises a plurality of genetic loci, the plurality of genetic loci including a first genetic locus; generating, based on the received sequence information, an encoding for the nucleic acid sample at least in part by encoding the first genetic locus using a first value when the first genetic locus is homozygous for a major allele and using a second value different from the first value when the first genetic locus is not homozygous for the major allele; comparing the generated encoding of the nucleic acid sample with a plurality of previously-generated encodings for a respective plurality of nucleic acid samples; and when it is determined that, as a result of the comparing, the generated encoding of the nucleic acid sample matches at least one encoding in the plurality of previously-generated encodings, the at least one encoding being associated with at least one person, providing an indication that the nucleic acid sample is consistent with the at least one person. In some embodiments, the comparing is performed using bitwise instructions native to the at least one computer hardware processor executing the method. 
     In some embodiments, generating the encoding comprises generating a lossy encoding. In some embodiments, the lossy encoding retains information related to one or more features of a nucleic acid sequence that may be useful for identifying an individual. For example, in some embodiments, the lossy encoding encodes information related to a SNP. A SNP is a single-nucleotide substitution of one base (e.g., cytosine, thymine, uracil, adenine, or guanine) for another at a specific position, or locus, in a genome, where the substitution is present in a population to an appreciable extent (e.g., more than 1% of the population). 
     In some embodiments, the presence or absence of a SNP in a nucleic acid sequence may by itself be used to identify an individual. Thus, in some embodiments, the lossy encoding may encode a sequence by encoding only information indicative of the presence or absence of a SNP in a nucleic acid sequence. In some embodiments, the lossy encoding loses information related to specific nucleotide composition. In some embodiments, the loss of information related to specific nucleotide composition allows the encodings to be implemented in methods described herein at speeds greater than the corresponding nucleic acid sequence information (e.g., greater than the raw data). 
     In some embodiments, generating the encoding comprises generating a binary encoding. In some embodiments, the first value is a binary value. In some embodiments, the first value consists of a first bit and the second value consists of a second bit different from the first bit. In some embodiments, the first bit is zero. In some embodiments, the first bit is zero and the second bit is one. In some embodiments, only two different values may be used for generating an encoding, for example, if the encoding is intended only to retain information related to the presence or absence of a particular feature. 
     For example, when encoding nucleic acid sequence information based on the presence or absence of a SNP, the absence of a SNP may be encoded by using a first value (e.g., 0) when a locus is homozygous for a major allele. Alternatively, the presence of a SNP may be encoded by using a second value (e.g., 1) when the locus is not homozygous for a major allele (e.g., the locus is homozygous for a minor allele or the locus is heterozygous). 
     A variant of the similar nucleic acid sequence located at a given locus is called an allele. As with most multicellular organisms, humans have two sets of chromosomes. These chromosomes are referred to as homologous chromosomes, having the same genes in the same loci. If both alleles at a locus on the homologous chromosomes are the same, they and the organism are homozygous with respect to that gene or location. If the alleles are different, they and the organism are heterozygous with respect to that gene or location. 
     In a given population, the allele occurring with the greatest frequency at a given locus is referred to as the major allele. Alternative variants at this same locus are referred to as minor alleles. If a major allele is present at a specific locus in both homologous chromosomes, the locus is said to be homozygous for a major allele. If a minor allele is present at a specific locus in both homologous chromosomes, the locus is said to be homozygous for a minor allele. If a pair of homologous chromosomes contains a major allele at a specific locus in one chromosome and a minor allele at the corresponding locus in the other chromosome, the locus is said to be heterozygous. 
     In some embodiments, the received sequence information obtained from the nucleic acid sample comprises sequence information for only one person (e.g., one contributor). In some embodiments, the received sequence information obtained from the nucleic acid sample comprises sequence information for more than one person (e.g., more than one contributor). In some embodiments, when the generated encoding of the nucleic acid sample matches two different encodings in the plurality of previously-generated encodings, the two different encodings being associated with two different people, the method further comprises providing an indication that the nucleic acid sample is consistent with the two different people. 
     In some embodiments, generating the encoding comprises using the second value when the first genetic locus is homozygous for a minor allele or the first genetic locus is heterozygous. In some embodiments, the presence of the second value in the generated encoding indicates the presence of a SNP at the first genetic locus. In some embodiments, the use of binary bits to identify SNPs is advantageous because it simplifies and condenses the sequence information into an encoding capable of much faster implementations. In some embodiments, the use of binary bits to encode SNPs is advantageous because it allows for the binning of SNP indicators (e.g., the locus is homozygous for a minor allele or the locus is heterozygous) and non-SNP indicators (e.g., the locus is homozygous for a major allele). 
     In some embodiments, in methods described herein, the generating further comprises encoding each of the plurality of genetic loci using the first value or the second value. In some embodiments, a plurality of genetic loci are pre-selected for encoding. In some embodiments, the plurality of genetic loci are pre-selected based on known population genetics. Population genetics, in some embodiments, may provide information related to the distribution and change in the frequency of alleles within populations. 
     In some embodiments, systems described herein may be used to execute methods described herein. In some embodiments, the system comprises: at least one database storing a plurality of encodings for a respective plurality of nucleic acid samples; at least one computer hardware processor; at least one non-transitory computer-readable storage medium storing processor-executable instructions that, when executed by the at least one computer hardware processor, cause the at least one computer hardware processor to perform: receiving sequence information obtained from a nucleic acid sample, wherein the sequence information comprises a plurality of genetic loci, the plurality of genetic loci including a first genetic locus; generating, based on the received sequence information, an encoding for the nucleic acid sample at least in part by encoding the first genetic locus using a first value when the first genetic locus is homozygous for a major allele and using a second value different from the first value when the first genetic locus is not homozygous for the major allele; comparing the generated encoding of the nucleic acid sample with the plurality of encodings stored in the at least one database; and when it is determined that, as a result of the comparing, the generated encoding of the nucleic acid sample matches at least one encoding in the plurality of encodings stored in the at least one database, the at least one encoding being associated with at least one person, providing an indication that the nucleic acid sample is consistent with the at least one person. 
     In some embodiments, the at least one computer hardware processor is configured to perform a plurality of native bitwise instructions. In some embodiments, native bitwise instructions include a population count bitwise instruction, an “XOR” bitwise instruction, and an “AND” bitwise instruction. Additionally or alternatively, native bitwise instructions include a bitwise OR instruction, a bitwise NAND instruction, a bitwise NOT instruction, an arithmetic shift instruction, a logical shift instruction, a circular shift instruction. and/or any other suitable bitwise instructions that the at least one computer hardware processor is configured to execute, as aspects of the technology described herein are not limited in this respect. 
     Some embodiments are directed to a method comprising using at least one computer hardware processor to perform: receiving sequence information obtained from a nucleic acid sample, wherein the sequence information comprises at least one short tandem repeat (STR) locus, the at least one STR locus comprising a unit of nucleotides repeated a number of times; generating, based on the received sequence information, an encoding for the nucleic acid sample at least in part by encoding the at least one STR locus using a value that corresponds to the number of times the unit of nucleotides is repeated; comparing the generated encoding of the nucleic acid sample with a plurality of previously-generated encodings for a respective plurality of nucleic acid samples; and when it is determined that, as a result of the comparing, the generated encoding of the nucleic acid sample matches at least one encoding in the plurality of previously-generated encodings, the at least one encoding being associated with at least one person, providing an indication that the nucleic acid sample is consistent with the at least one person. In some embodiments, the comparing is performed using bitwise instructions native to the at least one computer hardware processor executing the method. 
     In some embodiments, generating the encoding comprises generating a lossy encoding. In some embodiments, the lossy encoding retains information related to one or more features of a nucleic acid sequence that may be useful for identifying an individual. In some embodiments, the lossy encoding encodes information related to an STR. An STR is a tract of repetitive sequence in which a unit of nucleotides (e.g., ranging in length from 2-13 base pairs) is repeated, anywhere from a few times to hundreds of times in a row. The number of times the unit of nucleotides is repeated in a particular STR can vary from one individual to another. Thus, in some embodiments, the number of times the unit of nucleotides is repeated in a particular STR may be used to identify an individual. 
     In some embodiments, the lossy encoding may encode a sequence by encoding only information indicative of the number of times the unit of nucleotides is repeated in a particular STR. Thus, in some embodiments, the lossy encoding may be indicative of the number of repeating units in the particular STR and/or the identity of the particular STR variant, but the lossy encoding cannot by itself be used to identify nucleotide composition of the particular STR. In some embodiments, the loss of information related to specific nucleotide composition allows the encodings to be implemented in methods described herein at speeds greater than the corresponding nucleic acid sequence information. 
     In some embodiments, more than two different values may be used when generating an encoding, for example, if the encoding is intended to retain information related to more than one feature of a nucleic acid sequence. For example, in some embodiments, it may be desirable to encode information related to more than one STR locus. As any given STR locus may be one of a limited number of variants, encoding more than one STR locus may increase the uniqueness of the encoding. Thus, in some embodiments, the certainty with which one or more individuals may be identified from a nucleic acid sample scales with the number of values used to encode the nucleic acid sequence information obtained from the nucleic acid sample. 
     In a binary encoding, the number of bits used to encode a particular feature may depend on the number of possible values for the particular feature. In the foregoing example illustrating generating an encoding that encodes for the presence or absence of a SNP, a single bit (e.g., 1 or 0) may be used since the number of possible outcomes is limited to two values (“presence” or “absence”). In some embodiments, a single bit (e.g., 1 or 0) may be used to encode for the presence or absence of a particular variant at an STR locus. In some embodiments, it may be advantageous to use multiple bits for encoding an STR locus, as a given STR locus typically comprises multiple variants. 
     The number of values encoded by a given number of bits follows the formula: 2n, where n is the number of bits. For example, a one bit encoding (21=2) may be used to encode either of two values (e.g., 1 or 0). As such, a two bit encoding (22=4) may be used to encode any one of four values (e.g., 00, 01, 10, or 11), a three bit encoding may be used to encode any one of eight values (23=8), a four bit encoding may be used to encode any one of sixteen values (24=16), a five bit encoding may be used to encode any one of 32 values (25=32), etc. Thus, the maximum number of STR locus variants that may be assigned unique values using a binary encoding of length n is less than or equal to 2n. In other words, a binary encoding of length n may be used to encode, uniquely, up to 2n values. 
     In some embodiments, the value may correspond to the absolute number of times the unit of nucleotides is repeated in the STR locus. The absolute number of repeats may greatly vary across STR loci. For example, some STR loci may consist of a unit of nucleotides repeated only a few times while other STR loci may consist of a unit of nucleotides repeated hundreds of times. Thus, when it is desirable to generate an encoding using a value that directly corresponds to the absolute number of repeats in the locus, this variation in repeat number may be taken into consideration when selecting the number of bits to be used. In some embodiments, the value may consist of 1 bit, between 1-3 bits, between 2-4 bits, between 3-5 hits, between 4-6 bits, between 5-7 bits, between 6-8 bits, between 7-9 bits, between 8-10 bits, 10 bits, or more than 10 bits. In some embodiments, the value may consist of 5 bits. 
     Although the absolute number of repeats may greatly vary across STR loci to include relatively large numbers, the actual number of variants at any given locus may be small by comparison. Typically, each STR allele can be shared by 5-20% of individuals. Thus, in some embodiments, it may be advantageous to encode an STR locus using a value that directly corresponds to an identifier for a particular variant at the locus. As the number of possible values is minimized in this approach, the encoding may provide for faster implementations. In some embodiments, the value may be one of between 2-30 possible values (e.g., one of 2 possible values, one of between 2-12 possible values, one of between 10-20 possible values, one of between 20-30 possible values, or one of 30 possible values). In some embodiments, the value is one of between 5-25 possible values (e.g., one of 5 possible values, one of between 5-15 possible values, one of between 10-20 possible values, one of between 15-20 possible values, or one of 25 possible values). In some embodiments, the value is one of around 20 possible values (e.g., one of 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, or 25 possible values). 
     In some embodiments, an STR encoding may be generated based on the common known STR alleles for a given STR locus. In some embodiments, a “1” bit may be used in the STR encoding that is unique to a particular allele at an STR locus. For example, the STR locus TPDX may comprise a number of repeating [AATG] units which may vary from individual to individual. Table 14 below lists examples of different TPDX alleles, along with 16-bit encodings that could be used to represent each allele. 
     
       
         
           
               
             
               
                 TABLE 14 
               
             
            
               
                   
               
               
                 Examples of TPOX alleles and corresponding encodings 
               
            
           
           
               
               
               
            
               
                 Allele 
                 Number of repeats 
                 Encoding 
               
               
                   
               
               
                 [AATG] 6   
                  6 
                 0000000000000001 
               
               
                 [AATG] 7   
                  7 
                 0000000000000010 
               
               
                 [AATG] 8   
                  8 
                 0000000000000100 
               
               
                 [AATG] 9   
                  9 
                 0000000000001000 
               
               
                 [AATG] 10   
                 10 
                 0000000000010000 
               
               
                 [AATG] 11   
                 11 
                 0000000000100000 
               
               
                 [AATG] 12   
                 12 
                 0000000001000000 
               
               
                 [AATG] 13   
                 13 
                 0000000010000000 
               
               
                 [AATG] 14   
                 14 
                 0000000100000000 
               
               
                 [AATG] n   
                 Other alleles 
                 0000001000000000 
               
               
                   
               
            
           
         
       
     
     As shown in Table 14, in some embodiments, a unique value may be assigned to each of one or more known common STR alleles. In some embodiments, an encoding for a particular STR locus may be generated for a sample comprising a mixture of contributors. In some embodiments, an encoding may be generated that encodes each allele present in nucleic acid sequence information. For example, a mixed sample having alleles with 7, 9, and 12 repeats may be encoded as “0000000001001010” according to the representative encodings shown in Table 14. 
     In some embodiments, the at least one genetic locus is pre-selected for encoding. In some embodiments, the at least one STR locus is selected from the core STR loci of the CODIS database or equivalent. CODIS is an index of pointers to assist US public crime laboratories to compare and exchange genetic profiles (e.g., DNA profiles). A record in the CODIS database, known as a CODIS DNA profile, consists of an individual&#39;s genetic profile, together with the sample&#39;s identifier and an identifier of the laboratory responsible for the profile. 
     CODIS identifies genetic markers at the following STR loci: the original set: D3S1358, vWA, FGA, D8S1179, D21S11, D18551, D5S818, D13S317, D7S820, D16S539, THO1, TPDX, CSF1PO, and AMEL; and the additional set: D1S1656, D2S441, D2S1338, D10S1248, D12S391, D19S433, and D22S1045 (the “COINS STR loci”). In some embodiments, the at least one STR locus is selected from the CODIS STR loci. In some embodiments, the at least one STR locus is selected from Table 15 below. 
     
       
         
           
               
             
               
                 TABLE 15 
               
               
                   
               
               
                 STR Loci 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 CSF1PO 
                 D22S1045 
                 D6S1043 
                 DYS464 
               
               
                 (US core locus) 
                 (European  
                   
                   
               
               
                   
                 recommended  
                   
                   
               
               
                   
                 locus) 
                   
                   
               
               
                 FGA (FIBRA) 
                 DYS19 
                 CD4 
                 DY5635 
               
               
                 (US core locus) 
                 (European core  
                   
                   
               
               
                   
                 Y-STR;  
                   
                   
               
               
                   
                 SWGDAM  
                   
                   
               
               
                   
                 recommended) 
                   
                   
               
               
                 TH01 
                 DYS385 a/b  
                 F13A1 
                 Y-GATA-A4 
               
               
                 (US core locus) 
                 (European  
                   
                   
               
               
                   
                 core Y-STR;  
                   
                   
               
               
                   
                 SWGDAM  
                   
                   
               
               
                   
                 recommended) 
                   
                   
               
               
                 TPOX 
                 DYS389 I/II 
                 F13B 
                 Y-GATA-A7.1 
               
               
                 (US core locus) 
                 (European core  
                   
                   
               
               
                   
                 Y-STR; 
                   
                   
               
               
                   
                 SWGDAM  
                   
                   
               
               
                   
                 recommended) 
                   
                   
               
               
                 VWA 
                 DYS390 
                 FES/FPS 
                 Y-GATA-A7.2 
               
               
                 (US core locus) 
                 (European core  
                   
                   
               
               
                   
                 Y-STR; 
                   
                   
               
               
                   
                 SWGDAM  
                   
                   
               
               
                   
                 recommended) 
                   
                   
               
               
                 D3S1358 
                 DYS391 
                 HPRTB 
                 Y-GATA-A10 
               
               
                 (US core locus) 
                 (European core  
                   
                   
               
               
                   
                 Y-STR; 
                   
                   
               
               
                   
                 SWGDAM  
                   
                   
               
               
                   
                 recommended) 
                   
                   
               
               
                 D5S818 
                 DYS392 
                 LPL 
                 Y-GATA-H4 
               
               
                 (US core locus) 
                 (European core  
                   
                   
               
               
                   
                 Y-STR; 
                   
                   
               
               
                   
                 SWGDAM  
                   
                   
               
               
                   
                 recommended) 
                   
                   
               
               
                 D7S820 
                 DYS393 
                 Penta D 
                 ACTBP2  
               
               
                 (US core locus) 
                 (European core  
                   
                 (SE33) 
               
               
                   
                 Y-STR; 
                   
                   
               
               
                   
                 SWGDAM  
                   
                   
               
               
                   
                 recommended) 
                   
                   
               
               
                 D8S1179 
                 DYS438 
                 Penta E 
                 Amelogenin 
               
               
                 (US core locus) 
                 (SWGDAM  
                   
                   
               
               
                   
                 recommended) 
                   
                   
               
               
                 D13S317 
                 DYS439 
                 D6S1043 
                 D3S1359 
               
               
                 (US core locus) 
                 (SWGDAM  
                   
                   
               
               
                   
                 recommended) 
                   
                   
               
               
                 D16S539 
                 SE33 
                 D14S1434 
                 D7S809 
               
               
                 (US core locus) 
                 (German core  
                   
                   
               
               
                   
                 locus) 
                   
                   
               
               
                 D18S51 
                 CD4 
                 DYS388 
                 D8S347 
               
               
                 (US core locus) 
                   
                   
                   
               
               
                 D21S11 
                 F13A1 
                 DYS434 
                 D11S554 
               
               
                 (US core locus) 
                   
                   
                   
               
               
                 D2S1338 
                 F13B 
                 DYS437 
                 D13S308 
               
               
                 (European locus) 
                   
                   
                   
               
               
                 D19S433 
                 FES/FPS 
                 DYS447 
                 FABP 
               
               
                 (European locus) 
                   
                   
                   
               
               
                 D1S1656 
                 HPRTB 
                 DYS448 
                 FOLP23 
               
               
                 (European 
                   
                   
                 (DHFRP2) 
               
               
                 recommended locus) 
                   
                   
                   
               
               
                 D2S441 
                 LPL 
                 DYS456 
                   
               
               
                 (European 
                   
                   
                   
               
               
                 recommended locus) 
                   
                   
                   
               
               
                 D10S1248 
                 Penta D 
                 DYS458 
                   
               
               
                 (European 
                   
                   
                   
               
               
                 recommended locus) 
                   
                   
                   
               
               
                 D12S391 
                 Penta E 
                 DYS460 
                   
               
               
                 (European 
                   
                   
                   
               
               
                 recommended locus) 
               
               
                   
               
            
           
         
       
     
     In some embodiments, it may be advantageous to encode more than one STR locus in order to increase the uniqueness of a genetic profile being encoded. Thus, in some embodiments, the encoding encodes at least two STR loci. In some embodiments, the encoding encodes a plurality of the CODIS STR loci. In some embodiments, the encoding encodes all of the CODIS STR loci. In some embodiments, the encoding encodes a plurality of STR loci independently selected from the STR loci recited in Table 15. 
     In some embodiments, systems described herein may be used to execute methods described herein. In some embodiments, the system comprises: at least one database storing a plurality of encodings for a respective plurality of nucleic acid samples; at least one computer hardware processor; at least one non-transitory computer-readable storage medium storing processor-executable instructions that, when executed by the at least one computer hardware processor, cause the at least one computer hardware processor to perform: receiving sequence information obtained from a nucleic acid sample, wherein the sequence information comprises at least one short tandem repeat (STR) locus, the at least one STR locus comprising a unit of nucleotides repeated a number of times; generating, based on the received sequence information, an encoding for the nucleic acid sample at least in part by encoding the at least one STR locus using a value that corresponds to the number of times the unit of nucleotides is repeated; comparing the generated encoding of the nucleic acid sample with a plurality of previously-generated encodings for a respective plurality of nucleic acid samples; and when it is determined that, as a result of the comparing, the generated encoding of the nucleic acid sample matches at least one encoding in the plurality of previously-generated encodings, the at least one encoding being associated with at least one person, providing an indication that the nucleic acid sample is consistent with the at least one person. 
     In some embodiments, the at least one computer hardware processor is configured to perform a plurality of native bitwise instructions. In some embodiments, native bitwise instructions include a population count bitwise instruction, an “XOR” bitwise instruction, and an “AND” bitwise instruction. Additionally or alternatively, native bitwise instructions include a bitwise OR instruction, a bitwise NAND instruction, a bitwise NOT instruction, an arithmetic shift instruction, a logical shift instruction, a circular shift instruction, and/or any other suitable bitwise instructions that the at least one computer hardware processor is configured to execute, as aspects of the technology described herein are not limited in this respect. 
       FIG.  12 A  depicts an example of generating encodings based on sequencing information (e.g., genetic profiles) of different individuals. A first individual  1201  has homologous chromosomes  1211  with three specific loci shown. For each locus, each chromosome is shown as having a major allele (black box) or a minor allele (white box). As shown, individual  1201  has a first locus comprising heterozygous allele “Mm,” a second locus comprising heterozygous allele “mM,” and a third locus comprising homozygous major allele “MM.” According to some methods provided herein, these loci can be encoded according to  1221 , where “0” encodes a locus that is homozygous for a major allele and “1” encodes a locus that is not homozygous for a major allele. Thus, for the first individual  1201 , the three loci can be represented by the encoding “110.” 
     In order to distinguish individual genetic profiles or sequencing information representative of one or more individuals, specific loci may be analyzed. For example, a second individual  1202  has homologous chromosomes  1212  with three loci corresponding to the sites depicted in homologous chromosomes  1211 . The first locus comprises homozygous major allele “MM,” the second locus comprises homozygous minor allele “mm,” and the third locus comprises heterozygous allele “Mm.” These loci are encoded according to  1222  to generate an encoding of “011” for these loci. Similarly, an encoding for the corresponding three loci can be generated for a third individual  1203  having homologous chromosomes  1213 . Having two homozygous major alleles and one homozygous minor allele, sequencing information for the third individual  1203  is encoded according to  1223  to generate an encoding of “001” for the three loci. As shown in  FIG.  12 A , the encodings can be compiled into a database of encodings  1230 . 
     In some embodiments, it may be advantageous to select a set of loci and/or SNPs for inclusion in the analysis if the SNP is (1) relatively rare (has a low minor allele frequency, or “mAF”), (2) is not well-correlated with ancestry, (3) is physically far enough from another SNP within any chromosome that they do not tend to be inherited together, and, optionally, (4) is not related to health status. For example, in the context of a forensic investigation, the loci and/or SNPs selected for inclusion may be SNPs most often found in healthy individuals. However, in the context of SNP analysis of a medical or biological sample, for instance, to diagnose and/or prognose cancer, it may be desirable to include loci and/or SNPs, for example, that predict unregulated or deregulated cell proliferation, neovascularization, and metastasis. 
     It should be appreciated that an encoding generated based on nucleic acid sequencing information is not limited to three values, as shown in  FIG.  12 A . It should also be appreciated that generating an encoding is not necessarily limited to nucleic acid sequencing information that is representative of a single contributor (e.g., one person). In some embodiments, one encoding may comprise sequencing information for more than one contributor (e.g., more than one person). For example, a nucleic acid sample may comprise a mixture of genetic profiles. Upon subjecting the nucleic acid sample to nucleic acid sequencing, allele variation at a specific locus may be indicative of a mixture of genetic profiles. 
     Methods and systems of the disclosure may provide superior properties over the existing methods of building and deconvoluting genetic profiles in a forensic setting.  FIG.  12 B  depicts a crime scene  1240  in which a nucleic acid sample comprising nucleic acid  114  was obtained. An encoding may be generated based on the allele zygosity at specific loci. For example, a first locus comprising a homozygous minor allele and a second and third locus comprising homozygous major alleles are encoded according to  1224  as “100.” The encoding generated for the nucleic acid sample may subsequently be compared to a database  1231  comprising a plurality of encodings to potentially identify a matching encoding, e.g., encoding “D.” 
       FIG.  13    shows a non-limiting illustrative environment  1300  in which embodiments described herein may operate. In the illustrative environment, an individual  1302  may use any suitable device  1304  to conduct methods described herein. For instance, the device  1304  may be a laptop computer, a mobile device, a desktop computer, a desktop monitor, or any other device that is compatible with the methods described herein. 
     In the illustrated embodiment, sequence information  1310  is received by the device  1304  via connection  1311 , which may include wired and/or wireless connection. For example, device  1304  can receive sequence information  1310  via wired and/or wireless internet connection (e.g., via e-mail, via online data storage, etc.). Connection  1311  is also contemplated to include non-internet (e.g., offline) connections, such as connection to external data storage media. 
     In this embodiment, device  1304  is communicatively coupled to one or more computers (e.g., servers) each configured to perform processing related to generating an encoding of sequence information and/or comparing the generated encoding with a plurality of previously generated encodings. As shown, device  1304  is coupled to a single server  1306  via wired and/or wireless connection  1305 A, though in other embodiments any suitable number of servers may be used and distributed in any manner. For instance, in some embodiments, at least ten, at least one hundred, at least one thousand, or at least ten thousand servers may be used. For embodiments in which multiple servers are used, the servers may not be located in the same physical location and may be distributed across multiple physical locations. 
     Each server, such as server  1306 , may be configured (alone or in combination with one or more other servers) to perform processing related to generating an encoding of sequence information and/or comparing the generated encoding with a plurality of previously generated encodings. In some embodiments, one or more of the servers may be configured to store processor-executable instructions. In some embodiments, device  1304  may be configured to store processor-executable instructions. In some embodiments, one or more of the servers may be configured to execute one or more instructions related to the steps of generating the encoding of sequence information and/or comparing the generated encoding with a plurality of previously generated encodings. In some embodiments, the device  1304  may be configured to execute one or more instructions related to the steps of generating the encoding of sequence information and/or comparing the generated encoding with a plurality of previously generated encodings. 
     In the illustrated embodiment, the server  1306  is connected to a storage device  1308  via wired and/or wireless connection  1305 B. Storage device(s)  1308  may be any suitable storage device(s) or article(s) of manufacture capable of storing information. For example, storage device(s)  208  may be any non-transitory computer readable storage medium or media such as a computer memory (RAM and/or ROM), one or more hard disk drives, one or more optical disks (CDs and/or DVDs), one or more magnetic tapes, one or more flash memories, one or more circuit configurations in Field Programmable Gate Arrays and/or any other suitable device(s). 
     In the illustrated embodiment, one or more of device  1304 , server  1306 , and storage device(s)  1308  can be configured to execute and/or support one or more instructions related to the steps of generating the encoding of sequence information and/or comparing the generated encoding with a plurality of previously generated encodings. In some embodiments, one or more of device  1304 , server  1306 , and storage device(s)  1308  can be configured to perform a plurality of native bitwise instructions. In some embodiments, native bitwise instructions include a population count bitwise instruction, an “XOR” bitwise instruction, and an “AND” bitwise instruction. Additionally or alternatively, native bitwise instructions include a bitwise OR instruction, a bitwise NAND instruction, a bitwise NOT instruction, an arithmetic shift instruction, a logical shift instruction, a circular shift instruction, and/or any other suitable bitwise instructions that the at least one computer hardware processor is configured to execute, as aspects of the technology described herein are not limited in this respect. 
       FIG.  3 A  shows an illustrative process  300  comprising steps of generating an encoding of sequence information based on allele zygosity and comparing the generated encoding with a plurality of previously generated encodings. Process  300  may be performed, at least in part, by one or more of device  1304 , server  1306 , and storage device(s)  1308 . 
     Process  1400  begins in act  1402 , where sequence information obtained from a nucleic acid sample is received. The received sequence information comprises a plurality of genetic loci, including a first genetic locus. In some embodiments, the received sequence information may comprise sequence information for only one person. In some embodiments, the received sequence information may comprise sequence information for more than one person. 
     Next, process  1400  proceeds to decision block  1404 , where it is determined whether the first genetic locus of the sequence information received in  1402  is homozygous for a major allele. As described herein, a genetic locus is homozygous for a major allele when an allele occurring with the greatest frequency in a given population is present in both homologous chromosomes at that locus. 
     The determination of whether the first genetic locus is homozygous for a major allele may be made in any suitable way. For example, the determination may be made that the first genetic locus is not homozygous for a major allele if the first genetic locus is homozygous for a minor allele or if the first genetic locus is heterozygous. In some embodiments, the determination may be made at least in part by comparing the locus to publically available genetic information for a given population. 
     If it is determined, in decision block  1404 , that the first genetic locus is homozygous for a major allele, process  1400  proceeds to act  1406 , where the first genetic locus is encoded using a first value. If it is determined, in decision block  1404 , that the first genetic locus is not homozygous for a major allele, process  1400  proceeds to act  1408 , where the first genetic locus is encoded using a second value. 
     In some embodiments, the act (e.g.,  1406  or  1408 ) of generating an encoding comprises generating a lossy encoding. A “lossy encoding” can represent the compression of data into a form which, when it is re-expanded, does not contain all of the original information. In some embodiments, the act (e.g.,  1406  or  1408 ) of generating an encoding comprises generating a binary value. In some embodiments, the act  1406  of encoding the first genetic locus using a first value comprises encoding the first genetic locus using a first bit. In some embodiments, the act  1408  of encoding the first genetic locus using a second value comprises encoding the first genetic locus using a second bit. In some embodiments, the act  1406  of encoding the first genetic locus using a first bit comprises encoding the first genetic locus using a “0”. In some embodiments, the act  1408  of encoding the first genetic locus using a second bit comprises encoding the first genetic locus using a “1”. 
     After the encoding process in act  1406  or act  1408 , process  1400  proceeds to act  1410 , where the generated encoding of the nucleic acid sample is compared with a plurality of previously generated encodings for a respective plurality of nucleic acid samples. In some embodiments, the comparing is performed using bitwise instructions native to at least one computer hardware processor executing the process  1400 . 
     After the comparing step in act  1410 , process  1400  proceeds to decision block  1412 , where it is determined, as a result of the comparing in act  1410 , whether the generated encoding of the nucleic acid sample matches the at least one of the plurality of previously generated encodings for the respective plurality of nucleic acid samples. 
     If it is determined, in decision block  1412 , that, as a result of the comparing in act  1410 , the generated encoding of the nucleic acid sample matches at least one encoding in the plurality of previously generated encodings, the at least one encoding being associated with at least one person, then process  1400  proceeds to act  1414 , where an indication is provided that the nucleic acid sample is consistent with the at least one person. 
     In some embodiments, the generated encoding of the nucleic acid sample matches two different encodings in the plurality of previously generated encodings, the two different encodings being associated with two different people. In such embodiments, act  1414  comprises providing an indication that the nucleic acid sample is consistent with the two different people. 
     During process  1400 , decision block  1404  and acts  1406  and  1408  may advantageously be repeated for any number of subsequent loci (e.g., a second genetic locus, a third genetic locus, etc.) in the received sequence information to generate an encoding comprising more than one value. Such an embodiment may be useful, for example, when implementing SNP analysis. By analyzing loci that are known to occur at a specific frequency in a given population, accuracy will be increased in the determining step represented in decision block  1412 . 
     For example,  FIG.  1 A  depicts an individual  102  with three loci that correspond to a first site that is homozygous for a major allele (“MM”), a second site that is homozygous for a minor allele (“mm”), and a third site that is heterozygous (“Mm”). Using process  1400 , one could generate an encoding for the three loci of “011.”  FIG.  1 A  further depicts an individual  1203  with three loci that correspond to a first site that is homozygous for a major allele (“MM”), a second site that is homozygous for a major allele (“MM”), and a third site that is homozygous for a minor allele (“mm”). Using process  300 , one could generate an encoding for the three loci of “001.” 
     In some embodiments, an encoding of “1” can indicate the presence of a SNP. Thus, in the foregoing example with individual  102  (“011”) and individual  1203  (“001”), it could be said that both individuals have a SNP at the third site of the three loci while neither individual has a SNP at the first site. However, individual  1202  may be distinguished from individual  1203  in that the former has a SNP at the second site of the three loci. As the number of encoded loci increases, there is a decrease in the probability) that sequence information for any given individual will match the encoding. 
     It should be appreciated that systems and methods provided herein are not limited to SNP analysis, which is illustrated in the above example. In some aspects, techniques described herein may be used for STR analysis. For example, an encoding can be generated based on one or more of the defined core STR loci of the CODIS database or equivalent. Sequencing information obtained from a nucleic acid sample may comprise one or more of these core STR loci, and an encoding may be generated for one or more of the loci. 
       FIG.  14 B  shows an illustrative process  1450  for forensic identification using STR analysis, in accordance with some embodiments of the technology described herein. The process  1450  includes generating an encoding of sequence information based on the number of repeated motifs in an STR and comparing the generated encoding with a plurality of previously generated encodings. Process  1450  may be performed by any suitable computing device(s). For example process  1450  may be performed by one or more of device  204 , server  206 , and storage device(s)  208 . 
     Process  1450  begins in act  1452 , where sequence information obtained from a nucleic acid sample is received. In some embodiments, the received sequence information may consist of sequence information for only one person. In some embodiments, the received sequence information may consist of sequence information for more than one person. The received sequence information may comprise at least one STR locus, which may comprise a unit of nucleotides repeated a number of times. As described previously, an STR is a tract of repetitive nucleic acid sequence in which certain units of nucleotides (ranging in length from 2-5 base pairs) are repeated, typically 5-50 times. 
     Next, process  1450  proceeds to act  1454 , where the number of times the unit of nucleotides is repeated in the STR is determined for the STR locus of the sequence information received in  1452 . In some embodiments, the STR locus may comprise a single unit of nucleotides that is repeated some number of times. In some embodiments, the STR locus comprises multiple units of nucleotides that are each independently repeated some number of times. 
     For example, the STR locus D8S1179 (chromosomal location: 8q24.13) is one of the genetic markers of the CODIS loci. In some individuals, D8S1179 consists of a single unit of nucleotides (e.g., “TCTA”) repeated some number of times, which may be represented as [TCTA]n, where n denotes the number of times the unit is repeated. In other individuals, D8S1179 consists of multiple units of nucleotides repeated some number of times, for example, as represented by the formula [TCTA]n[TCTG]n[TCTA]n, where each instance of n can independently vary (e.g., the STR locus can be [TCTA]1[TCTG]1[TCTA]11, [TCTA]2[TCTG]1[TCTA]13, etc.). 
     When the STR consists of multiple units of nucleotides repeated some number of times, the number determined in act  1451  can be made in any suitable way. As described in the above example, D8S1179 can consist of repeat structures [TCTA]n and [TCTA]n[TCTG]n[TCTA]n. In some embodiments, a practitioner of the technology described herein may choose to determine the value of the latter structure by summing each value for n (e.g., the number of times determined in act  1454  for [TCTA]2[TCTG]1[TCTA]13 is 2+1+13, or 16). In some embodiments, the practitioner may choose to exclude certain units from the number determined in act  1454  (e.g., TCTG is excluded from consideration and the number of times determined for [TCTA]2[TCTG]1[TCTA]13 is 2+13, or 15). 
     Once the number is determined in act  1454 , process  1450  proceeds to act  1456 , where an encoding is generated using a value that corresponds to the number of times the unit of nucleotides is repeated. It should be appreciated that process  1450  is one illustrative embodiment of the technology described herein, and that an encoding may be generated to encode any characteristic of an STR locus. For example, in some embodiments, an encoding may be generated that encodes one or more of the following in an STR: sequence length of the unit of nucleotides that is repeated (e.g., using a value that corresponds to a value of 4 for [TCTA]n); number of times the unit of nucleotides is repeated (e.g., using a value that corresponds to the value of n in [TCTA]n); and overall sequence length of the STR (e.g., using a value that corresponds to the product of 4 and n in [TCTA]n). 
     After the encoding process in act  1456 , process  1450  proceeds to act  1460 , where the generated encoding of the nucleic acid sample is compared with a plurality of previously generated encodings for a respective plurality of nucleic acid samples. In some embodiments, the comparing is performed using bitwise instructions native to at least one computer hardware processor executing the process  1450 . 
     After the comparing step in act  1460 , process  1450  proceeds to decision block  1462 , where it is determined, as a result of the comparing in act  1460 , whether the generated encoding of the nucleic acid sample matches the at least one of the plurality of previously generated encodings for the respective plurality of nucleic acid samples. 
     If it is determined, in decision block  1462 , that, as a result of the comparing in act  1460 , the generated encoding of the nucleic acid sample matches at least one encoding in the plurality of previously generated encodings, the at least one encoding being associated with at least one person, then process  1450  proceeds to act  1464 , where an indication is provided that the nucleic acid sample is consistent with the at least one person. 
     In some embodiments, the generated encoding of the nucleic acid sample matches two different encodings in the plurality of previously generated encodings, the two different encodings being associated with two different people. In such embodiments, act  1464  comprises providing an indication that the nucleic acid sample is consistent with the two different people. 
     During process  1450 , acts  1454  and  1456  can advantageously be repeated (as indicated by the dashed line) for any number of subsequent STR loci in the received sequence information to generate an encoding comprising more than one value. Such an embodiment may be desirable, for example, when implementing STR analysis. By analyzing STR loci that are known to occur at a specific frequency in a given population, accuracy will be increased in the determining step represented in decision block  1462 . 
     EXAMPLES 
     Example 1: SNP Allele Comparisons 
     The DNA bases are encoded as A, C, G, and T. A SNP typically has a major allele that is most common in a population of people and a minor allele with a lower allele frequency than the major allele. Most SNPs have typically only two alleles, but more alleles are possible. Let M represent a major allele and m represent a minor allele. With two alleles for a SNP, then there are four possibilities for the SNP for an individual: MM, Mm, mM, and mm. For comparing two individuals, Table 16 shows the possible allele combinations. To compare a set of SNPs, size N, between two individuals, 2×N allele comparisons are needed with care to treat Mm and mM as two common alleles. 
     
       
         
           
               
             
               
                 TABLE 16 
               
             
            
               
                   
               
               
                 Possible SNP Allele Comparisons between Two Individuals 
               
            
           
           
               
               
               
            
               
                 Individual 1 
                 Individual 2 
                 # of Common Alleles 
               
               
                   
               
               
                 MM 
                 MM 
                 2 
               
               
                 Mm 
                 MM 
                 1 
               
               
                 mM 
                 MM 
                 1 
               
               
                 mm 
                 MM 
                 0 
               
               
                 MM 
                 Mm 
                 1 
               
               
                 Mm 
                 Mm 
                 2 
               
               
                 mM 
                 Mm 
                 2 
               
               
                 mm 
                 Mm 
                 1 
               
               
                 MM 
                 mM 
                 1 
               
               
                 Mm 
                 mM 
                 2 
               
               
                 mM 
                 mM 
                 2 
               
               
                 mm 
                 mM 
                 1 
               
               
                 MM 
                 mm 
                 0 
               
               
                 Mm 
                 mm 
                 1 
               
               
                 mM 
                 mm 
                 1 
               
               
                 mm 
                 mm 
                 2 
               
               
                   
               
            
           
         
       
     
     The logic binary bit operators for XOR and AND are shown in Tables 17 and 18. 
     
       
         
           
               
             
               
                 TABLE 17 
               
             
            
               
                   
               
               
                 Logic XOR Operator 
               
            
           
           
               
               
               
               
            
               
                 Bit 1 
                 Bit 2 
                 Operator 
                 Result 
               
               
                   
               
               
                 0 
                 0 
                 XOR 
                 0 
               
               
                 0 
                 1 
                 XOR 
                 1 
               
               
                 1 
                 0 
                 XOR 
                 1 
               
               
                 1 
                 1 
                 XOR 
                 0 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 18 
               
             
            
               
                   
               
               
                 Logic AND Operator 
               
            
           
           
               
               
               
               
            
               
                 Bit 1 
                 Bit 2 
                 Operator 
                 Result 
               
               
                   
               
               
                 0 
                 0 
                 AND 
                 0 
               
               
                 0 
                 1 
                 AND 
                 0 
               
               
                 1 
                 0 
                 AND 
                 0 
               
               
                 1 
                 1 
                 AND 
                 1 
               
               
                   
               
            
           
         
       
     
     SNP alleles may be mapped to a single binary bit for rapid comparisons between two samples. Table 19 illustrates the binary encoding of alleles. 
     
       
         
           
               
             
               
                 TABLE 19 
               
             
            
               
                   
               
               
                 Binary Encoding of SNP Alleles 
               
            
           
           
               
               
            
               
                 Alleles 
                 Binary Encoding 
               
               
                   
               
               
                 MM 
                 0 
               
               
                 Mm 
                 1 
               
               
                 mm 
                 1 
               
               
                   
               
            
           
         
       
     
     Panels (or sets) of SNPs can be encoded as hex strings for easier representation of SNPs with four different SNP alleles for a sample represented by one hexadecimal letter. An example of encoding four SNPs loci as a hexadecimal representation are shown in Table 8, with encodings shown in Table 9. Note that 64 or 256 SNP loci can be encoded in 64-bit and 256-bit computer hardware registers. 
     
       
         
           
               
             
               
                 TABLE 20 
               
             
            
               
                   
               
               
                 Hex Encoding of Four SNP Alleles 
               
            
           
           
               
               
               
            
               
                 Base 10 
                 Base 16-Hex 
                 Base 2-Binary 
               
               
                   
               
               
                  0 
                 0 
                 0000 
               
               
                  1 
                 1 
                 0001 
               
               
                  2 
                 2 
                 0010 
               
               
                  3 
                 3 
                 0011 
               
               
                  4 
                 4 
                 0100 
               
               
                  5 
                 5 
                 0101 
               
               
                  6 
                 6 
                 0110 
               
               
                  7 
                 7 
                 0111 
               
               
                  8 
                 8 
                 1000 
               
               
                  9 
                 9 
                 1001 
               
               
                 10 
                 A 
                 1010 
               
               
                 11 
                 B 
                 1011 
               
               
                 12 
                 C 
                 1100 
               
               
                 13 
                 D 
                 1101 
               
               
                 14 
                 E 
                 1110 
               
               
                 15 
                 F 
                 1111 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 21 
               
             
            
               
                   
               
               
                 Sample Minor Alleles of Individuals and Mixtures 
               
            
           
           
               
               
            
               
                 Sample 
                 Minor Alleles encoded as Hexadecimal digits 
               
               
                   
               
               
                 Ind-1 
                 0600144000480820000020200000 0006010000086000420000000003 
               
               
                 Ind-2 
                 0000000000204805000084001402 00a0000000000059610080401000 
               
               
                 Ind-2 
                 0000000000204805000084081402 00a0000010000059610080401400 
               
               
                 Ind-3 
                 0200000000400000000404001000 0002000000000800000200000000 
               
               
                 Ind-3 
                 0200000000000000000404001000 0002000000000800000200000040 
               
               
                 Mix-1 
                 002000000020580500408408140a 00a0000010000059610080421700 
               
               
                 Mix-2 
                 0004909800040000000060000200 1082500e00000444000210802902 
               
               
                 Mix-3 
                 1210004002800000404840041044 08400010000a2098400000001050 
               
               
                 Mix-4 
                 32288040038100200804462a5000 568220205c485c38048398000440 
               
               
                   
               
            
           
         
       
     
     Two samples for individuals can be compared by mapping the binary representation of SNP alleles onto hardware bit representations and comparing the samples directly with the computer hardware XOR (exclusive OR) instruction. The 1 bits in the result represents all of positions where there is a difference in the minor alleles between the two individuals, see Tables 22 and 23. The computer hardware population count instruction tallies all of the 1 bits in the result to identify (count) all of the minor allele differences between the two samples. In Table 22, the first replicate for individual  2  has three dropped minor alleles as compared to the second replicate. In Table 23, each replicate has a single minor allele difference from the other replicate. 
     
       
         
           
               
             
               
                 TABLE 22 
               
             
            
               
                   
               
               
                 Comparison of Replicate Samples for Individual 2 
               
            
           
           
               
               
            
               
                 Sample 
                 Minor Alleles encoded as Hexadecimal digits 
               
               
                   
               
               
                 Ind-2 
                 0000000000204805000084001402 00a0000000000059610080401000 
               
               
                 Ind-2 
                 0000000000204805000084081402 00a0000010000059610080401400 
               
               
                 XOR 
                 0000000000000000000000080000 0000000010000000000000000400 
               
               
                 Pop. count 
                 3 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 23 
               
             
            
               
                   
               
               
                 Comparison of Replicate Samples for Individual 3 
               
            
           
           
               
               
            
               
                 Sample 
                 Minor Alleles encoded as Hexadecimal digits 
               
               
                   
               
               
                 Ind-3 
                 0200000000400000000404001000 0002000000000800000200000000 
               
               
                 Ind-3 
                 0200000000000000000404001000 0002000000000800000200000040 
               
               
                 XOR 
                 0000000000400000000000000000 0000000000000000000000000040 
               
               
                 Pop. count 
                 2 
               
               
                   
               
            
           
         
       
     
     Using this approach and parallelization, it is possible to compare very large numbers of samples rapidly on typical symmetric multiprocessing (SMP) computers, a laptop, or any computing device. 
     To compare an individual sample to a mixture sample, the XOR result can be bit masked to only consider the minor alleles of the individual by anding (logical AND operation) the XOR result to the individual profile with the hardware AND instruction. Table 24 illustrates the comparison of Individual  3  with Mixture  4  with one minor allele mismatch between the individual and the mixture. 
     
       
         
           
               
             
               
                 TABLE 24 
               
             
            
               
                   
               
               
                 Comparison of Individual 3 with Mixture 4 
               
            
           
           
               
               
            
               
                 Sample 
                 Minor Alleles encoded as Hexadecimal digits 
               
               
                   
               
               
                 Ind-3 
                 0200000000400000000404001000 0002000000000800000200000000 
               
               
                 Mix-4 
                 32288040038100200804462a5000 568220205c485c38048398000440 
               
               
                 XOR 
                 3028804003c100200800422a4000 568020205c485438048198000440 
               
               
                 AND 
                 0000000000400000000000000000 0000000000000000000000000000 
               
               
                 Pop. count 
                 1 
               
               
                   
               
            
           
         
       
     
     A traditional comparison of SNP loci requires 2×N allele comparisons. For a 64-bit computer, the number of operations are reduced to the scale of N/64 operations. For very large sets of samples, the method may out perform a traditional approach by a factor of 100-to 1,000-fold. 
     A second method is a variant of the above method using the massively parallel computing hardware in standard graphics processing units (GPUs) like the Tesla K80. The graphics memory of the CPU can be loaded with target samples and multiple batches of query samples can be rapidly compared using the CPU hardware instructions for XOR, AND, and population count. Using the parallel hardware of the CPU, hundreds of samples can be compared to thousands of samples using the CPU XOR and AND operations. This approach may outperform a traditional approach by a factor of 10,000-to 100,000-fold. 
     A third method leverages the Bigtable approach that gave rise to Big Data NO SQL databases. A traditional approach maps alleles for each sample in a table. An inverted table approach maps the alleles to the samples. A tally of the most frequently occurring sample names for a set of minor alleles for a sample yields an ordered list of best possible matches between the sample and entries in the database. This is a Big Data alternative method using NO SQL and New SQL database technologies. 
     Example 2: Search Method Identifies Relatives 
     In  FIG.  15   , a sample (ZR5HE:IX-23) was searched against hundreds of other samples. The results indicate no additional samples for this individual, but did detect both a 2nd degree (ZR5HE:IX-22) and a 3rd degree relative (OELSG:IX-21). 
     A similar comparison is graphed in  FIGS.  16 A- 16 B  using data from 4 generations of relatives (descendants) shown in green and 1 million unrelated individuals. In  FIG.  16 A , the first peak on the left in the green line indicate 1st degree relatives, 2nd peak represents 2nd degree relatives, 3rd peak represents 3rd degree relatives—this is illustrated in detail in  FIG.  16 B . The blue line indicates random matches to 1 million individuals with four different ethnic backgrounds with the first peak on the left indicating individuals with a shared ethnic background. 
     In  FIG.  16 B  for the 3rd degree relatives shown in the red line, there are smaller peaks to the right of the main red peak indicating 3rd degree relatives with different ethnic backgrounds due to admixture. The left most main peak, represents individuals with the same ethnic background as the individual of interest—this is examined in  FIGS.  17 A- 17 B  with labeling of percent sharing of ethnic background with the person being searched. 
     The comparison method enables the comparisons of (a) individuals vs. individuals, (b) individuals versus mixtures, (c) mixtures versus individuals, and (d) mixtures versus mixtures.  FIG.  18    illustrates how individuals can be identified by comparing mixtures. The methods of the disclosure, including the SNP panels described herein, provide superior properties when compared to existing methods of building and/or deconvoluting a DNA profile. Prior to the development of the methods of the disclosure, Voskoboinik and Darvasi published methods for deconvoluting complex DNA mixtures, (see, Voskoboinik, L. and Darvasi, A. Forensic Identification of an Individual in Complex DNA Mixtures. 2011. Forensic Science International: Genetics 5:428-435) however, there are important differences between the methods of Voskoboinik and Darvasi and the methods of the disclosure. For example, fundamentally, the methods of the disclosure are quantitative. The quantitative methods of the disclosure allow the user to both build an individual DNA profile from a complex DNA mixture as well as deconvolute a complex DNA mixture to component profiles without any prior knowledge of any DNA sequence or genetic marker present of any contributor to any complex DNA mixture under analysis. 
     In further contrast to the methods of Voskoboinik and Darvasi, the methods of the disclosure include multiple complex DNA mixtures to build an individual DNA profile. The methods of the disclosure for building an individual DNA profile detect the presence or absence of a particular SNP in each complex DNA mixture. The set of SNPs that are present in each of the complex DNA mixtures, also referred to as an overlapping population of SNPs, an intersection of the complex DNA mixtures, or a product of the multiplication of the complex DNA mixtures, represents those SNPs belonging to common contributors to each of the complex DNA mixtures in addition to those SNPs that are present in each mixture by chance. As the number of complex DNA mixtures included in the analysis increases, the accuracy with which the methods identify common contributors to each mixtures increases because the probability that each common SNP occurs in each mixture by chance alone becomes vanishingly small (i.e. rapidly approaches zero). 
     In further contrast to the methods of Voskoboinik and Darvasi, and in contrast to the methods of the disclosure for building individual DNA profiles, the methods of the disclosure for deconvolution or resolution of a component and/or individual contributor from a complex DNA mixture may be performed by analyzing a single complex DNA mixture. In certain embodiments of the methods of the disclosure for deconvolution or resolution of a component and/or individual contributor from a complex DNA mixture, the method may analyze more than one complex DNA mixture. The methods of the disclosure for deconvoluting or resolving a complex DNA mixtures into one or more components detect a signal amplitude of each SNP of a SNP panel to distinguish major versus minor contributors to the complex DNA mixture. These methods can detect differences in signal amplitude across a high-dynamic range. For example, these methods can resolve a DNA profile of a minor contributor to the mixture when as little as 0.001% to 49% of the DNA in the complex mixture belongs to the minor contributor. The resolution of DNA profiles using these methods increases as the number of SNP loci increase in the SNP panel used. 
     As used herein, the term complex DNA mixture refers to a DNA mixture comprised of DNA from one, two, or more contributors. Preferably, the complex DNA mixtures of the methods described herein include DNA from at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more contributors. In practice and in theory, there is no upper limit to the number of contributors to a complex DNA mixture of the disclosure. Moreover, with respect to methods of building an individual DNA profile, there is no upper limit to either the number of contributors to a complex DNA mixture or the number of complex DNA mixtures analyzed to build the individual DNA profile. For example, with respect to methods of building an individual DNA profile, the number of complex DNA mixtures that may be included in the analysis may be at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. 16, 17, 18, 19, 20, or more contributors. 
     Selection of SNP Markers 
     A single nucleotide polymorphism (SNP) is a single position in the genome that tends to vary between individuals. Millions of SNPs have been identified in the human genome. Not all of these SNPs are appropriate for analyzing mixtures of DNA. 
     When selecting a set of loci and/or SNPs for inclusion in a SNP panel of the disclosure, it is best if the SNP is (1) relatively rare (has a low minor allele frequency), (2) is not well-correlated with ancestry, (3) is physically far enough from another SNP within any chromosome that they do not tend to be inherited together, and, optionally, (4) is not related to health status. For example, in the context of a forensic investigation, the loci and/or SNPs selected for inclusion may be SNPs most often found in healthy individuals. However, in the context of analysis of medical or biological sample or a genetically heterogeneous medical or biological sample, for instance, to diagnose and/or prognose cancer. it may be desirable to include Loci and/or SNPs, for example, that predict unregulated or deregulated cell proliferation, neovascularization, and metastasis. 
     As a panel for analysis of complex DNA mixtures, it is important to assemble a collection of SNPs that is large enough to provide the statistical power for identifying an individual in a mixture, but is small enough to be easily run on the sequencing instrument available. For analysis of the loci and/or SNPs of the SNP panels described herein, any sequencing instrument may be used. Exemplary, but non-limiting, systems for amplifying large numbers of SNPs include: Fluidigm Access Array and Life Technology Ampliseq. Each of these methods utilizes proprietary design principles to identify PCR primers that can amplify a subset of the desired SNPs. Both of these systems are available to the public. 
     Four exemplary panels of SNPs are described herein. Three of these panels were used for mixture analysis: the 480 panel; the 975 panel; the OptMix panel. The OptMix panel is a subset of the Kinship panel, which was designed to assess the degree of relatedness between two people from DNA samples. 
     As used in the following descriptions, a FST (Fixation Index) is a measurement of how closely any given SNP correlates with ancestry. For example, a low FST indicates that the allele correlates poorly with ancestry. Moreover, a mAF (minor allele frequency) describes the frequency that an allele is present on a chromosome in a population. 
     Any one of the following panels, including any SNP panel of the disclosure, may be subject to an empirical screening process. An empirical screening process may include one or more of the following steps in any combination:
         Delete loci that tend to give ambiguous results (e.g. mAR not at expected values in reference samples),   Delete loci that tend to produce a low number of reads (for example, &lt;10% of the average number of reads/locus),   Delete loci that produce impossible results in known family tree, and/or   Delete loci that tend to generate data from only one strand of DNA.   The 480 panel: Amplification was performed using Fluidigm Access Array. Loci were selected as follows:   FST &lt;0.06: Poor correlation between ancestry and genotype on ALFRED database (see, for example, Pakstis et al. Hum Genet (2010) 127:315-324)   Average Heterozygosity=0.058-0.13 on ALFRED (should correspond to mAF˜0.03-0.07)   No health related data on SNP in the NIH/NCBI dbSNP database   mAF=0.03-0.07 on dbSNP database   Average Heterozygosity=0.058-0.13 on dbSNP (should correspond to MAF˜0.03-0.07), meaning that the alleles are relatively rare in the population   Elimination of duplicate SNPs and ambiguously mapped SNPs.   Minimum distance between alleles of 500,000 bases (of NCBI build 37, Tian C, et al. (2008) PLoS Genetics 4(1): 29-39)=1430 SNPs.   Selected 950 SNPs, 530 of which were compatible with Fluidigm DNA amplification platform   The 975 panel: Amplification was performed using Ampliseq. Same process as described for the 480-panel, however, include all 1430 SNPs rather than selecting from this group the 950 SNPs used in the 480-panel.   Kinship panel: Amplification was performed using Ampliseq. Similar criteria as described for the 480-SNP panel, with the following distinctions:   a low mAF, and in certain embodiments, between 0.01 and 0.3   Distance between loci &gt;110,000 by   OptMix panel: Amplification was performed using Ampliseq. Similar criteria as described for the Kinship panel, with the following distinctions:   Distance between loci &gt;500,000   mAF&lt;0.06   Delete loci that tend to give ambiguous results (mAR not at expected values in reference samples)   Delete loci that tend to produce a low number of reads (&lt;10% of the average number of reads/locus)   Delete loci that produce impossible results in known family tree   Delete loci that tend to generate data from only one strand of DNA.       

     Table 25 provides a list of SNPs included in the an embodiment of the OptMix Panel of the disclosure. 
     
       
         
           
               
               
             
               
                   
               
               
                   
                 SNP 
               
               
                 SNP# 
                 Reference 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 1 
                 rs10014900 
               
               
                 2 
                 rs16872711 
               
               
                 3 
                 rs3026840 
               
               
                 4 
                 rs10015135 
               
               
                 5 
                 rs16874072 
               
               
                 6 
                 rs3087374 
               
               
                 7 
                 rs1001742 
               
               
                 8 
                 rs16874114 
               
               
                 9 
                 rs3092829 
               
               
                 10 
                 rs1003469 
               
               
                 11 
                 rs16876526 
               
               
                 12 
                 rs3106532 
               
               
                 13 
                 rs10042810 
               
               
                 14 
                 rs16878072 
               
               
                 15 
                 rs3108124 
               
               
                 16 
                 rs10042938 
               
               
                 17 
                 rs16878691 
               
               
                 18 
                 rs3109091 
               
               
                 19 
                 rs10045099 
               
               
                 20 
                 rs16879548 
               
               
                 21 
                 rs3127158 
               
               
                 22 
                 rs10054189 
               
               
                 23 
                 rs16879674 
               
               
                 24 
                 rs3136795 
               
               
                 25 
                 rs10059981 
               
               
                 26 
                 rs16882710 
               
               
                 27 
                 rs3138158 
               
               
                 28 
                 rs10066520 
               
               
                 29 
                 rs16884281 
               
               
                 30 
                 rs314756 
               
               
                 31 
                 rs10079950 
               
               
                 32 
                 rs16885867 
               
               
                 33 
                 rs319884 
               
               
                 34 
                 rs1008461 
               
               
                 35 
                 rs16894006 
               
               
                 36 
                 rs3213395 
               
               
                 37 
                 rs10093823 
               
               
                 38 
                 rs16895698 
               
               
                 39 
                 rs3214070 
               
               
                 40 
                 rs1009682 
               
               
                 41 
                 rs16899390 
               
               
                 42 
                 rs3218995 
               
               
                 43 
                 rs10097827 
               
               
                 44 
                 rs16906840 
               
               
                 45 
                 rs324882 
               
               
                 46 
                 rs10099140 
               
               
                 47 
                 rs16907089 
               
               
                 48 
                 rs325609 
               
               
                 49 
                 rs10116365 
               
               
                 50 
                 rs16907395 
               
               
                 51 
                 rs347433 
               
               
                 52 
                 rs10125854 
               
               
                 53 
                 rs16912069 
               
               
                 54 
                 rs354255 
               
               
                 55 
                 rs1013579 
               
               
                 56 
                 rs16912603 
               
               
                 57 
                 rs356296 
               
               
                 58 
                 rs10164423 
               
               
                 59 
                 rs16916228 
               
               
                 60 
                 rs35677470 
               
               
                 61 
                 rs10178469 
               
               
                 62 
                 rs16917429 
               
               
                 63 
                 rs3732596 
               
               
                 64 
                 rs10179948 
               
               
                 65 
                 rs16918105 
               
               
                 66 
                 rs3732868 
               
               
                 67 
                 rs10185703 
               
               
                 68 
                 rs16918622 
               
               
                 69 
                 rs3733472 
               
               
                 70 
                 rs1019540 
               
               
                 71 
                 rs16920971 
               
               
                 72 
                 rs3733709 
               
               
                 73 
                 rs10196787 
               
               
                 74 
                 rs16928182 
               
               
                 75 
                 rs3734690 
               
               
                 76 
                 rs10201330 
               
               
                 77 
                 rs16928482 
               
               
                 78 
                 rs3739446 
               
               
                 79 
                 rs10206295 
               
               
                 80 
                 rs16928989 
               
               
                 81 
                 rs3739916 
               
               
                 82 
                 rs10216611 
               
               
                 83 
                 rs16933296 
               
               
                 84 
                 rs3741571 
               
               
                 85 
                 rs10228665 
               
               
                 86 
                 rs16941516 
               
               
                 87 
                 rs3742209 
               
               
                 88 
                 rs10229451 
               
               
                 89 
                 rs16942885 
               
               
                 90 
                 rs3743175 
               
               
                 91 
                 rs10237037 
               
               
                 92 
                 rs16945135 
               
               
                 93 
                 rs3744453 
               
               
                 94 
                 rs10247070 
               
               
                 95 
                 rs16947335 
               
               
                 96 
                 rs3751474 
               
               
                 97 
                 rs1024787 
               
               
                 98 
                 rs16947417 
               
               
                 99 
                 rs3754913 
               
               
                 100 
                 rs10249706 
               
               
                 101 
                 rs16948164 
               
               
                 102 
                 rs3759732 
               
               
                 103 
                 rs10258384 
               
               
                 104 
                 rs16948633 
               
               
                 105 
                 rs3764459 
               
               
                 106 
                 rs10259889 
               
               
                 107 
                 rs16949858 
               
               
                 108 
                 rs3765148 
               
               
                 109 
                 rs10280153 
               
               
                 110 
                 rs16950754 
               
               
                 111 
                 rs3769071 
               
               
                 112 
                 rs10280515 
               
               
                 113 
                 rs16951027 
               
               
                 114 
                 rs3773371 
               
               
                 115 
                 rs10413635 
               
               
                 116 
                 rs16961669 
               
               
                 117 
                 rs3775534 
               
               
                 118 
                 rs10439364 
               
               
                 119 
                 rs16964136 
               
               
                 120 
                 rs3780660 
               
               
                 121 
                 rs1044281 
               
               
                 122 
                 rs16964707 
               
               
                 123 
                 rs3787158 
               
               
                 124 
                 rs10445895 
               
               
                 125 
                 rs16966016 
               
               
                 126 
                 rs3789257 
               
               
                 127 
                 rs10456051 
               
               
                 128 
                 rs16967852 
               
               
                 129 
                 rs3790262 
               
               
                 130 
                 rs10474648 
               
               
                 131 
                 rs16971135 
               
               
                 132 
                 rs3792491 
               
               
                 133 
                 rs10483173 
               
               
                 134 
                 rs16973356 
               
               
                 135 
                 rs3793354 
               
               
                 136 
                 rs10484358 
               
               
                 137 
                 rs16976488 
               
               
                 138 
                 rs3795244 
               
               
                 139 
                 rs10484658 
               
               
                 140 
                 rs16977658 
               
               
                 141 
                 rs3795348 
               
               
                 142 
                 rs10485047 
               
               
                 143 
                 rs16979618 
               
               
                 144 
                 rs3796352 
               
               
                 145 
                 rs10485311 
               
               
                 146 
                 rs16985057 
               
               
                 147 
                 rs3798012 
               
               
                 148 
                 rs10485490 
               
               
                 149 
                 rs16986694 
               
               
                 150 
                 rs3799007 
               
               
                 151 
                 rs10485548 
               
               
                 152 
                 rs16989572 
               
               
                 153 
                 rs3810840 
               
               
                 154 
                 rs10485764 
               
               
                 155 
                 rs16989682 
               
               
                 156 
                 rs3810925 
               
               
                 157 
                 rs10486523 
               
               
                 158 
                 rs16990450 
               
               
                 159 
                 rs3812852 
               
               
                 160 
                 rs10487308 
               
               
                 161 
                 rs16990824 
               
               
                 162 
                 rs3813474 
               
               
                 163 
                 rs10488002 
               
               
                 164 
                 rs16991498 
               
               
                 165 
                 rs3819971 
               
               
                 166 
                 rs10488501 
               
               
                 167 
                 rs16997765 
               
               
                 168 
                 rs3824534 
               
               
                 169 
                 rs10488698 
               
               
                 170 
                 rs17006704 
               
               
                 171 
                 rs3857470 
               
               
                 172 
                 rs10488723 
               
               
                 173 
                 rs1700688 
               
               
                 174 
                 rs3857487 
               
               
                 175 
                 rs10488758 
               
               
                 176 
                 rs17007024 
               
               
                 177 
                 rs389089 
               
               
                 178 
                 rs10488831 
               
               
                 179 
                 rs17008011 
               
               
                 180 
                 rs3915009 
               
               
                 181 
                 rs10489168 
               
               
                 182 
                 rs17009521 
               
               
                 183 
                 rs3917118 
               
               
                 184 
                 rs10492034 
               
               
                 185 
                 rs17010346 
               
               
                 186 
                 rs3920484 
               
               
                 187 
                 rs10492176 
               
               
                 188 
                 rs17013082 
               
               
                 189 
                 rs3945008 
               
               
                 190 
                 rs10492251 
               
               
                 191 
                 rs17014898 
               
               
                 192 
                 rs3948463 
               
               
                 193 
                 rs10492273 
               
               
                 194 
                 rs17020274 
               
               
                 195 
                 rs3967819 
               
               
                 196 
                 rs10492340 
               
               
                 197 
                 rs17020633 
               
               
                 198 
                 rs4073420 
               
               
                 199 
                 rs10492523 
               
               
                 200 
                 rs17021617 
               
               
                 201 
                 rs4130603 
               
               
                 202 
                 rs10492683 
               
               
                 203 
                 rs17023499 
               
               
                 204 
                 rs4142466 
               
               
                 205 
                 rs10493050 
               
               
                 206 
                 rs17028543 
               
               
                 207 
                 rs4149418 
               
               
                 208 
                 rs10493204 
               
               
                 209 
                 rs17030351 
               
               
                 210 
                 rs415135 
               
               
                 211 
                 rs10494246 
               
               
                 212 
                 rs17031645 
               
               
                 213 
                 rs4151467 
               
               
                 214 
                 rs10494795 
               
               
                 215 
                 rs17036738 
               
               
                 216 
                 rs4236939 
               
               
                 217 
                 rs10494933 
               
               
                 218 
                 rs17038089 
               
               
                 219 
                 rs4242335 
               
               
                 220 
                 rs10495982 
               
               
                 221 
                 rs17039555 
               
               
                 222 
                 rs4253449 
               
               
                 223 
                 rs10496694 
               
               
                 224 
                 rs17043820 
               
               
                 225 
                 rs4271931 
               
               
                 226 
                 rs10497363 
               
               
                 227 
                 rs17044733 
               
               
                 228 
                 rs4316524 
               
               
                 229 
                 rs10497796 
               
               
                 230 
                 rs17045327 
               
               
                 231 
                 rs4318657 
               
               
                 232 
                 rs10497880 
               
               
                 233 
                 rs17046580 
               
               
                 234 
                 rs438323 
               
               
                 235 
                 rs10498177 
               
               
                 236 
                 rs17047517 
               
               
                 237 
                 rs4386077 
               
               
                 238 
                 rs10501273 
               
               
                 239 
                 rs17048581 
               
               
                 240 
                 rs4388439 
               
               
                 241 
                 rs10502273 
               
               
                 242 
                 rs17049231 
               
               
                 243 
                 rs439012 
               
               
                 244 
                 rs10502421 
               
               
                 245 
                 rs17050809 
               
               
                 246 
                 rs4393596 
               
               
                 247 
                 rs10502634 
               
               
                 248 
                 rs17053338 
               
               
                 249 
                 rs4394199 
               
               
                 250 
                 rs10503042 
               
               
                 251 
                 rs17054660 
               
               
                 252 
                 rs4394904 
               
               
                 253 
                 rs10503375 
               
               
                 254 
                 rs17055965 
               
               
                 255 
                 rs4405494 
               
               
                 256 
                 rs10503703 
               
               
                 257 
                 rs17056745 
               
               
                 258 
                 rs441624 
               
               
                 259 
                 rs10504514 
               
               
                 260 
                 rs17058466 
               
               
                 261 
                 rs4426962 
               
               
                 262 
                 rs10504646 
               
               
                 263 
                 rs17059415 
               
               
                 264 
                 rs4429602 
               
               
                 265 
                 rs10505465 
               
               
                 266 
                 rs17061334 
               
               
                 267 
                 rs4438580 
               
               
                 268 
                 rs10505743 
               
               
                 269 
                 rs17061779 
               
               
                 270 
                 rs4440352 
               
               
                 271 
                 rs10506991 
               
               
                 272 
                 rs17062602 
               
               
                 273 
                 rs4442208 
               
               
                 274 
                 rs10507309 
               
               
                 275 
                 rs17063732 
               
               
                 276 
                 rs4443280 
               
               
                 277 
                 rs10507372 
               
               
                 278 
                 rs17063897 
               
               
                 279 
                 rs4445380 
               
               
                 280 
                 rs10507969 
               
               
                 281 
                 rs17066802 
               
               
                 282 
                 rs4451134 
               
               
                 283 
                 rs10510180 
               
               
                 284 
                 rs17069342 
               
               
                 285 
                 rs4452447 
               
               
                 286 
                 rs10510527 
               
               
                 287 
                 rs17070015 
               
               
                 288 
                 rs4461068 
               
               
                 289 
                 rs10510709 
               
               
                 290 
                 rs17071395 
               
               
                 291 
                 rs4469289 
               
               
                 292 
                 rs10510790 
               
               
                 293 
                 rs17071680 
               
               
                 294 
                 rs4478182 
               
               
                 295 
                 rs10511062 
               
               
                 296 
                 rs17072430 
               
               
                 297 
                 rs4480127 
               
               
                 298 
                 rs10511671 
               
               
                 299 
                 rs17072652 
               
               
                 300 
                 rs4483642 
               
               
                 301 
                 rs10512455 
               
               
                 302 
                 rs17074679 
               
               
                 303 
                 rs4489951 
               
               
                 304 
                 rs10512749 
               
               
                 305 
                 rs17079205 
               
               
                 306 
                 rs449077 
               
               
                 307 
                 rs10513169 
               
               
                 308 
                 rs17082035 
               
               
                 309 
                 rs4500099 
               
               
                 310 
                 rs10513316 
               
               
                 311 
                 rs17082406 
               
               
                 312 
                 rs4504735 
               
               
                 313 
                 rs10513600 
               
               
                 314 
                 rs17082882 
               
               
                 315 
                 rs450652 
               
               
                 316 
                 rs10513684 
               
               
                 317 
                 rs17085668 
               
               
                 318 
                 rs4513926 
               
               
                 319 
                 rs10515282 
               
               
                 320 
                 rs17088873 
               
               
                 321 
                 rs451505 
               
               
                 322 
                 rs10516481 
               
               
                 323 
                 rs17089231 
               
               
                 324 
                 rs4540898 
               
               
                 325 
                 rs10517293 
               
               
                 326 
                 rs17089348 
               
               
                 327 
                 rs4541963 
               
               
                 328 
                 rs10518156 
               
               
                 329 
                 rs17099016 
               
               
                 330 
                 rs4542003 
               
               
                 331 
                 rs10518233 
               
               
                 332 
                 rs17100629 
               
               
                 333 
                 rs4545048 
               
               
                 334 
                 rs10518580 
               
               
                 335 
                 rs17101019 
               
               
                 336 
                 rs45573433 
               
               
                 337 
                 rs10518890 
               
               
                 338 
                 rs17101326 
               
               
                 339 
                 rs45574736 
               
               
                 340 
                 rs10520293 
               
               
                 341 
                 rs17101375 
               
               
                 342 
                 rs4558436 
               
               
                 343 
                 rs10520879 
               
               
                 344 
                 rs17101479 
               
               
                 345 
                 rs4559766 
               
               
                 346 
                 rs10521400 
               
               
                 347 
                 rs17112145 
               
               
                 348 
                 rs457417 
               
               
                 349 
                 rs10521761 
               
               
                 350 
                 rs17116121 
               
               
                 351 
                 rs4575127 
               
               
                 352 
                 rs1055300 
               
               
                 353 
                 rs17116968 
               
               
                 354 
                 rs4588690 
               
               
                 355 
                 rs10743150 
               
               
                 356 
                 rs17117895 
               
               
                 357 
                 rs4602844 
               
               
                 358 
                 rs10782775 
               
               
                 359 
                 rs17118223 
               
               
                 360 
                 rs4614050 
               
               
                 361 
                 rs1079384 
               
               
                 362 
                 rs17123673 
               
               
                 363 
                 rs4622794 
               
               
                 364 
                 rs10811817 
               
               
                 365 
                 rs17125182 
               
               
                 366 
                 rs4624663 
               
               
                 367 
                 rs10841280 
               
               
                 368 
                 rs17125478 
               
               
                 369 
                 rs4639045 
               
               
                 370 
                 rs10858044 
               
               
                 371 
                 rs17127960 
               
               
                 372 
                 rs4639092 
               
               
                 373 
                 rs10866057 
               
               
                 374 
                 rs17128116 
               
               
                 375 
                 rs4641724 
               
               
                 376 
                 rs10894631 
               
               
                 377 
                 rs17133162 
               
               
                 378 
                 rs4646583 
               
               
                 379 
                 rs10894740 
               
               
                 380 
                 rs17140460 
               
               
                 381 
                 rs4647255 
               
               
                 382 
                 rs10902671 
               
               
                 383 
                 rs17141070 
               
               
                 384 
                 rs4651133 
               
               
                 385 
                 rs10925642 
               
               
                 386 
                 rs17141233 
               
               
                 387 
                 rs4656427 
               
               
                 388 
                 rs10928474 
               
               
                 389 
                 rs17147659 
               
               
                 390 
                 rs4663621 
               
               
                 391 
                 rs10934891 
               
               
                 392 
                 rs17147932 
               
               
                 393 
                 rs4663942 
               
               
                 394 
                 rs10939840 
               
               
                 395 
                 rs17148348 
               
               
                 396 
                 rs4686131 
               
               
                 397 
                 rs10977642 
               
               
                 398 
                 rs17154851 
               
               
                 399 
                 rs4687402 
               
               
                 400 
                 rs10985311 
               
               
                 401 
                 rs17157492 
               
               
                 402 
                 rs4692073 
               
               
                 403 
                 rs10991911 
               
               
                 404 
                 rs17161478 
               
               
                 405 
                 rs4696333 
               
               
                 406 
                 rs10993282 
               
               
                 407 
                 rs17167011 
               
               
                 408 
                 rs470330 
               
               
                 409 
                 rs11021359 
               
               
                 410 
                 rs17170870 
               
               
                 411 
                 rs4713842 
               
               
                 412 
                 rs11023830 
               
               
                 413 
                 rs17170899 
               
               
                 414 
                 rs4726191 
               
               
                 415 
                 rs11047406 
               
               
                 416 
                 rs17172001 
               
               
                 417 
                 rs4737839 
               
               
                 418 
                 rs11048174 
               
               
                 419 
                 rs17174781 
               
               
                 420 
                 rs4741012 
               
               
                 421 
                 rs11052670 
               
               
                 422 
                 rs17179483 
               
               
                 423 
                 rs4741126 
               
               
                 424 
                 rs1105608 
               
               
                 425 
                 rs17181902 
               
               
                 426 
                 rs4741411 
               
               
                 427 
                 rs1106228 
               
               
                 428 
                 rs17182699 
               
               
                 429 
                 rs4744157 
               
               
                 430 
                 rs11062739 
               
               
                 431 
                 rs17184553 
               
               
                 432 
                 rs4744244 
               
               
                 433 
                 rs1106665 
               
               
                 434 
                 rs17191796 
               
               
                 435 
                 rs474503 
               
               
                 436 
                 rs11071515 
               
               
                 437 
                 rs17192622 
               
               
                 438 
                 rs4760319 
               
               
                 439 
                 rs11079203 
               
               
                 440 
                 rs17193986 
               
               
                 441 
                 rs4763862 
               
               
                 442 
                 rs11111200 
               
               
                 443 
                 rs17194266 
               
               
                 444 
                 rs4767004 
               
               
                 445 
                 rs11124126 
               
               
                 446 
                 rs17194872 
               
               
                 447 
                 rs477188 
               
               
                 448 
                 rs11126472 
               
               
                 449 
                 rs17195147 
               
               
                 450 
                 rs4771973 
               
               
                 451 
                 rs11127757 
               
               
                 452 
                 rs17195948 
               
               
                 453 
                 rs477377 
               
               
                 454 
                 rs11128026 
               
               
                 455 
                 rs17196895 
               
               
                 456 
                 rs4777085 
               
               
                 457 
                 rs11129773 
               
               
                 458 
                 rs17199261 
               
               
                 459 
                 rs4777309 
               
               
                 460 
                 rs11162827 
               
               
                 461 
                 rs17200082 
               
               
                 462 
                 rs4781565 
               
               
                 463 
                 rs11180595 
               
               
                 464 
                 rs17210682 
               
               
                 465 
                 rs4783491 
               
               
                 466 
                 rs11182474 
               
               
                 467 
                 rs17224880 
               
               
                 468 
                 rs4783514 
               
               
                 469 
                 rs11211099 
               
               
                 470 
                 rs17229226 
               
               
                 471 
                 rs4783754 
               
               
                 472 
                 rs11222339 
               
               
                 473 
                 rs17244884 
               
               
                 474 
                 rs4784320 
               
               
                 475 
                 rs1126700 
               
               
                 476 
                 rs17245425 
               
               
                 477 
                 rs4784929 
               
               
                 478 
                 rs11488811 
               
               
                 479 
                 rs17246669 
               
               
                 480 
                 rs4786719 
               
               
                 481 
                 rs11520742 
               
               
                 482 
                 rs17251406 
               
               
                 483 
                 rs4807536 
               
               
                 484 
                 rs11542344 
               
               
                 485 
                 rs17252590 
               
               
                 486 
                 rs4808178 
               
               
                 487 
                 rs11544160 
               
               
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                 rs9831161 
               
               
                 1525 
                 rs16852780 
               
               
                 1526 
                 rs2838443 
               
               
                 1527 
                 rs9839647 
               
               
                 1528 
                 rs16852915 
               
               
                 1529 
                 rs2843705 
               
               
                 1530 
                 rs9842772 
               
               
                 1531 
                 rs16853650 
               
               
                 1532 
                 rs284633 
               
               
                 1533 
                 rs9846767 
               
               
                 1534 
                 rs16856148 
               
               
                 1535 
                 rs286913 
               
               
                 1536 
                 rs9860789 
               
               
                 1537 
                 rs16856802 
               
               
                 1538 
                 rs288266 
               
               
                 1539 
                 rs9879860 
               
               
                 1540 
                 rs16858692 
               
               
                 1541 
                 rs2889718 
               
               
                 1542 
                 rs9883072 
               
               
                 1543 
                 rs16858789 
               
               
                 1544 
                 rs289698 
               
               
                 1545 
                 rs989215 
               
               
                 1546 
                 rs16859945 
               
               
                 1547 
                 rs2904523 
               
               
                 1548 
                 rs9894393 
               
               
                 1549 
                 rs16860912 
               
               
                 1550 
                 rs291939 
               
               
                 1551 
                 rs9897758 
               
               
                 1552 
                 rs16861659 
               
               
                 1553 
                 rs2948653 
               
               
                 1554 
                 rs9913935 
               
               
                 1555 
                 rs16865908 
               
               
                 1556 
                 rs2974020 
               
               
                 1557 
                 rs994426 
               
               
                 1558 
                 rs16867729 
               
               
                 1559 
                 rs2978565 
               
               
                 1560 
                 rs9946654 
               
               
                 1561 
                 rs16868772 
               
               
                 1562 
                 rs300259 
               
               
                 1563 
                 rs9948159 
               
               
                 1564 
                 rs16869867 
               
               
                 1565 
                 rs3008483 
               
               
                 1566 
                 rs9958933 
               
               
                 1567 
                 rs16871128 
               
               
                 1568 
                 rs3025153 
               
               
                   
               
            
           
         
       
     
     Any panel generated using one or more of the criteria provided herein, or any one of the above-listed panels, may be combined with one or more SNPs that predict or correlate with, any other SNP that predicts or correlates with a characteristic used to differentiate individuals. For example, any panel generated using one or more of the criteria provided herein, or any one of the above-listed panels, may be combined with one or more SNPs that predict or correlate with, any other SNP that predicts or correlates with the occurrence of an externally visible trait, biogeographic ancestry and/or kinship to provide a more extensive DNA profile. Moreover, any panel generated using one or more of the criteria provided herein, or any one of the above-listed panels, may be combined with one or more SNPs that predict or correlate with, any other SNP that predicts or correlates with the occurrence of a biological disease or condition, including, but not limited to, youth, age, an increased risk for developing a disease or condition (for example, increased risk of developing cancer or mental senility), blood type, proliferative disease (including cancer), metabolic disease, inflammatory disease, neurological disease, cardiovascular disease, immunological disease (including, autoimmune conditions), respiratory disease, liver disease, kidney disease, intestinal disease and/or infectious disease. 
     Resolving Individual Contributors in Complex DNA Mixtures 
     Voskoboinik and Darvasi described a theoretical method to detect known individuals in complex DNA mixtures by using a panel of 500 to 1,000 SNPs with minor allele frequency of around 0.05. They showed that a known individual can be reliably detected with low false match probability in DNA mixtures of up to 10 people. 
     By way of illustration, a 1,000 SNP panel for a given individual (referred to as subject 1), is depicted in  FIG.  1   , in which the location of a black line indicates the presence of a minor allele SNP at that locus. This resultant pattern of black lines is statistically unique to this individual to within a vanishingly small number (&lt;10-40). A mixture of 5 peoples&#39; DNA, including subject 1, when analyzed with this “barcoding” method appears as shown in  FIG.  2   . The barcode pattern is more filled in, that is, more loci have a minor allele SNP present because of the combined contribution of the 5 people. Using the methods described by Voskoboinik and Darvasi, if subject 1&#39;s SNP profile is known, the methods of the disclosure can reliably detect the presence of subject 1 in this mixture with a low false match probability (&lt;10-15). A substantial limitation of the approach of Voskoboinik and Darvasi arises when the user doesn&#39;t have a reference SNP profile to compare to the DNA mixture, but wants to determine the individual contributors&#39; SNP profiles for direct comparison to other forensic reference samples/profiles. 
     The central principle underlying the methods of the disclosure is the ability to confirm the contributions of common unknown individuals to multiple complex DNA mixtures when DNA SNP profile of any of the individual contributors is not known a-priori. This ability provides more than just a significant improvement over existing methods (e.g. Voskoboinik and Darvasi), but rather a new capacity to analyze mixtures that would have been impossible to resolve prior to the development of the SNP panels and methods of the disclosure. 
     The methods of the disclosure measure the intersection, or overlapping population of genetic markers, e.g. minor allele SNPs, across multiple DNA mixtures. Due to statistical random chance, a certain number of SNPs will be shared by different individuals. For any SNP at a given loci, the probability that it will be shared by chance across multiple mixtures decreases as the number of mixtures considered increases if each individual is only occurs in one of the considered mixtures. However, if the same individual is a DNA contributor in all of the mixtures, then the probable number of shared loci across those mixtures will increase and should include some or all of the shared individual contributor&#39;s minor alleles. For example, after comparing five 5-person DNA mixtures with one common contributor across them, subject 1&#39;s  127  SNP profile can be reliably reproduced to within 11 SNPs (shown in  FIG.  3   ). The image depicted in  FIG.  3    is identical to subject 1&#39;s profile shown in  FIG.  1   , the profile depicted in  FIG.  3    having only 11 extra SNPs. 
     The methods of the disclosure use vector multiplication to find common SNPs across data sets (for instance, each complex DNA mixture may be considered a data set) to build an individual profile from an analysis of multiple complex DNA mixtures. According to these methods, the presence of a minor allele SNP is represented by the value 1 and its absence by a zero in the data. For example, to compare three DNA mixtures, these methods multiply the first two mixtures&#39; SNP panels together, and then multiply that product by the third mixture to find the common minor allele SNPs shared among all three mixtures. By counting the number of shared SNPs, these methods can estimate whether the data sets (or complex DNA mixtures) have zero, one or more contributors in common. 
     Significantly, the methods of the disclosure provide an ability to build individual profiles from complex DNA mixtures without any “known” individual profiles or data from any of the contributors to the complex DNA mixture. This important feature of the methods of the disclosure enable the user to build individual profiles from complex DNA mixtures that would have been impossible prior to the development of the SNP panels and methods described herein. 
     Direct Devolution of Complex DNA Mixtures to Individuals 
     Using single nucleotide polymorphisms (SNPs) sequenced from a panel of loci on the human genome, the disclosure provides a method for direct deconvolution of a complex DNA mixture to individual contributors and/or components. According to embodiments of these methods, at each locus, a minor allele ratio (mAR) is calculated as the number of sequences called with that locus&#39; minor allele, divided by the total number of observed sequences at that locus. For an individual DNA profile, mARs typically fall around 0 (homozygous major), 0.5 (heterozygous) or 1.0 (homozygous minor). For a mixture of DNA contributors, mAR ranges between 0 and 1.0. Within mixtures, the observed mAR values directly correlate with the number of contributing individuals and their relative DNA molar concentrations. These correlations can be leveraged to identify the presence of and/or separate individual contributors&#39; DNA profiles. 
       FIG.  4    demonstrates a typical mAR plot for a mixture of two individual DNA profiles, combined in a DNA molar ratio of 4:1. Two partial DNA profiles are visible in  FIG.  4   . Both contributors&#39; homozygous major alleles fall around a mAR of 0.0. Minor alleles separate into two bands centered on mAR=0.1 and mAR=0.5, corresponding to the two non-equimolar contributors. These unique, individual profiles can be independently extracted and compared against reference DNA profiles or additional deconvoluted mixtures for identification. If an extracted minor allele band matches a reference SNP profile with high confidence, the individual contributor is identified. If the band has a high proportion of minor allele matches with a band extracted from a different mixture, this suggests that there is a common contributor to both mixtures and the two allele bands can be combined to provide a more complete DNA profile for that unknown contributor than could be obtained from analysis of a single mixture. This principle is demonstrated in  FIG.  5   . 
     Calculating Probability of Random Man not Excluded 
     In parallel to deconvolution, the forensic standard false inclusion metric, the probability of a random man not excluded, P(RMNE), can be calculated directly from the profiles generated from the methods of the disclosure. P(RMNE) quantifies the likelihood of falsely identifying a random individual from the population present in the mixture. For example, homozygous major allele profiles are extracted and, in conjunction with population-averaged minor-allele frequencies, define the parameters for a P(RMNE) calculation. 
     The disclosure provides a model to declare and/or determine whether an individual is present within a mixture while accounting for mismatched alleles. Minor allele calls are compared between an interrogatory sample and a mixture, declaring each locus a match or mismatch. To account for potential sources of non-trivial error, the method provides a detection module that allow for one or more mismatches. For this reason, an individual as a whole is declared “present in mixture” if the number of mismatches is small, or declared “absent from mixture” if the number of allele mismatches is large. Selection of an optimal minor allele mismatch level involves balancing true detection sensitivity and false-positive inclusions. 
     If at any particular locus, both the individual and the mixture contain a minor allele, a match is declared for that locus. However, if an individual presents with one or more minor alleles at a particular locus but the mixture appears homozygous major, a mismatch is called. The rare case where a mixture is called homozygous minor at a locus is also considered; a match is called for a homozygous minor or heterozygous individual, and a mismatch otherwise. 
     A model to evaluate P(RMNE) for any number of allowed allele mismatches, considering variance in mAF between loci, has been developed. To ensure a precise calculation of the P(RMNE) value, four methods are calculated and compared:
         Direct Evaluation of the probability distribution function (pdf)   Approximation of the pdf via a binomial distribution (see also Voskoboinik and Darvasi)   Exact calculation of the pdf utilizing the Discrete Fourier Transform—Characteristic Function (DFT-CF) method, and   A Monte Carlo simulation.       

     Previously, the probability of a random man not excluded has been formulated by Voskoboinik and Darvasi as: 
     
       
         
           
             
               
                 
                   
                     P 
                     ⁡ 
                     ( 
                     
                       R 
                       ⁢ 
                       M 
                       ⁢ 
                       N 
                       ⁢ 
                       E 
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ∏ 
                         
                           i 
                           = 
                           0 
                         
                         S 
                       
                       
                         
                           ( 
                           
                             1 
                             - 
                             
                               p 
                               i 
                             
                           
                           ) 
                         
                         2 
                       
                     
                     ≈ 
                     
                       
                         P 
                         
                           _ 
                         
                       
                       
                         2 
                         ⁢ 
                         S 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     A mixed DNA sample is genotyped at N SNP loci where S is the number of homozygous major loci in a mixture, is the population estimated mAF of allele i and is the average mAF taken across all S loci. This model of false inclusion assumes all minor allele-containing loci must match between a reference and a mixture. If all N-S alleles match, then a reference DNA sample will be called homozygous major with probability at every locus called homozygous major in the mixture. A subject can be excluded from a mixture at a particular locus if they have a minor allele when that locus is homozygous major in the mixture. Exclusion due to homozygous minor loci in the mixture is about three orders of magnitude less likely than exclusion due to homozygous major loci (Voskoboinik and Darvasi). Allele mismatches are not considered in this equation. As mentioned by Voskoboinik and Darvasi and described previously, averaging minor allele frequencies using the approximation in equation 1 boosts computational speed of evaluating P(RMNE), at the cost of a reduction in the model&#39;s accuracy. This approximation of P(RMNE) in equation 1 is valid for small mixtures with no sequencing error. However, the model is not accurate enough for forensic admissibility. A more precise model considering allele mismatches and allele specific mAFs is required. 
     Rather than fix an estimated allele call error rate as in Voskoboinik and Darvasi the approximation in equation 1 can be improved to include allele mismatches by rewriting as a binomial distribution: 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       M 
                     
                     ( 
                     
                       R 
                       ⁢ 
                       M 
                       ⁢ 
                       N 
                       ⁢ 
                       E 
                     
                     ) 
                   
                   ≈ 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         0 
                       
                       M 
                     
                     
                       
                         
                           
                             
                               P 
                               
                                 _ 
                               
                             
                             
                               2 
                               ⁢ 
                               k 
                             
                           
                           ( 
                           
                             1 
                             - 
                             
                               P 
                               
                                 _ 
                               
                             
                           
                           ) 
                         
                         
                           2 
                           ⁢ 
                           
                             ( 
                             
                               S 
                               - 
                               k 
                             
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               S 
                             
                           
                           
                             
                               k 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
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     Where M is the maximum number of allowed mismatching loci. M greater than zero results from any number of deficiencies in the genotyping process such as drop out, low copy number, amplification, sequencing errors and others. For equation 2, P(RMNE) is approximated as a Binomial distribution with a “probability of success” equal to the average minor allele frequency across all forensically valid loci, Using this improvement over equation 1, PM(RMNE) can be quickly evaluated for all M less than S. Given a desired probability of false inclusion tolerance t, a threshold can be placed on the maximum number of allowed allele mismatches, M, such that PM(RMNE)&lt;t. 
     The probability of a random man not excluded can be further improved to include both locus-dependent mAFs, the inclusion of possible mismatches where the mixture is homozygous minor and the suspect is not, and an arbitrary number of allele mismatches: 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       M 
                     
                     ( 
                     RMNE 
                     ) 
                   
                   = 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         0 
                       
                       M 
                     
                     
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                       ⁠ 
                       
                         
                           
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                               A 
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                                   A 
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                               B 
                               k 
                             
                           
                           
                             
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                                 i 
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                                   k 
                                 
                               
                             
                             
                               
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     Where represents all sets of (S-k) loci wherein both the individual and the mixture are called homozygous major and represents all sets of k loci wherein the individual is called with one or more minor alleles and the mixture is called homozygous major. Similarly, let Q equal the number of alleles wherein the mixture is called homozygous minor (mAR&gt;0.99). represents all sets of (Q-k) loci wherein both the individual and the mixture are called homozygous minor and represents all sets of k loci wherein the individual is called with less than two minor alleles and the mixture is called homozygous minor. In practice, Q is observed as zero and equation 3 reduces to: 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       M 
                     
                     ( 
                     RMNE 
                     ) 
                   
                   = 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         0 
                       
                       M 
                     
                     
                       
                         ∏ 
                         
                           A 
                           k 
                         
                       
                       
                         
                           ∏ 
                           
                             i 
                             ∈ 
                             
                               A 
                               k 
                             
                           
                         
                         
                           
                             
                               ( 
                               
                                 1 
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                                   p 
                                   i 
                                 
                               
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                                   c 
                                 
                               
                             
                             
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                                     p 
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                   ) 
                 
               
             
           
         
       
     
     The cumulative distribution function (cdf), evaluated over a range of M mismatched loci, presented in equation 4 is equivalent to the Poisson-Binomial distribution where the probability of a homozygous major allele call, defines the probability of success for trial i. Equations 3 and 4 directly calculate the probability that a random individual, with T minor alleles, has M mismatching and T-M matching minor allele loci for all combinations of possible mismatching alleles. This is a powerful tool allowing a user to immediately quantify, for a given mixture, how the choice of the number of allowed mismatched loci due to all sources of analytical error affects the likelihood that a random individual would be falsely called “present in mixture”, or the P(RMNE). This will also lend confidence to the judicial system that P(RMNE) is being accurately calculated for imperfectly matching data. 
     While this generalization adds precision to previous models, equation 4 requires computing all combinations of M mismatching loci over S-M homozygous major loci must be considered. This creates a large computational running time prohibiting calculation for large k. To be precise, the cost of evaluating this distribution function for M mismatching loci is—a polynomial algorithm. Calculating this probability distribution function for M=4 and N=299 on a MacBook Pro with 4 GB of RAM and an Intel 2.7 GHz i7 takes upwards of an hour. 
     To mitigate the long running time of direct calculation but retain the fidelity of the Poission-Binomial model, the DFT-CF method of evaluating the Poisson-Binomial distribution is utilized (see also Hong, Yili. Computational Statistics &amp; Data Analysis, Volume 59, March 2013, Pages 41-51). It is an exact method, simultaneously evaluating the above probability distribution function for all in running time. The same MacBook Pro is able to evaluate the RMNE for any number of mismatches in seconds. A faster formulation for P(RMNE) with higher precision has been formulated (MIT 19461L). 
     EXAMPLES 
     Example 1: Selection of SNP Markers 
     Four exemplary panels of SNPs are described herein. Three of these panels were used for mixture analysis: the 480 panel; the 975 panel; the OptMix panel. The OptMix panel is a subset of the Kinship panel, which was designed to assess the degree of relatedness between two people from DNA samples. 
     The 480 panel: Amplification was performed using Fluidigm Access Array. Loci were selected as follows: 
     FST &lt;0.06: Poor correlation between ancestry and genotype on ALFRED database 
     Average Heterozygosity=0.058-0.13 on ALFRED (should correspond to MAF˜0.03-0.07) 
     No health related data on SNP in the NIH/NCBI dbSNP database 
     mAF=0.03-0.07 on dbSNP database 
     Average heterozygosity=0.058-0.13 on dbSNP (should correspond to MAF 0.03-0.07), meaning that the alleles are relatively rare in the population 
     Elimination of duplicate SNPs and ambiguously mapped SNPs. 
     Minimum distance between alleles of 500,000 bases (of NCBI build 37)=1430 SNPs. 
     Selected 950 SNPs, 530 of which were compatible with Fluidigm DNA amplification platform 
     The 975 panel: Amplification was performed using Ampliseq. Same process as described for the 480-panel, however, include all 1430 SNPs rather than selecting from this group the 950 SNPs used in the 480-panel. 
     Kinship panel: Amplification was performed using Ampliseq. Similar criteria as described for the 480-SNP panel, with the following distinctions: 
     mAF between 0.01 and 0.3 
     Distance between loci &gt;110,000 bp 
     OptMix panel: Amplification was performed using Ampliseq. Similar criteria as described for the Kinship panel, with the following distinctions: 
     Distance between loci &gt;500,000 
     mAF&lt;0.06 
     Delete loci that tend to give ambiguous results (mAR not at expected values in reference samples) 
     Delete loci that tend to produce a low number of reads (&lt;10% of the average number of reads/locus) 
     Delete loci that produce impossible results in known family tree 
     Delete loci that tend to generate data from only one strand of DNA. 
     Example 2: Deconvoluting/Resolving Complex DNA Mixtures 
     The forensic standard false inclusion metric, the probability of a random man not excluded, P(RMNE), can be calculated directly from the profiles generated from the methods of the disclosure. P(RMNE) quantifies the likelihood of falsely identifying a random individual from the population present in the mixture. For example, homozygous major allele profiles are extracted and, in conjunction with population-averaged minor-allele frequencies, define the parameters for a P(RMNE) calculation. The mathematical formula for this calculation is shown in  FIG.  6   . 
       FIG.  9    shows the results from a mixture analysis using 468 SNPs with a minor allele frequency of approximately 0.05. For this analysis, mixtures containing equal amounts of DNA from 8, 5, 3, 10 and 15 individuals were amplified using Fluidigm multiplexed PCR technology and sequenced on Ion Torrent PGM. Calculations of probability of detection vs. P(RMNE) demonstrate that a P(RMNE) of less than 10-9 can be achieved in a 3-5 person mixture with minimal detriment to the probability of detection (Pd) ( FIG.  10   ). 
       FIG.  11    shows the results from a mixture analysis using 975 SNPs with a minor allele frequency of approximately 0.05. Mixtures containing equal amounts of DNA from 8, 10, 15, and 20 individuals were amplified using Ampliseq multiplexed PCR technology and sequenced on Ion Torrent PGM. Calculations of probability of detection vs. P(RMNE) demonstrate that a P(RMNE) of less than 10-9 can be achieved in a 8-10 person mixture with a Pd of 1 ( FIG.  12   ). 
     REFERENCES 
     
         
         Ballantyne, K. N. et al., 2012, For. Sci. Int. Gen., 6:208-218. 
         Buckleton, J. S. et al. Forensic DNA Evidence Interpretation, CRC Press, Boca Raton, 2005. 
         Eriksson, N. et al., PLOS Genetics, 2010, e1000993. 
         Hong, Yili. On computing the distribution function for the Poisson binomial distribution. Computational Statistics &amp; Data Analysis, Volume 59, March 2013, Pages 41-51, ISSN 0167-9473. 
         Kidd, K. K. et al., 2012, For. Sci. Int. Gen., 6:646-652. 
         Liu, F. et al., PLOS Genetics, 2012, e1002932. 
         Nassir, R. et al., 2009, BMC Genetics, 10:39. 
         Pakstis et al. Hum Genet (2010) 127:315-324. 
         Tian C, et al. (2008) PLoS Genetics 4(1): 29-39. 
         Voskoboinik, L. and Darvasi, A. Forensic Identification of an Individual in Complex DNA Mixtures. 2011. Forensic Science International: Genetics 5:428-435. 
         Walsh, S. et al., 2011, For. Sci. Int. Gen., 5:170-180. 
       
    
     All publications, patents and sequence database entries mentioned herein, including those items listed below, are hereby incorporated by reference for the teachings referenced herein as if each individual publication or patent was specifically and individually indicated to be incorporated by reference. In case of conflict, the present application, including any definitions herein, will control. 
     Advanced DNA Forensics Software Platform 
     According to various embodiments, one or more functions may be performed using a DNA forensics software platform as more fully described below. It is appreciated that DNA forensics is transitioning from sizing of short tandem repeat (STR) alleles to high throughput sequencing (HTS) of STRs and/or single nucleotide polymorphisms (SNPs). DNA microarrays also provide an inexpensive method for rapidly characterizing hundreds of thousands to millions of SNPs in a sample. The significant increase in number of DNA loci cannot be handled by current forensics solutions. Below is described describes an advanced DNA forensics software platform that enables one or more of the following functions:
         (1) Identification   (2) Kinship identification   (3) Mixture Analysis   (4) Saturated Mixture Analysis   (5) Identification of Trace Profiles   (6) Biogeographic Ancestry (BGA) prediction   (7) Phenotype/Externally Visible Trait (EVT) prediction   (8) Geolocation   (9) Medical Genetics   (10) Mixture Deconvolution   (11) Mixture-to-Mixture Analysis   (12) Identification of Unknowns   (13) sample annotation   (14) multi-site networking   (15) data security   (16) system backup, and more ( FIG.  1   ). Key concepts are the integration of advanced DNA forensics modules into a unified system with a local database that coordinates with other sites. One example system architecture uses a web-based solution with web services.  FIG.  13    shows an advanced DNA forensics system modules and example architecture.
 
Details
       

     Forensics samples can be characterized by HTS sequencing pipelines or DNA microarrays  1 .  FIG.  2    illustrates the high level steps of sample sequencing and HTS raw data processing to detect sequence variants.  FIG.  14    shows and example sample characterization pipeline according to various embodiments. 
     Genomic Sequence Variants 
     Human cells contain nuclear DNA and mitochondrial DNA. Cells typically have multiple mitochondria per cell. Unrelated individuals typically have on the order of four million single nucleotide polymorphisms (SNPs) variations, differences in short tandem repeats (STRs) sequences, copy-number variations (CNVs), and other types of sequence differences. Multiple technologies have been developed to characterize DNA sequence variants. These individual sequence variants have important forensics applications. 
     Whole Genome Shotgun (WGS) DNA Sequencing 
     High Throughput Sequencing (HTS) whole genome sequencing (WGS) generates random coverage of the nuclear genome. WGS methods generate sequences to cover the target&#39;s genome with X-level of coverage. The depth of coverage and sequence quality determine the detectability of variants and the accuracy of the sequence data. Some WGS datasets with shorter sequence lengths may not be long enough to characterize some of the longer STR alleles. 
     Exome Sequencing 
     HTS exome sequencing targets the exons of genes and nearby flanking sequences. Gene, promoter, splicing, and coding sequence variants may impact gene expression, splicing, or function. Characterizing functional variants for individuals is restricted in some jurisdictions for forensics applications. Advanced DNA forensics system can have capabilities for characterizing functional variants that can be disabled/hidden depending upon legal jurisdictions. 
     DNA MicroArray Sequencing 
     DNA microarrays can characterize four million or more SNPs and identify CNVs in samples. Phasing of linked SNPs is possible to create individual chromosome haplotypes and microhaplotypes. Haplotypes and microhaplotypes have applications in kinship and biogeographic ancestry prediction. This is an alternate technology to HTS variant characterization method. 
     HTS Single Nucleotide Polymorphism (SNP) DNA Forensics 
     HTS can detect SNP variants and linked variants (microhaplotypes). SNP or combined SNP and STR panels have been designed for thousands to tens of thousands of loci2. 
     Short Tandem Repeats (STRs) Forensics 
     Capillary electrophoresis sizing of STRs is the current standard for DNA forensics. Sizing STRs works well for samples from individuals and some mixtures with two contributors. A few mixtures with three or four contributors have been able to be analyzed, but it advised against analysis for DNA forensics. FITS sequencing of STRs determines STR allele sequences and linked variants. Encountered issues are variants in flanking sequences, novel STR alleles, sequencing artifacts, sequencing errors, and PCR artifacts3. Known and novel STR alleles should need to be named consistently. Known STR alleles for some loci can be obtained from the NIST STRbase4. Illumina currently markets the ForenSeq panel5,6 of combined STRs and SNPs. 
     Insertion/Deletion DNA Forensics 
     Like SNPs, insertions or deletions of DNA can be used as variants for differentiating individuals. 
     Mitochondrial DNA (mtDNA) Forensics 
     Whole or targeted mitochondrial genomes can be sequenced7. Mitochondrial DNA is valuable for the analysis of degraded DNA samples for suspect or remains identification, kinship analysis, and biogeographic ancestry prediction. 
     Microhaplotypes 
     Closely linked variants define microhaplotypes8 that can be used as genetic markers. 
     Data Processing 
     In certain specific embodiments, the advanced DNA forensics system processes the variants characterized by multiple technologies: CE sized STRs, microarrays, FITS data, etc. Some of the data formats to be supported include: BAM (binary sequence alignment/map) or FASTQ, Variant Call Format (VCF), Illumina GenomeStudio software data export, Illumina ForenSeq Excel files, etc. 
     HTS Analysis Pipeline 
     The HTS data analysis pipeline takes as input both BAM and FASTQ files for variant characterization for targeted SNP and STR loci. Sequence data will come from Ion Torrent/Thermal Fisher, Illumina, Roche, PacBio, Oxford, etc., sequencers. The analysis pipeline identifies SNP and STR alleles, sequence counts, counts by strand, and linked SNP variants (microhaplotypes) in flanking sequences. 
     Experiments &amp; Samples 
     High throughput sequencers can generate from 4 million to over 8 billion sequences per run. The number of samples sequenced at a time varies from a single sequence to multiple parallel lanes of multiplexed samples. Individual samples within a multiplexed experiment are marked by short DNA barcodes added to the 5′ and sometimes 3′ ends of DNA for samples. Samples may be reference samples from known individuals or unknown samples collected from objects, clothing, food, etc. Sample annotation on samples can be collected and managed within the advanced forensics DNA software platform or may be managed in external systems with sample names or reference links connecting the characterized samples with forensics DNA samples. Annotation on individuals may be extensive, including name, age, appearance, photographs, fingerprints, known relatives, etc. Sample annotation can also contain information on site of collection, location coordinates, date of collection, photographs, etc. 
     Applications 
     When samples are characterized by different techniques, sample profiles from one data source can be compared with data from other sources when sufficient numbers of shared loci exist. 
     Identification 
     Search a sample against the set of known individual reference profiles to identify matches to known samples/individuals. Searching of SNP or STR sample profiles will be implemented. Searching of sample profiles across different panels is possible when a sufficient number of loci are common in both panels. 
     Implementation: The MIT application “Extremely Fast Forensics HTS DNA SNP and STR Sequence Analysis” (MIT case #18133L, Appendices A and B) shows an example of the identification search methodology. 
     Mixture Analysis/Mixture Search 
     Search a reference sample against a set or database of profiled mixture samples to determine if an individual contributed DNA to the mixture sample (reference-to-mixture) 9 . Search a mixture against a set or database of profiled reference samples to determine the contributors to the mixture (mixture-to-references). Search a mixture against a set or database of profiled mixture samples to determine the mixture samples with common individual contributors (mixture-to-mixtures). MIT case #18133L method implements each of these mixture analysis methods: reference-to-mixtures, mixture-to-references, and mixture-to-mixtures.  FIG.  3    illustrates mixture analysis with STR sequences for 3 (Mix03p), 4 (Mix04p), 5 (Mix05p), and 12 (Mix12p) contributor mixtures with counts of called reference STR alleles not matched in each mixture.  FIG.  15    shows one example of an STR mixture analysis. 
     Analysis of Saturated Mixtures 
     Identification of one or more individuals in saturated mixtures (mixtures with large numbers of DNA contributors such that more than 70% of the SNPs have observed minor alleles) by leveraging differences in DNA contributor concentration differences to identify profiles of major DNA contributors to the saturated mixture (MIT 19785L, Appendix D). 
     Identification of Individuals with only Trace DNA Profiles present in DNA mixtures 
     An individual may contribute one, two, or more, or a fraction of a cell&#39;s DNA to a forensic sample. These are referred to as trace profiles. The advanced forensics system contains methods for identification of trace profiles within DNA mixtures and identifying them as unknown or matching them to known reference samples (MIT 19786L, Appendix L). 
     Mixture Deconvolution Methods 
     Advanced DNA forensics of mixtures includes multiple methods to identify individuals in mixtures without known reference samples. 
     The Plateau mixture deconvolution method (e.g., discussed herein) leverages imbalances in DNA concentrations between contributors to determine individual profiles. This method applies to mixture profiles of SNPs or STRs.  FIG.  16    illustrates the Plateau method applied to a mixture of two individuals with DNA concentrations of 100 to 1. 
     The Venn mixture deconvolution method (e.g., Appendix N) applies Venn set logic to DNA mixtures to identify individuals or overlapping individuals between one, two, or more mixtures.  FIG.  17    illustrates a Venn method applied to four mixtures with the identification of four of the six DNA contributors. 
     The Venn Matrix mixture deconvolution method (MIT 19092L Appendix E) first leverages identification of individuals within a set of mixtures, subtracting their profiles, and then applying the Venn mixture deconvolution method to identify novel mixture contributors with no known reference samples. 
     Detection of Unknowns 
     The Venn, Plateau, and Venn Matrix methods can identify unknown profiles in DNA mixtures (MIT 19127L, Appendix G). 
     Mixture-to-Mixture Analysis—Multiple samples &amp; sites Analysis (e.g., MIT 19093L, Appendix F) 
     Frequently, people of forensic interest appear in multiple samples and/or locations. The mixture-to-mixtures analysis approach enables the visualization of overlap between individuals and multiple mixtures (as shown in  FIG.  18   ). 
     Estimating Number of Individuals in mixtures 
     Forensic analysts need to identify the number of contributors to DNA mixtures for proper estimation of statistical significance of profile matches for some analytical methods. Due to variability between individuals and chance, this is a difficult problem. The amount of trace DNA left by individuals on touch samples include high DNA shedders, variable DNA shedders, and low DNA shedders. Low DNA shedders can be difficult to detected or undetectable in some touch samples. Machine learning algorithms can estimate the number of contributors in mixtures based on either SNP profiles ( FIG.  19   ) or STR profiles ( FIG.  20   ). 
     Estimating the relative contributions of individuals of DNA to mixtures 
     The relative concentrations of contributors to a forensics sample can be estimated using the relative strengths of the amplified alleles ( FIG.  21   ). Three additional methods for estimating DNA contributor DNA concentrations are described in Appendix H (MIT 19399L). 
     Gender Prediction 
     The gender of an individual can be predicted for single contributor samples by examining SNP or STR loci on the X and Y chromosomes outside of the pseudoautosomal regions (PAR) shared by the sex chromosomes. Females will have 1 or 2 alleles (major:major, major:minor, and minor:minor); and males for these loci should only have 1 allele. For non-PAR Y chromosome loci, females should not have any read counts and males should have 1 allele. Duplication events on the Y chromosome are common and some Y loci may have 2 alleles for males. Unusual combinations of sex chromosomes should also be considered for women who might have 1 or 3 X chromosomes (Turner syndrome:X—1:2,000 to 1:5,000 or Triple X syndrome:XXX—1:1,000) or men with 2 X or 2 Y chromosomes (Klinefelter syndrome:XXY 1:500 to 1:1,000 and XYY—1:1,000). 
     Kinship 
     Shared DNA by inheritance can be used to predict kinship between related individuals. Autosomal, mitochondrial, X and Y chromosome inheritance, and microhaplotype sharing of alleles can inform kinship predictions. Mothers pass their mtDNA genome to all of their children. Fathers pass their Y chromosome and in some cultures their last name to their sons. A child inherits half of their genetics from each of their parents. The KinLinks application illustrates application of kinship prediction using HTS SNP panels 10 . Two methods for rapid (MIT 19709L, Appendix K) and precise Bayesian (Appendix 0) predictions of kinship are also disclosed. 
     Surname Prediction 
     In some instances, it is possible to predict likely last names of individuals directly from Y chromosome loci profiles  11 . 
     Biogeographic Ancestry (BGA) 
     Being able to predict the biogeographic ancestry (BGA) of an individual from a DNA sample ( FIG.  22   ) has multiple forensics applications from remains identification to narrowing suspect profiles with exclusion of non-matching ethnicities. 
     Externally Visible Traits (EVTs)/Phenotype 
     Appearance and phenotype are determined by genetic variants. Variants have been characterized for predicting eye color, hair color, hair texture, nose structure, and additional facial features. Attempts are underway to predict facial appearance from DNA. Daniel describes the SNaPshot system for forensic phenotyping including BGA prediction. 
     Medical Genetics 
     Medical conditions also have forensics applications, but may not be permissible to ascertain in some legal jurisdictions. Some sequence variants contribute directly to medical conditions. For example, knowing that a suspect is lactose intolerant may enable to reduction of candidate suspects to a smaller set. 
     Geolocation 
     DNA from microorganisms (bacteria, archaea, fungi), plants, insects, and animals may be present in samples. The geographic distribution of these organisms may enable the geolocation prediction of sample origin or sample history. 
     Statistics 
     Linkage disequilibrium between two DNA loci indicates linkage of alleles by population structure or physical linkage nearby on the same chromosome. 
     Random match probability (RMP) is the probability that two unrelated individuals have identical genotypes by chance alone. 
     Random-Man-Not-Excluded P(RMNE) or Combined Probability of Inclusion (CPI) attempts to explain the occurrence of the observed alleles on a statistical basis, treating each allele independently using population allele frequencies. 
     Likelihood Ratios (LR) 13 —ratio of probabilities that the DNA in the profile is from the suspect over the probability of the profile is from a random individual. 
     Minor Allele Count method 
     The counts of minor allele reads (MAC) can be used as an equivalent or an alternative to the minor allele ratio (mAR) approach described in this document (MIT 19787L, Appendix M). 
     System Details 
     The advanced DNA forensics system may include the following system features:
         User authentication &amp; authorization   Usage logging   Parameter setting tracking of settings used   User controls   Parameter settings   Algorithm role access   BGA, EVTs, Medical genetics   Disable features in some locations   User role-based access control   System Operating modes   Research—all settings available   Forensics—certain settings locked down so that user must use validated settings for sample analysis   Networking between sites   Data can be exchanged between network sites using web services   System maintenance   User administration interfaces for maintaining system, updates   System troubleshooting, logs   Data backup, export, and import   Data encryption   Data export   CODIS compatible output format
 
Database Design
       

     The standard of universally unique identifier (UUID) 14  will be adopted to enable distributed instances to uniquely identify information without any central coordination. If the UUID is used as a primary database table key, there is an additional performance consideration when inserting new database table records with the UUIDs likely in random order versus the standard incrementing order that comes with an auto-incrementing integer primary key. To avoid this, each database table will be designed with both an auto-incrementing integer primary key followed immediately by a UUID primary key with associated index table. All foreign keys (references by other database tables) will be to the UUID primary key and not to the integer primary key. This design strategy enables easy data exchange between sites without impacting database performance. The result is that all data at each site will be uniquely identified and portable to any other site. 
     The initial data model concepts are illustrated next and in  FIG.  23 A-C . The “Ref:” subfields are references to other data models.
         Site—geographic BIP-IT designation   Ref: location   Site name   User—BIP-IT user; site-specific   Ref: site   User name, account, etc.   Log—activity log   Ref: user   Action &amp; timestamp   Data files/Results—data files   Ref: site   File details   Instrument   Instrument name, type   Experiment—supports multiplexing of samples   Ref: site   Name, type, notes, run date   Barcode—DNA sequence identifier for a multiplexed sample   Name, sequence   Sample—individual DNA sample—reference, mixture, etc.   Ref: site, experiment, barcode   Name, type, details   Person—an individual within a DNA sample   External id(s)—to enable higher level data fusion with other systems   Genotype—XY, XX, XYY, etc.   Location—coordinates   Latitude, longitude, MGRS (military grid reference system)   Algorithm—software algorithm   Name, version, updated at   Parameter—parameters for software algorithms   Ref: algorithm   Name, limits, default value   Folder—file system like folders for tracking samples of interest   Ref: site, user   Name   Relative—relationship between two individuals   Ref: two People, algorithm   Relationship, related, degree, confidence   Ancestry—biogeographic ancestry prediction   Ref: person, region, algorithm   Fraction, confidence   Region—geographic region or ethnic/racial group   Ref: location   Name, type, country, continent   Phenotype—externally visible trait prediction   Ref: algorithm   Trait name, trait value, prediction, confidence   Locus—genetic location   Name, chromosome, position   Panel—collection of genetic loci   Name, type, SNP count, STR count, loci   STR Allele—identified STR alleles   Ref: locus, STR   Name, sequence, STR pattern (regular expression), is novel   Sample Data   Ref: sample, panel   Sample data—SNPs &amp; STRs, data type   Mask   Ref: sample, panel, sample data   Sample data bit mask   Population Frequencies—population frequencies for SNPs and STRs   Ref: source, locus, region   Frequency   Linked—linking, phasing, and micro-haplotypes of genetic markers   Ref: sample   Organisms (Geolocation)—non-human organisms identified in sample   Name, taxonomy   Hit   Ref: sample 1 , sample 2 , mask 1 , mask 2     Comparison details   Source   Name   Disease   Disease name, Online Mendelian Inheritance in Man 15  (MIM ID)   Gene   Ref: source, organism   Name, symbol, NCBI gene ID, chromosome   Disease Gene   Ref: disease, gene   Biosequence   Ref: organism   Type, accession, protein sequence, mRNA sequence   Structure   Ref: organism   Structure name, PDB entry, resolution   Residue   Ref: structure   Residue, structure atoms   Genetics—additional data   Mapping tables—linking data between tables       

     Various embodiments and aspects may be practiced alone or in combination with any other aspects or embodiments described herein. 
     Detecting Multiple Individuals with High Confidence in Saturated Mixtures 
     High throughput sequencing of DNA single nucleotide polymorphism (SNP) panels has significant advantages for analysis of DNA mixtures. Isaacson et al. (Robust detection of individual forensic profiles in DNA mixtures. Forensic Science International: Genetics 14, 31-37) describe how to analyze complex DNA mixtures with many individual contributors. This approach leverages SNPs with low minor allele to major allele population ratios. For very high numbers of individual contributors, the number of minor alleles present in the mixture saturates most SNP loci. This creates challenges for current mixture analysis approaches resulting in no detection of contributing individuals or lower significance of detections. Detection of individuals in saturated mixtures is an unsolved forensics community need. Various embodiments described herein provide techniques for confidently identifying individuals in saturated DNA mixtures. 
     Most SNPs have two alleles which occur with different allele frequencies in a population. The most common allele for a given SNP is called the major allele, and the least common allele is called the minor allele. The DNA profile of an individual can be matched to a DNA mixture by comparing the individual&#39;s minor alleles to the mixture. When a sufficient number of the SNP loci where the individual has a minor allele also have the minor allele in the mixture, then that individual can be identified in the mixture. The confidence of this identification is inversely proportional to the number of loci where the individual has a minor allele but the mixture only contains major alleles, or likely mismatches. 
     A DNA mixture is said to be saturated if it has a minor allele at so many of its SNP loci that nearly any individual could be identified in the mixture. In this case, current mixture analysis cannot identify any individuals with high confidence. 
     Individuals frequently contribute different amounts of DNA to DNA mixtures. As a result, the number of reads of a minor allele at a given SNP locus is proportional to the contribution percentages of each person in the mixture who has a minor allele at that locus. Therefore, the SNP loci with the highest number of minor allele reads are the loci where the top contributors to the mixture have minor alleles. The minor allele loci of the lower contributors are proportionally lower when not shared by other individuals in the mixture. This is because the minor allele loci unique to each low contributor occur with low minor allele reads, the SNP loci where multiple low contributors have a minor allele occur with moderate minor allele reads, and the SNP loci where one or more low contributors share a minor allele with one or more high contributors occur with high minor allele reads. Finally, it can be inferred that high contributors have major alleles at SNP loci with low minor allele reads in the mixture, since these loci would appear with high minor allele reads in the mixture if one or more high contributors had the minor allele at these loci. The mixture minor allele reads represent an approximate sum of individual minor alleles contributed to the mixture weighted by the DNA concentrations of the individuals. 
     Because high contributors have major alleles at the loci with low minor allele reads in the mixture, treating these mixture minor alleles as major alleles for these high contributors is a close approximation of the contributed alleles. Note that low DNA contributors likely have chance sharing of minor alleles with high contributors.
 
This method of mixture desaturation works by converting the bottom k minor alleles by minor allele count in the mixture to major alleles, such that the mixture has N % major alleles. For a mixture with  M major  allele positions on a panel of P loci, k=NP−M. More individuals are identified at low N, whereas fewer individuals are identified with higher confidence at high N. Ns between 45% and 80% work well. Table 1 shows the value performance of N=45% desaturation compared to current mixture analysis on saturated mixtures.
 
     
       
         
           
               
             
               
                 TABLE 26 
               
             
            
               
                   
               
               
                 Performance of N = 45% mixture desaturation.  
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 V1D5J: 
                   
                   
                   
                   
                 URK5V: 
                 URK5V: 
                   
                   
                   
                   
               
               
                 Reference 
                 IX-30 
                 mix55fabric 
                 mix162 
                 mix160 
                 mix186 
                 IX-32 
                 IX-25 
                 mix52 
                 mix88 
                 mix187 
                 mix51 
               
               
                   
               
               
                 24 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 
                   1.26E−10 
                 
                 
                   2.31E−54 
                 
                 1 
                 1 
                 
                   8.00E−73 
                 
               
               
                 86 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 
                   1.98E−52 
                 
                 1 
                 1 
                 1 
               
               
                 94 
                 1 
                 
                   6.28E−69 
                 
                 1 
                 
                   6.22E−16 
                 
                 
                   8.09E−72 
                 
                 
                   1..25E−09 
                 
                 1 
                 
                   2.30E−29 
                 
                 
                   6.25E−72 
                 
                 1 
                 
                   3.34E−47 
                 
               
               
                 57 
                 1 
                 
                   2.88E−66 
                 
                 
                   5.47E−19 
                 
                 
                   6.61E−32 
                 
                 1 
                 1 
                 
                   3.45E−11 
                 
                 
                   4.60E−15 
                 
                 1 
                 1 
                 
                   4.89E−49 
                 
               
               
                 93 
                 1 
                 
                   8.39E−83 
                 
                 1 
                 
                   3.88E−44 
                 
                 
                   6.24E−22 
                 
                 1 
                 
                   6.45E−17 
                 
                 1 
                 
                   2.69E−24 
                 
                 
                   1.25E−34 
                 
                 
                   7.13E−20 
                 
               
               
                 69 
                 1 
                 1 
                 
                   6.89E−44 
                 
                 
                   7.59E−59 
                 
                 1 
                 
                   1.95E−10 
                 
                 
                   7.97E−20 
                 
                 1 
                 
                   1.58E−17 
                 
                 
                   5.88E−19 
                 
                 1 
               
               
                 68 
                 1 
                 1 
                 1 
                 1 
                 1 
                 
                   1.63E−12 
                 
                 
                   7.97E−20 
                 
                 1 
                 1 
                 1 
                 1 
               
               
                 76 
                 
                   3.79E−10 
                 
                 1 
                 1 
                 1 
                 1 
                 
                   1.02E−10 
                 
                 
                   5.87E−19 
                 
                 1 
                 1 
                 1 
                 1 
               
               
                 78 
                 1 
                 1 
                 1 
                 1 
                 
                   7.67E−46 
                 
                 1 
                 
                   1.22E−17 
                 
                 1 
                 1 
                 1 
                 1 
               
               
                 83 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 
                   5.37E−12 
                 
                 1 
                 1 
                 1 
                 1 
               
               
                  4 
                 1 
                 
                   6.48E−15 
                 
                 
                   2.73E−58 
                 
                 
                   3.78E−73 
                 
                 1 
                 1 
                 
                   1.51E−10 
                 
                 1 
                 1 
                 
                   2.50E−15 
                 
                 1 
               
               
                 NA01246 
                 
                   4.22E−19 
                 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 NA08106 
                 
                   1.86E−15 
                 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 19 
                 
                   5.73E−14 
                 
                 1 
                 1 
                 1 
                 1 
                 
                   5.88E−23 
                 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 NA10069 
                 
                   1.08E−10 
                 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
               
                 Italic cells show new reference to mixture hits detected with desaturation, and the cells contain the probability that the random man is not excluded (PRMNE) of the match. The bold cells contain reference to mixture hits that were identified using both current mixture analysis and mixture desaturation. 
               
            
           
         
       
     
     The minor allele ratio (mAR) at a SNP locus is defined as the number of minor allele reads divided by the total reads at that locus. The mixture de-saturation method described using the minor allele reads can also use the mAR. Loci with high mAR in the mixture are the loci where one or more high contributors has a minor allele, and all of each high contributor&#39;s minor allele loci have high mAR in the mixture. However, the minor allele loci of low contributors are more evenly distributed in the mixture.  FIGS.  42  and  43    illustrate this distribution of loci using mAR. In particular,  FIG.  42    shows the distribution of the minor allele loci of four high contributors in a mixture. Loci are rank ordered by mAR values. Loci colored purple are loci where no high contributor has a minor allele. Green, blue, grey and red loci are where one, two, three, or four high contributors have the minor allele, respectively. Notice that non-purple loci exist with high MAR in the mixture.  FIG.  43    shows the distribution of minor allele loci of two minor contributors in a mixture. Blue, red, and green loci have zero, one, and two minor contributors that possess a minor allele at that locus, respectively. Notice how these loci are more evenly distributed in the mixture compared to those of the major contributors. 
     Venn Matrix Method for Complex DNA Mixture Deconvolution 
     In some embodiments, a Venn Matrix method may be used to analyze complex mixtures. In one implementation, search results of a mixture against known references, unknown sub-profiles previously identified, and other mixtures to select a set of mixtures that likely overlap for deconvolution of complex DNA mixtures. Starting with the FastID search results for a mixture, select all known individuals and unknown sub-profiles for this mixture and all potentially overlapping mixtures also identified by FastID. Next, subtract these individuals and sub-profiles from each of the set of potentially overlapping mixtures (if identified in that mixture) creating sets of reduced mixtures. This subtraction reduces the potential set of alleles that might be in common between two mixtures by chance alone. Next, apply the Venn deconvolution method (MIT 16637) to the set of reduced mixtures. Finally, apply the Mixture-to-Mixture matrix visualization (MIT new: DNA Mixture-to-Mixture Analysis) to the integrated results of the set of mixtures mapped onto individual references and unknown sub-profiles. This approach works for both short tandem repeats (STRs) and single nucleotide polymorphisms (SNPs) complex DNA mixtures. According to some embodiments, the Venn method enables the identification of individuals and groups of individuals common in two or more complex DNA mixtures. Previously, no guidance has been provided to determine which mixtures to consider for deconvolution.  FIG.  44    illustrates that two unrelated are likely to share a set of alleles in common by chance alone. The chance overlap between two individuals can be estimated for SNP and STR DNA loci. For SNP loci, each individual typically has two alleles (e.g., AA, AG, GG or alternative DNA base combinations), with each of the alleles inherited from each parent. Table 1 illustrates the possibilities for SNP sharing between two unrelated individuals at one locus. For resolution of more individuals in a complex mixture, a minor allele ratio (MAR) close to 0.05 is ideal [Isaacson, et al. 2014]. For SNPs with this MAR, an individual will have approximately 10% of the positions (2 alleles×0.05 MAR) with one minor allele and 1% with two minor alleles (10% x 10%). This creates a sparse barcode pattern of minor alleles for each individual that has a low probability of random sharing with unrelated individuals (10%×10%=1%). This can be expressed as f 1  as the fraction of SNPs with minor alleles for individual  1  and f 2  for individual  2 . The expected sharing of minor alleles, E, is E=f 1 ×f 2 . This formula also applies to DNA mixtures for estimating the expected amount of chance minor allele sharing between two mixtures. The chance overlap between two STR samples can be estimated by summing the observed allele frequencies at each locus as f i . An example of observed STR allele frequencies in the U.S. population is shown in Table 27. 
                     TABLE 27                  Example of Possible       SNP Allele Sharing       between 2 Individuals                                         AA   AG   GG                                                 AA   2   1   0           AG   1   2   1           GG   0   1   2                        
DNA Mixture-to-Mixture Analysis
 
In some embodiments, a novel method may be used for analyzing DNA overlaps between one DNA mixture and other DNA mixtures with shared DNA contributors. Two or more DNA mixtures can have no common contributors, and any detected common DNA alleles result from chance. When two or more DNA mixtures have common contributors, the overlap between the mixtures will be enriched above chance by the alleles of the common contributors. The Lincoln FastID or equivalent methods enable the comparisons of samples, both individual reference samples and complex DNA mixtures (e.g., samples from crime scenes, clothing, money, weapons, etc.). Included in these results are identifications of overlaps between mixtures. The Lincoln Venn Mixture Deconvolution method can identify sub-profiles of one or more individuals common to two or more mixtures. A DNA mixture may match zero or more reference samples, zero or more DNA mixtures. When a mixture matches one or more mixtures, visualization of identified reference sample matches, identified sub-profiles, and novel unknown sub-profiles, the entire set of results can be visualized side-by-side in a scatter plot/bubble chart or matrix for immediate insights into the individuals (both known and unknown) common to the set of overlapping mixtures (crime scenes). This is done by organizing the reference hits for each mixture into a matrix of matches between mixtures and individuals. The significance of the matching results (e.g., probability of random man not excluded P(RMNE), likelihood ratio (LR), etc.) can be encoded into the visualization by symbol shape and size. The mixture-to-mixture analysis approaches applies to SNPs, STRs, DNA microarray profiles, etc.
 
     Criminal justice DNA forensics currently relies upon DNA analysis of allele lengths by sizing of a set of short tandem repeats (STRs). The United States is expanding from 13 to 20 DNA loci to facilitate alignment with DNA forensics used in Europe. Advances in DNA sequencing technologies will shift DNA forensics from sizing STR alleles to sequencing both STR and single nucleotide polymorphisms (SNPs). Inclusion of SNPs enables additional advanced capabilities, including analysis of DNA mixtures with two or more contributors. Current STR sizing has very limited DNA mixture analysis resolution with difficulties with differences in DNA concentrations and mixtures with more than two contributors. MIT Lincoln Laboratory has pioneered advanced DNA mixture analysis with both STR panels and SNP panels (with up to 15,000 SNPs). Methods have been developed that can correctly identify 12 contributors in STR mixtures and multiple individuals in mixtures of 15 to 20 individuals with SNP panels. 
     DNA Mixture Analysis 
     A sample with DNA from one contributor will be a partial or full profile for the individual.  FIG.  45    illustrates an example mixture, mix 41 . The profile of minor alleles is illustrated in  FIG.  45 A . The FastID search results against references and mixtures are shown in  FIG.  45 B . The profile for individual  83  is matched for all except for 3 SNP minor alleles.  FIG.  45 C  shows the minor allele ratio profile for individual  83 ; it has fewer minor alleles than mix 41  indicating that mix 41  has additional contributors. Mixture  41  also matches against five other mixtures, mix 9 , mix 18 , mix 52 , mix 88 , and mix 186 . In  FIG.  45 D , the individuals identified by FastID search results are plot in a matrix of individuals versus mixtures scatter plot. Note that there are multiple reference samples of individuals  69 ,  78 , and  93 . In  FIG.  1   d   , it becomes immediately clear that the overlap of mix 41  and the other five mixtures all include individual  83 . The approach enables the visualization and analysis of mixture-to-mixture overlaps. This example can be extended to include identified sub-profiles from mixtures and unknown individuals. 
     Identifying Unknowns in DNA Mixtures 
     Unknowns are individuals whose DNA is present in forensic samples and there is no reference sample for this individual in the set of individuals with profiles in the reference database. A forensics DNA sample can contain DNA from 0, 1, or more individuals. Trace amounts of DNA may result in only a partial profile for an individual. The following are methods to detect unknowns in forensics samples:
         A sample consistent with having a profile of an individual based on the amplified loci but having no matches to known individuals is a candidate profile for an unknown.   A mixture of two or more individuals where some but not all of the individuals are known contains unknowns. Subtracting the known profiles from the mixture leaves the signature profiles for the unknowns.   The Venn method can be used to deconvolve a set of mixtures and references to identify unknown individuals.   The Plateau method can be used to deconvolve mixtures into sub-profiles of known and/or unknown individuals.   The Venn Matrix method can be used to deconvolve a set of mixtures and references to identify unknown individuals.
 
Sample from Unknown Contributor
 
A sample profile can contain 0, 1, or more individual contributors. For samples with 2 or more contributors, the DNA amplifies in proportion to the ratio of the DNA in the original sample. For SNP profiles, the ratio of major:major, major:minor, and minor:minor alleles is directly affected by the number of contributors. SNP panels will have different minor allele frequencies for different loci, but the general rule of allele frequencies with q representing the minor allele frequency for a loci, then the SNP frequencies for a loci are represented by p*p+2*p*q+q*q=1 with p=1—q and p representing the major allele frequency. For unrelated individuals, the sharing of minor:minor alleles for both individuals will be a rare event by chance alone with frequencies approximating q∧4*N where N is the number of SNPs for a two person mixture and q∧6*N for a three person mixture, etc. In an opposite pattern, the number of major:minor allele positions increases with the number of contributors to mixtures with major:minor positions =2*p*q+2*p*q−4*p∧2*q∧ 2  (the addition of the two major:minor positions for each individual minus the chance overlap of shared major:minor positions for the two individuals). Thus, the observed major:major, major:minor, and minor:minor alleles observed for a sample are a reflection of the number of contributors to the sample. Samples consistent with having single contributors are candidate profiles for unknown individuals.  FIGS.  46  and  47    are example profiles for individual profiles for SNP panels of 2,655 and 14,933 SNPs.
 
Locus Allele Method
 
The Locus Allele method can be used to isolate sub profiles of contributors to a mixed DNA sample after one or more contributor(s) have already been identified. The Locus Allele method identifies alleles present in the mixture sample that cannot have been contributed by any of the identified contributors ( FIG.  3   ). These alleles are collected into a sub-profile of alleles from unknown contributors ( FIG.  4   ). Sub-profile signatures consistent from being from a single contributor are candidate profiles for individual unknown contributors to the mixture. The general population frequencies of these alleles determine the resolution power for identifying this individual (i.e., random man not excluded P(RMNE), Likelihood Ratio (LR), etc.).
 
The Venn method shown in  FIG.  50    can deconvolve a set of mixtures and references to identify unknown individuals. The Plateau method shown in  FIG.  51    can deconvolve mixtures into sub-profiles of known and/or unknown individuals. The Venn Matrix method shown in  FIG.  52    can deconvolve a set of mixtures and references to identify unknown individuals.
 
Estimating Individual Contributions to DNA Mixtures
 
DNA mixtures contain contributions from two or more individuals. High throughput sequencing (HTS) technologies now enable mixture analysis and deconvolution of DNA mixtures into individual profiles. Forensics sequencing panels have been created for short tandem repeats (STRs) and single nucleotide polymorphisms (SNPs). This example implementation provides a new method for estimating the proportion of DNA contributed by individuals for HTS sequenced SNP mixtures. For each individual, the average of the minor allele ratios (maR) is computed for loci where the individual has one minor allele and one major allele (heterozygous). The ratio of this average to the sum of the computed individual averages represents an estimate of the percentage that each individual contributed to the mixture.
 
The most common allele at a SNP locus is referred to as the major allele (M). The less common allele is referred to as the minor allele (m). For each locus, an individual will have two major alleles (MM), one major allele and one minor allele (mM), or two minor alleles (mm). The minor allele ratio (maR) at a locus is defined as the number of minor allele reads observed divided by the total reads observed. After individual profiles have been identified for a mixture by FastId, Plateau Method, Venn Method, Venn Matrix method, or other means, the average of the maR for the mM alleles for each individual is determined. An individual&#39;s proportion to the mixture is estimated by the average of the mixture maR divided by the sum of the averages for all identified profiles.
 
Note that the median can be used as an alternative to the average in these calculations.
       

     Example 1—Dilution Mixture Series 
     A dilution series of seven mixtures of two individuals is illustrated in  FIG.  53    and Table 28 for DNA contributor ratios of 50:50, 60:40, 75:25, 90:10, 99:1, 200:1, and 400:1. Table 28 calculates the estimated contributions for each individual identified in the mixture. The mixture 90:10 contains an additional trace contribution for an unknown individual representing an estimated 3.8% of the total DNA contributed to the mixture ( FIG.  53    and Table 28). Table 29 compares the estimated concentrations with the planned concentrations. Note that variability in pipetting DNA and PCR amplification for the experiments may contribute to differences between the planned concentration and the actual concentration. Estimates differed from planned concentrations by 0.2% to 2.3% with the addition of the unknown trace signature reducing the estimate for reference 1 in the 90:10 mixture from 90%; note that 90%-3.8% is 86.2% compared to the estimated 84.5% which differs by 1.7% of the modified expected value. 
     
       
         
           
               
             
               
                 TABLE 28 
               
             
            
               
                   
               
               
                 Calculation of contributions for individuals for Dilution Series 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Ref 1 
                   
                 Ref 2  
                   
                   
                   
                   
               
               
                 Planned 
                 ave 
                 Est. 1% 
                 ave. 
                 Est. 2% 
                 Unknown 
                 Est. % 
                 Sum 
               
               
                   
               
               
                  50:50 
                 
                   0.314 
                 
                 
                   52.3% 
                 
                 
                   0.287 
                 
                 
                   47.7% 
                 
                   
                   
                 0.601 
               
               
                  60:40 
                 
                   0.349 
                 
                 
                   60.1% 
                 
                 
                   0.232 
                 
                 
                   39.9% 
                 
                   
                   
                 0.581 
               
               
                  75:25 
                 
                   0.402 
                 
                 
                   73.0% 
                 
                 
                   0.149 
                 
                 
                   27.0% 
                 
                   
                   
                 0.551 
               
               
                  90:10 
                 
                   0.462 
                 
                 
                   84.5% 
                 
                 
                   0.064 
                 
                 
                   11.6% 
                 
                 0.021 
                 3.8% 
                 0.546 
               
               
                 99:1 
                 
                   0.493 
                 
                 
                   98.6% 
                 
                 
                   0.007 
                 
                 
                    1.4% 
                 
                   
                   
                 0.500 
               
               
                 200:1  
                 
                   0.495 
                 
                 
                   99.3% 
                 
                 
                   0.004 
                 
                 
                    0.7% 
                 
                   
                   
                 0.498 
               
               
                 400:1  
                 
                   0.497 
                 
                 
                   99.6% 
                 
                 
                   0.002 
                 
                 
                    0.4% 
                 
                   
                   
                 0.499 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 29 
               
             
            
               
                   
               
               
                 Comparison of Planned concentrations with observed concentrations  
               
               
                 for Dilution Series 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                 2  
                 2  
                   
               
               
                   
                 1  
                 1  
                   
                 Ex- 
                 Ob- 
                   
               
               
                   
                 Expected 
                 Observed 
                 1 Delta 
                 pected 
                 served 
                 2 Delta 
               
               
                   
               
               
                 
                    50:50 
                 
                 
                     50% 
                 
                 
                   52.3% 
                 
                 
                    2.3% 
                 
                 
                     50% 
                 
                 
                   47.7% 
                 
                 
                   −2.3% 
                 
               
               
                 
                    60:40 
                 
                 
                     60% 
                 
                 
                   60.1% 
                 
                 
                    0.1% 
                 
                 
                     40% 
                 
                 
                   39.9% 
                 
                 
                   −0.1% 
                 
               
               
                 
                    75:25 
                 
                 
                     75% 
                 
                 
                   73.0% 
                 
                 
                   −2.0% 
                 
                 
                     25% 
                 
                 
                   27.0% 
                 
                 
                    2.0% 
                 
               
               
                 
                    90:10 
                 
                 
                     90% 
                 
                 
                   84.5% 
                 
                 
                   −5.5% 
                 
                 
                     10% 
                 
                 
                   11.6% 
                 
                 
                    1.6% 
                 
               
               
                   
                 
                   (86.5%) 
                 
                   
                 
                   (−2.0%) 
                 
                 
                   (9.6%) 
                 
                   
                 
                   (2.0%) 
                 
               
               
                 
                   99:1 
                 
                 
                     99% 
                 
                 
                   98.6% 
                 
                 
                   −0.4% 
                 
                 
                     1% 
                 
                 
                    1.4% 
                 
                 
                    0.4% 
                 
               
               
                 
                   200:1  
                 
                 
                   99.5% 
                 
                 
                   99.3% 
                 
                 
                   −0.2% 
                 
                 
                    0.5% 
                 
                 
                    0.7% 
                 
                 
                    0.2% 
                 
               
               
                 
                   400:1  
                 
                 
                   99.75%  
                 
                 
                   99.6% 
                 
                 
                   −0.15%  
                 
                 
                   0.25% 
                 
                 
                    0.4% 
                 
                 
                   0.15% 
                 
               
               
                   
               
            
           
         
       
     
     Example 2—Touch Mixture 
     In the second example, a mixture was created from individuals touching an object,  FIG.  2   . The touch order for the individuals was recorded. Note that there is no truth information that can be compared to in this example. Individual  8  was not detected in the mixture, but may be represented by the signature marked “unknown”. Individual  6  was also detected but was not recorded as touching the object. Table 3 estimates the relative contributions to the mixture by the individuals with both the average and median estimation calculations. 
                     TABLE 30                  Contributor concentrations estimates for touch mixture                                                                     Un-               Ref 3   Ref 4   Ref 5   Ref 6   Ref 7   known   Sum                                                     mM   144   165   156   134   144   130           Count                                   Median   0.254   0.047   0.020   0.036   0.085   0.022   0.464       Average   0.273   0.065   0.036   0.056   0.090   0.031   0.551       Median   54.7%   10.1%   4.3%    7.8%   18.3%   4.8%           Estimate                                   Average   49.6%   11.8%   6.5%   10.2%   16.4%   5.6%           Estimate                    
Slope Intercept Method
 
     After individual profiles have been identified for a mixture by FastId, Plateau Method, Venn Method, Venn Matrix method, or other means, a line of best fit is created for each individual&#39;s unique maR profile. The slope intercept of each maR profile is summed. Each individual slope intercept is divided by the sum of slope intercepts to determine individual DNA concentrations. 
     Example 1—Dilution Mixture Series 
     Table 31 compares the estimated concentrations with the planned concentrations. Note that variability in pipetting DNA and PCR amplification for the experiments may contribute to differences between the planned concentration and the actual concentration. The mixture 90:10 contains an additional trace contribution for an unknown individual representing an estimated 2.3% of the total DNA contributed to the mixture using this method. 
                     TABLE 31                  Comparison of Planned concentrations with observed concentrations        for Dilution Series                                                         2    2                1    1        Ex-   Ob-               Expected   Observed   1 Delta   pected   served   2 Delta                  50:50         50%       62.30%        12.30%         50%       37.70%       −13.30%            60:40         60%       48.60%       −11.40%         40%       51.40%        11.40%            75:25         75%       65.30%        −4.70%         25%       34.70%         9.70%            90:10         90%       90.60%         0.60%         10%        9.40%        −0.60%               87.70%              2.9%                        99:01         99%       98.70%         0.30%         1%        1.30%         0.30%           200:01       99.50%       99.30%        −0.20%       0.50%        0.69%         0.19%           400:01       99.75%       99.60%        −0.15%       0.25%        0.38%         0.12%                      
Extremely Fast Probability of Random Man not Excluded P(RMNE) Calculations
 
     In some embodiments, it is appreciated that High throughput sequencing (HTS) of DNA single nucleotide polymorphism (SNP) panels have significant advantages for analysis of DNA mixtures and trace DNA profiles. One method of calculating the significance of a match between a DNA mixture and a reference profile is the random man not excluded P(RMNE) calculation. Performance and precision issues are being observed with current implementations of the P(RMNE) calculations. Some embodiments are provided herein for performing an extremely fast P(RMNE) calculation method that also has higher precision than current methods. 
     Most SNPs have just two alleles. The most common SNP allele is named the major allele. The least common SNP allele is named the minor allele. In a mixture profile, the minor allele ratio is calculated as the ratio of minor allele reads divided by the total number of reads. Methods for calculating P(RMNE) have been presented that focus on the SNP loci with no called minor alleles in a mixture profile (e.g., SNPs with minor allele ratios &lt;=0.001 threshold). The P(RMNE) method described by Isaacson et al. was implemented in Sherlock&#39;s Toolkit. For larger DNA mixtures, an issue with precision was observed with the Sherlock&#39;s Toolkit implementation, see  FIG.  55   . Higher precision libraries were implemented in an effort to eliminate this precision issue ( FIG.  55   ). 
     A mixture will have N loci with no called minor alleles. Let p be the average minor allele ratio at these mixture loci. Let q be defined as 1−p such that p+q=1. For an individual with two alleles at a SNP loci the probability for these alleles can be represented as (p+q) 2 =p 2 +2pq+q 2 =1. A perfect reference match to a mixture has major:major (MM) alleles at every locus with no called minor alleles in the mixture profile. Mismatches are defined as reference loci with major:minor (mM) or minor:minor (mm) at these mixture loci with no called minor alleles. The number of mismatches is defined as L between a reference and a mixture. Let K be (1−q 2 /q 2  represent the ratio of transition from MM to non-MM (i.e., mM′ or mm). Let Combination represent that standard statistics combination operation for representing possible SNP loci that mismatch between a reference and a mixture. 
               Combination   ⁢           (     n   ,       i     )       =       (         n           i         )     =         n   !       i   ⁢     !       (     n   -   i     )     !           =         n   ⁡   (     n   -   1     )     ⁢         …   ⁢           (     n   -   i   +   1     )         i   !                 
P(RMNE) can be estimated by the term for no mutations, q 2N , times the possible combinations of L mismatches,
 
               (         N           L         )     ,         
times the transition term K L .
 
 P   RMNE ( L )= q   2N *Combination( N,L )* K   L  
 
To calculate individual P(RMNE) values:
 
 P   RMNE (0)= q   2N *Combination( N, 0)* K   L0   =q   2N  
 
Note that this is the same equation as proposed by Voskoboinik &amp; Darvasi 1  for SNP mixtures with no mismatches.
 
             	           P     R   ⁢   M   ⁢   N   ⁢   E       (   1   )     =         q     2   ⁢   N       *   Combination   ⁢           (     N   ,   1     )     *     K   1       =       q     2   ⁢   N       *   N   *   K         ⁢   
         P     R   ⁢   M   ⁢   N   ⁢   E       (   L   )     =         q     2   ⁢   N       *   Combination   ⁢           (     N   ,   L     )     *     K   L       =       q     2   ⁢   N       *         n   ⁡   (     n   -   1     )     ⁢         …   ⁢           (     n   -   L   +   1     )         L   !       *     K   L                   
Next, a series of P(RMNE) values for the mixture can be optimized for each value of L using the previous P RMNE (L−1) calculation:
 
     
       
         
           
             
               
                 P 
                 
                   R 
                   ⁢ 
                   M 
                   ⁢ 
                   N 
                   ⁢ 
                   E 
                 
               
               ( 
               
                 L 
                 + 
                 1 
               
               ) 
             
             = 
             
               
                 
                   q 
                   
                     2 
                     ⁢ 
                     N 
                   
                 
                 * 
                 Combination 
                 ⁢ 
                     
                 
                   ( 
                   
                     N 
                     , 
                     
                       L 
                       + 
                       1 
                     
                   
                   ) 
                 
                 * 
                 
                   K 
                   
                     L 
                     + 
                     1 
                   
                 
               
               = 
               
                 
                   
                     P 
                     
                       R 
                       ⁢ 
                       M 
                       ⁢ 
                       N 
                       ⁢ 
                       E 
                     
                   
                   ( 
                   L 
                   ) 
                 
                 * 
                 
                   
                     ( 
                     
                       n 
                       - 
                       L 
                     
                     ) 
                   
                   
                     L 
                     + 
                     1 
                   
                 
                 * 
                 K 
               
             
           
         
       
     
     This optimization has the additional benefit of multiplying a large value, 
                 (     N   -   L     )       L   +   1       ,         
with a small value, K, where calculating
 
               N   !       L   ⁢     !       (     N   -   L     )     !               
by itself can stress the precision capability of an implementation for large values for N and L.
 
The P(RMNE) calculations for 2K, 3K, and 4K SNP panels are illustrated in  FIGS.  56 ,  57   , AND  58 . The Taylor and Sherlock&#39;s Toolkit methods do not scale well and are not included. Note for the 2K SNP panel, the higher precision Mather  152  method fails completely after running for 98 minutes ( FIG.  59   ). Note that precision issues are observed for the Mather  64  method on the 2K, 3K, and 4K SNP panels ( FIGS.  56 ,  57 , and  58   ). The Mather  152  method also has precision issues for the 4K SNP panel ( FIG.  58   ). The method for calculating P(RMNE) in this disclosure is considerably faster than other methods, has high precision, and does not have stability issues related to SNP panels being evaluated.
 
High Performance Kinship Comparisons of DNA SNP Profiles
 
Individuals inherit DNA from each of their parents. For autosomal chromosomes, this results in two DNA alleles for single nucleotide polymorphisms (SNPs). Polymorphic loci are compared between two individuals to determine if they are related or unrelated. Four comparisons are needed to compare the possible alleles at each locus. For N loci, this is 4N comparisons. The alleles for one locus for an individual can be mapped onto binary hits labeled [ACGT][ACGT] with the first set of bits being used only when two of the same allele are present (e.g., TT encodes as hex 11, GG as 22, CC as 44, AA as 88, GT as 03, CT as 05, CG as 06, etc. A logical bit AND of the encoded alleles between two individuals will result in 0, 1, or 2 bits set in the result depending upon the number of shared alleles at the locus. The hardware population count instruction can count the number of bits set in a single computer instruction on most modern computer systems. Multiple alleles can be mapped onto computer register with 4 alleles for 32-bits, 8 alleles for 64-bits, and 32 alleles for 256-bit systems. With this encoding the alleles for two individuals can be compared in N/4, N/8, and N/32 AND instructions depending on computer system register size. This data encoding and comparison strategy enables high performance kinship comparisons between large numbers of individuals on current computer systems. Even higher performance (roughly 100-times faster) can be achieved by leveraging parallel cores on current graphics processing units (GPUs).
 
For a SNP locus with two possible alleles, an individual may have AA, AG, GA, or GG. Four comparisons are need to compare the alleles of two individuals Individual 1 ( a   1 a 2 ) and Individual 2 ( a   3 a 4 ) at a locus: a 1 ×a 3 , a 1 ×a 4 , a 2 ×a 3 , and a 2 ×a 4 . It might be possible to reduce the number of comparisons by using sorting order of alleles, but loci with alleles like AG and GT force extra comparisons. The number of comparisons can be reduced by mapping alleles to binary bit encodings. A one bit is set for the first allele in the lower set of binary bits [ACGT][ACGT] with one bit position for each possible DNA base. If the second allele is the same as the first allele, it is encoded in the left-most (upper) set of four bits. If the two alleles are different, then then each of the corresponding bits are set in the right-most (lower) bit set. This creates an 8-bit encoding for both alleles for an individual for a SNP locus. Table 32 illustrates hexadecimal bit encodings in binary. Shared alleles between two individuals can be compared with the logical AND operation (Table 33). If one allele is shared between two individuals, there will be a corresponding 1 bit in the right-most set of bits. If two alleles are shared, then there will be two 1 bits set in the 8-bit encoding. The hardware population count (popcount) instruction can count the number of bits set in the result in a single operation. Multiple loci can be mapped onto hardware registers with 8-bits required per locus. A 64-bit register can compare 8 alleles in one AND operation and a 256-bit register can compare 32 alleles in one AND operation. This data encoding and hardware instruction encoding will outperform traditional allele comparison algorithms. This method can be even further parallelized on graphics processing units (GPUs) like the NVidia K40 and K80 Tesla cards with likely greater than a 100× performance improvement over computer cores with parallelization with thousands of GPU cores.
 
     
       
         
           
               
             
               
                 TABLE 32 
               
             
            
               
                   
               
               
                 Hex Bit 
               
               
                 Representations 
               
            
           
           
               
               
               
            
               
                   
                 Base 16 - 
                 Base 2 - 
               
               
                 Base 10 
                 Hex 
                 Binary 
               
               
                   
               
            
           
           
               
               
               
            
               
                 0 
                 0 
                 0000 
               
               
                 1 
                 1 
                 0001 
               
               
                 2 
                 2 
                 0010 
               
               
                 3 
                 3 
                 0011 
               
               
                 4 
                 4 
                 0100 
               
               
                 5 
                 5 
                 0101 
               
               
                 6 
                 6 
                 0110 
               
               
                 7 
                 7 
                 0111 
               
               
                 8 
                 8 
                 1000 
               
               
                 9 
                 9 
                 1001 
               
               
                 10 
                 A 
                 1010 
               
               
                 11 
                 B 
                 1011 
               
               
                 12 
                 C 
                 1100 
               
               
                 13 
                 D 
                 1101 
               
               
                 14 
                 E 
                 1110 
               
               
                 15 
                 F 
                 1111 
               
               
                   
               
            
           
         
       
     
                     TABLE 33                  Logic AND Operator                                     Bit 1   Bit 2   Operator   Result                                                 0   0   AND   0           0   1   AND   0           1   0   AND   0           1   1   AND   1                        
Kinship Relationships
 
A parent and child share a common allele are all autosomal loci identity by descent (IBD). In a perfect set of data, all of the compared SNP loci will be at least 1 for this relationship. In contrast, siblings by chance alone may have no shared alleles at 25% of loci, 1 shared at 50%, and 2 shared at 25% by IBD. This makes it easy to distinguish between parent-child and sibling first degree relatives. Half-siblings should share roughly 50% of their autosomal SNP alleles by IBD as they randomly share or not the same chromosome segment from their shared parent. Grandparents and grandchildren, aunts/uncles and nieces/nephews have 25% IBD plus random allele matches. Alleles not inherited from a common ancestor may be identical by chance—identity by state (IBS).
 
High Throughput Sequencing Trace Profile Detection
 
Trace profiles are DNA profiles that exist in a DNA mixture at quantities that are too low to be detected by standard DNA mixture analysis techniques 1,2 . The minor alleles of trace profiles in DNA mixtures are often not detected because portions of these profiles are missing or hidden in the sequencing noise produced by High Throughput Sequencing (FITS). Three novel methods are introduced that enable the detection of trace profiles. The first method, mAR Zipper, enables better trace detection by creating new trace reference profiles that subset loci that are the most likely to have minor allele ratio (mAR) values above sequencing noise. This method creates special profiles of the strongest 50% of the SNP loci for references as the most likely to be above noise threshold in mixtures with trace profiles. The second and third methods (Experiment Read Count Minor allele cut-off, Experiment Read Count Optimization), enables the detection of trace profiles by reducing the amount of sequencing noise which makes it possible to distinguish some trace profiles from noise.
 
mAR Zipper Method
 
The most common allele at a SNP locus is referred to as the major allele (M). The less common allele is referred to as the minor allele (m). For each locus, an individual will have two major alleles (MM), two minor alleles (mm), or one major allele and one minor allele (mM). The minor allele ratio (mAR) at a locus is defined as the number of minor allele reads observed divided by the total number of reads observed. In traditional DNA mixture analysis, the SNP panel loci are characterized for reference and mixture profiles. To characterize a reference profile, loci that have one minor allele (mM) will have a mAR value between 0.1 and 0.9 with a majority having a mAR value near 0.5. Factors such as copy number variants, novel SNPs, and primer efficiency are likely sources to this large mAR range. Loci that have two minor alleles (mm) will have mAR values between 0.9 and 1. Loci without a minor allele (MM) will have mAR values less than 0.1.
 
Loci with high reference mAR values will have higher trace mixture mAR values. The loci colored blue in  FIG.  1    represent loci with mAR values greater than 0.5 in a reference profile. This reference profile represents the low contributor in the 1:400 two person mixture in  FIG.  2   . In  FIG.  2   , loci colored blue represent loci with mAR values greater than 0.5 in the reference profile of the minor contributor. A higher percentage of these blue loci are above the 0.001 cut-off used in DNA mixture analysis to determine if a minor allele is present at a specific locus in a mixture. To leverage this difference the reference trace profile loci are selected as a subset that only include loci with mAR values less than 0.1 (MM) and greater than 0.5 (strongest mM and mm loci). The reference trace profiles are compared against DNA mixtures using standard DNA mixture techniques.
 
       FIG.  60    shows reference mAR profiles of high and low contributors in the 1:400 defined mixture. Loci with mAR values greater than 0.1 are characterized as having at least one minor allele. Loci with mAR values greater than 0.5 are colored blue for the low contributor. Loci with mAR values less than 0.5 and greater than 0.1 are colored red for the low contributor. For the high contributor all loci with at least one minor allele are colored green. For both reference profiles loci without a minor allele (MM) are colored gray. 
       FIG.  61    shows a mAR plot of the 1:400 Defined Mixture experiment without any modifications on the left. Note the high number of red Low Ref loci below the Log(0.001) cut-off. On the right, the same 1:400 Mixture with only the MM and High Ref loci plotted from the low contributor. Note how fewer used loci fall below the 0.001 cut-off.
 
This method was tested on a 1:400 Defined DNA mixture and a DNA sample taken from a plastic object that had been touched by five separate individuals. The zipper method enabled the detection of the low contributor in the 1:400 Defined DNA mixture. Standard DNA mixture analysis was able to detect three of the five individuals that touched the plastic object. The mAR Mixture Zipper Method was able to detect four of the five individuals.
 
The cut-off values used to create the mAR zipper reference can be modified to reflect use-case. Using a higher mAR cut-off enables better detection of trace profiles but decreases mixture analysis capabilities due to fewer SNP comparisons. Using a lower cut-off value will decrease trace detection but increase mixture analysis.
 
Experiment Read Count Minor Allele Cut-Off Method
 
The Experiment Read Count Minor Allele Cut-Off method enables the detection of trace profiles by reducing the amount of sequencing noise which makes it possible to distinguish some trace profiles from noise. The mAR is calculated by dividing the number of minor alleles by the total number of reads at a locus. The mAR is used to determine if a minor allele exists at a locus. For DNA mixture analysis, if the mAR is greater than 0.001, then that locus is characterized as having at least one minor allele 1 . Loci that do not sequence well will have low total read counts. High throughput sequencing has a ˜1% error rate which results in inaccurate reads 3 . As sequencing depth increases the total number of erroneous reads also increases. When sequencing error occurs at the minor alleles of poorly performing loci there is a risk that these loci will be improperly characterized. To prevent improper characterization a minimum minor allele count is required for the mAR to be calculated. This minimum minor allele count is dependent on the total number of reads in the experiment. If the number of minor allele reads does not meet the minimum, that locus is characterized as not having a minor allele. Table 34 shows the effect of filtering based on Read Count Optimization on mAR. With a read count filter of 10 reads, some loci where a minor allele was previously counted (mM) are now counted as having two major alleles (MM). These filtered minor alleles are likely the result of sequencing noise.
 
                     TABLE 34                  Four loci and with mAR values before for and       after apply the Experiment Read Count       Optimization method.in a mixture. Note that with a       Read Count Optimization filter of 10, two of       these loci (1 and 2) are counted as having a minor       allele. If this filter were not used locus 3       would not be characterized as having a. minor allele       despite having the same number of minor       alleles as locus 4. Reducing the amount of sequencing       noise in a mixture improves mixture       analysis.                                             Minor Allele   Total   Unfiltered   Filtered           Locus   Reads   Reads   mAR   mAR                                                     1   11   100   0.11   0.11           2   11   10000   0.0011   0.0011           3   5   10000   0.0005   0           4   5   100   0.05   0                        
Experiment Read Count Optimization Method
 
An Experiment Read Count Optimization method enables the detection of trace profiles by reducing the amount of sequencing noise which makes it possible to distinguish some trace profiles from noise. If a trace profile exists in a DNA sample, sequencing that sample at very high coverage will results in more noise mixed in with the trace profile. This occurs because higher coverage results in more sequencing error. By limiting the number or reads in a forensics sample noise is reduced, which increases the trace signal. This method also optimizes high throughput sequencing by enabling more barcodes to be run per sequencing event.
 
 FIG.  62    shows an mAR plot of the 1:400 Defined Mixture experiment without any modifications on the left. Note the first ˜400 loci in the plot where loci that should be MM do not have any minor allele counts. On the right the sequencing depth of this experiment was reduced in half to 10 million reads. This change results in ˜700 loci that should be MM having no noise minor allele counts.
 
Minor Allele Count DNA Forensics Mixture Analysis
 
     The minor allele ratio (mAR) may be used to determine if a minor allele is present at a specific locus in high throughout sequencing (HTS) data. The mAR is calculated as the number of minor alleles divided by the total number of reads at a locus. For DNA forensics applications, the minor allele count (mAC) at a specific locus can substitute for the mAR to determine if a minor allele is present at a specific locus. For mAC data, noise becomes easier to be identified and removed from sequencing experiments by using mAC frequency filters. The mAC approach appears to be an equivalent or possibly even superior approach for DNA mixture analysis. 
     The minor allele count (mAC) is defined as the number of minor allele reads observed at a SNP locus. For high concentration DNA contributors in mixtures the loci with a minor allele, strongly correlate with high mAC values. This correlation is proportional to contributor DNA concentration. Minor alleles for low DNA concentration contributors correlate with low mAC values unless they overlap with minor alleles of other individuals. If all subjects present in a mixture do not have a minor allele at a particular locus then the mAC for that locus should be equal to zero (i.e., major:major alleles for all individuals contributing to the mixture). Sequencing errors can result in low mAC values greater than zero at loci where no contributor has a minor allele. In DNA forensic mixture analysis there can be several people in the HTS data at varying quantities. By taking into account sequencing platform and sequencing depth, mAC value due to sequencing noise can be estimated. With this estimate, a mAC threshold is set just above estimated noise. Loci with mAC values above the noise threshold are correctly identified as having a minor allele. 
       FIG.  63    shows plots of 1:99 two person defined mixture using the mAC on the left and mAR on the right. Note the similarities between the two plots. Using the mAC method, a threshold of 10 would be used to determine if a minor allele is present in a mixture. This value is slightly higher than the number of reads that would be expected at a locus due to noise. Using the mAR method, a threshold of 0.001 would be used to determine if a minor allele is present in a mixture. This value was determined empirically. It is noted that the system may use mAC values instead of mAR values.
 
Minor Allele Count Frequency Filter
 
The Minor Allele Count Frequency Filter method enables the detection of added profiles by reducing the amount of sequencing noise which results in fewer mismatches and better detection of trace profiles. Sequencing noise occurs at a constant rate 1  while sequencing signal varies due to DNA concentration, and primer performance. This results in high mAC variability in sequencing signal and low mAC variability in sequencing noise. This difference in mAC variability can be used to filter out the sequencing noise. By converting loci with high mAC frequencies to 0 (i.e., major:major allele call), noise is filtered from the mixtures.
 
 FIG.  63    shows plots of 10:90 two person defined mixture rank-ordered by mAC. Loci are colored by the mAC frequency. Eight-hundred and fifty-one loci did not have a minor allele. Three-hundred and twenty-two loci that should not have a minor allele have a mAC equal to 1. Twelve loci have a mAC equal to 7 that should not have a minor allele. Five loci have a mAC equal to 55. These loci have minor alleles that belong to the low contributor.
 
 FIG.  64    shows plots of 10:90 two person defined mixture using the mAC on the left and mAC Frequency Filter on the right. Any loci that had a mAC that occurred 12 or more time in this mixture was set to 0. This method correctly identified and removed the majority of sequencing noise from the mixture.
 
When individuals are present in trace quantities it can be challenging to separate sequencing noise from sequencing signal using mAR values. The use of mAR values to characterize SNPs enables noise to be incorrectly characterized on low performing primers and the loss of trace signal for very low concentration DNA contributors (e.g., less than 1/200). A poorly performing primer will have low total counts. When sequencing noise causes minor allele read counts at these loci those reads are magnified by using mAR values. If a mAR value greater than 0.0025 was used to positively identify a minor allele at a locus poorly performing loci with less than 400 total reads would only need one minor allele to put them over the mAR threshold. In this case, the locus would be incorrectly characterized as possessing the minor allele. When large differences in contribution concentrations exists the denominator (total counts) of the mAR can be so high that even moderate minor allele counts can be ignored using mAR values. For example, if 19 minor allele reads were detected at a locus but the total number of reads was 8,000 those minor alleles would be lost using mAR thresholds. In this case, the locus would be incorrectly characterized as lacking the minor allele.
 
Plateau Method for Forensic DNA SNP Mixture Deconvolution
 
     Identification of individuals in forensic DNA mixtures remains a challenge for forensic analysts. Recent advances in high throughput sequencing (HTS) are enabling analysis of DNA mixture samples with expanded panels of Short Tandem Repeats (STRs) and/or Single Nucleotide Polymorphisms (SNPs). No methods are currently known for direct deconvolution of DNA SNP mixtures into individual profiles. We present the plateau method for direct SNP DNA mixture deconvolution into sub-profiles based on differences in contributor&#39;s DNA concentrations in the mixture samples without reference profiles. The plateau method can detect profiles for individuals down to roughly 1:400 concentration ratios in HTS mixtures. 
     DNA forensics is a common tool used within law enforcement and US intelligence agencies to identify unknown suspects and to accurately link crime scene evidence to criminal perpetrators. Crime scene evidence often contains DNA from multiple people, confounding current DNA analysis techniques. Currently, the forensics community uniquely identifies individual DNA samples through extraction of short tandem repeats (STRs). Capillary electrophoresis is used to quantify STR allele lengths. This methodology has been proven accurate for individual profile identification. However, if a given reference DNA profile is contained within a DNA mixture, identifying an individual profile is difficult and usually impossible using this methodology. Thus, the ability to build individual profiles from a mixture and the direct deconvolution of a mixture into candidate and/or individual component DNA signatures are unmet needs. 
     STR analysis of DNA mixtures works for samples with two contributors where the ratio of DNA concentrations does not exceed 1:10. Special techniques are applied to rape samples to isolate the perpetrator&#39;s profile. Current methods are limited to the resolution of capillary electrophoresis (CE) sizing of polymerase chain reaction (PCR) amplified STR allele peaks. PCR amplification introduces stutter peak artifacts that limit the discrimination of contributor STR alleles from these stutter artifacts. Progressing from sizing of alleles to sequencing alleles with high throughput sequencing (HTS) enables massively parallel sequencing (MPS) of forensic and reference samples. HTS also enables the expansion of forensic panels from the current FBI CODIS panel 20 STR loci up to 24,000 SNP loci with the Thermal Fisher Scientific Ion AmpliSeq panels. Selecting SNPs with low fixation index (F ST ) coupled with targeted minor allele ratios facilitate designing SNP panels for mixture analysis 5,6 . 
     No methods currently exist for DNA mixture deconvolution. We introduce herein the Plateau method for direct deconvolution of some DNA mixtures with modest numbers of contributors and imbalances in DNA concentrations. 
     Mixture Analysis HTS SNP Panel Design 
     Optimal mixture analysis SNP panels need to work across all ethnicities. These panels can also be designed to minimize saturation on multiple contributor forensic samples. MIT Lincoln Laboratory has designed and tested HTS SNP panels using both the Fluidigm DNA amplification platform and the Thermal Fischer AmpliSeq platform. The following recommended guidelines can be applied to SNP selections for designing mixture analysis SNP panels:
         Select loci with low fixation index (F sT ) (e.g., &lt;0.6)
           Poor correlation between ancestry and genotype on ALFRED database,   
           Select loci with low average heterozygosity (e.g., 0.05 to 0.15),   Select loci with low minor allele frequency (mAF) (e.g., 0.03 to 0.07),   Avoid loci that tend to produce ambiguous results in reference samples,   Avoid loci that produce impossible results in parent-child pairs,   Avoid loci with consistently low read counts,   Avoid loci that tend to generate data from only one strand of DNA,   Avoid/resolve duplicate SNPs,   Avoid ambiguously mapped SNPs, and   Select loci with minimum distance between loci (e.g., 100,000 bases).
 
Other considerations include:
   Inclusion/exclusion of SNPs related to health
 
Ion Torrent HTS Sequencing
 
Buccal swabs (Bode cat #P13D04) were used to collect buccal cells from the inside cheeks of volunteers, rubbing up and down for at least 10 seconds, with pressure similar to that used while brushing teeth. DNA was isolated from swabs using the QIAamp DNA Investigator Kit (Qiagen cat #56504), using the “Isolation of Total DNA from Surface and Buccal Swabs” protocol, and eluted in 100 uL of low TE (carrier RNA not used; low TE has 0.1 mM of EDTA). Quantitation was done using Quantifilier HP kit (ThermoFisher cat #4482911) according to manufacturer. The standard run across all samples that quantities were calculated from was human genomic DNA from Aviva Systems Biology (cat #AVAHG0001). Target specific primers, consisting of 2,655 amplicons, were designed using the Ion AmpliSeq Designer online tool. The extracted DNA from volunteers, was pooled into mixtures, and the percent contribution of each volunteer is listed in Table 1. The AmpliSeq 2.0 library kit protocol was followed according to the manufacturer with this primer panel, with the exception that 19 cycles were done with no secondary amplification and the final elution was in 25 uL low TE instead of 50 uL. Each mixture was given a separate barcode. Library quantitation was done with the Ion Library Quantitation Kit (Thermofisher cat #4468802), according to the manufacturer.
       

     Samples were pooled and diluted to 50 pmol, using 150 base pairs per amplicon average for the calculation based on primer panel. Template preparation and sequencing were performed using manufacturer protocols (Thermofisher Ion Chef and Proton cat #A27198 and Proton chips cat #A26771). 
     HTS SNP Data Analysis 
     The GrigoraSNPs program was used to call SNP alleles from multiplexed HTS FASTQ sequences. The called SNPs were loaded into the MIT Lincoln Laboratory IdPrism HTS DNA Forensics system. 
     Plateau Method 
     The minor allele ratio (mAR) is calculated for each locus for mixture samples. The loci are sorted by mAR where loci with minor alleles with differences in contributor DNA concentrations will form plateaus with different mAR ratios. Sub-profiles plateaus are identified by a sliding window approach that identifies clusters of SNPS with very similar minor allele ratios. Observed instrument sequencing errors create random base sequence errors with very low minor allele ratios. SNPs below a minimum mAR threshold are classified as two major alleles. Random HTS sequencing errors can generate mAR values as high as 0.0025 for loci with two major alleles in reference samples on Thermal Fischer Proton and S5 platforms. All SNP alleles identified as major:major are shared by all identified sub-profiles. For each sub-profile, the SNPs to the left of each plateau can be classified as major:major for that sub-profile when loci are sorted by increasing mAR values. The minor:minor alleles observed are assigned to the right-most sub-profile identified.
 
A reference profile consists of MM, mM, and mm SNP alleles.  FIG.  1    illustrates chromosome 22 minor allele ratios (mAR) for reference 1. For reference samples, the mAR values at or near 0 represent MM alleles, near 0.5 —mM alleles, and 1.0—mm alleles. The sorted mAR profiles for two reference profiles are illustrated in  FIG.  2   . A mixture profile is composed of one or more individual contributors with mAR values ranging from 0 to 1. A dilution series of two person mixtures is shown in  FIG.  3    for the dilutions 25:75, 10:90, 1:99, and 1:200. The individual alleles are colored by contributing individual.  FIG.  4    illustrates the assigned alleles predicted by the Plateau method implemented in the MIT Lincoln Laboratory IdPrism DNA forensics system. The Plateau method can frequently separate individuals with DNA concentration differences of 15% or higher. Individual profiles can be resolved with DNA ratios as low as 1:400.  FIGS.  5  and  6    illustrates the Plateau method with defined mixtures of three and four individuals.  FIG.  77    illustrates the characterization of the identified individual sub-profiles compared to truth data for the individuals and mixtures in the two-person dilution series.
 
The sorted mAR plateaus in some DNA mixtures enable the direct deconvolution for the mixture into sub-profiles based on differences in individual mARs within the mixture. High confidence identifications can be made when references are known for some or all of the contributors. When no reference profiles exist for DNA contributors, the sub-profiles can be matched to other forensic samples and reference profiles obtained in the future. The Plateau method cannot resolve two or more individuals when the DNA concentrations are close to each other (e.g., roughly 10% of less on the Ion Torrent platform). Also, multi-contributor mixtures with more than five contributors may not be decomposable by this method. The detection range for this method appears to span from between 10 to 15% concentration difference down to approximately 1:400 for two contributor mixtures. To address forensic mixture deconvolution unmet needs, the Plateau method provides a method to confirm the co-occurrence of individual DNA profiles to build individual DNA profiles for unknown individuals from analysis of one or more DNA mixtures.
 
The Plateau method may be used for medical diagnosis and/or prognosis. In the field of cancer, biopsy samples often contain many cell types, of which a small proportion may form any part of a tumor. Consequently, DNA obtained from tumor biopsies is another form of complex DNA mixture. This method would resolve a question as to whether the tumors arose independently, or, on the other hand, if these tumors are related.
 
The Plateau method can identify individual(s) in DNA mixtures when the DNA SNP profile of any of the individual contributors is not known a-priori. This is the first SNP mixture deconvolution method to be described. Mixture direct deconvolution compliments DNA mixture analysis methods that match known references to DNA mixtures.
 
     
       
         
           
               
             
               
                 TABLE 35 
               
             
            
               
                   
               
               
                 DNA sample 
               
               
                 dilutions for 
               
               
                 defined mixtures 
               
            
           
           
               
               
               
            
               
                   
                 93 
                 4 
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                   
                 53.5 
                 46.5 
               
               
                   
                 43.4 
                 56.6 
               
               
                   
                 27.7 
                 72.3 
               
               
                   
                 11.3 
                 88.7 
               
               
                   
                 1.2 
                 98.9 
               
               
                   
                 0.6 
                 99.4 
               
               
                   
                 0.3 
                 99.7 
               
               
                   
                   
               
            
           
         
       
     
                     TABLE 36                  Analysis of Plateau sub-profiles versus Reference Samples.                                                     Number                        Number        of Minor                        of Con-   Refer-   Alleles       Sub-           Mixture   tributors   ence   (Truth)   mm   Profile   P(RMNE)               25:75   2   1 (4)               6.10E−106       10:90   2   1                        1:99   2   1                        1:200   2   1                        1:400   2   1                       25:75   2   2 (93)   502   73   573   3.31E−64       10:90   2   2               2.19E−110        1:99   2   2                        1:200   2   2                        1:400   2   2                        5:20:75   3   2                        5:20:75   3   3 (56)                        5:20:75   3   4 (24)                        2:17:32:47   4   1   504 mM   80 mm   573   2.64E−60        2:17:32:47   4   2                        2:17:32:47   4   5 (94)                        2:17:32:47   4   6 (78)   450 mM   80 mm   309   2.65E−60                    
Extremely Fast Forensics FITS DNA SNP and STR Sequence Analysis
 
Algorithm for extremely fast sequence analysis of High-Throughput Sequencing (FITS) forensics DNA samples that scales linearly in compute time with the number of DNA sequences being analyzed. DNA loci are identified by a lookup table with the start of the HTS sequence tag (extracted after the barcode sequence tag). SNP or STR loci are identified by locking in the flanking sequences immediately flanking the target SNP or STR. Standard analysis of HTS DNA sequences is of the complexity of Order(N×M×L) where N is the number of sequences, M is the number of loci, and L is the length of the HTS sequence. Using the flanking sequences for the SNP or STR reduces the computational complexity to identification of short (10 base pair) substrings on each side of the target SNP or STR; resulting in reduction of computational complexity to O(N×M). Each DNA sequence is compared against all possible loci to identify the correct loci for the sequence. Implementing a sequence tag lookup table reduces the complexity of the sequence analysis down to O(N) that scales linearly in compute time for the number of sequences to analyze, independently of sequence length and number of loci in the amplification panel. Observed computational runtimes on HTS experiments are reduced from roughly 300 (Intel) to 600 (AMD) minutes on 32 core SMP computers down to 12 minutes for 100 million sequences.
 
DNA forensics will shift in the near future from sizing of Short Tandem Repeats (STRs) to high-throughput sequencing of forensics DNA samples for both STRs and Single Nucleotide Polymorphisms (SNPs). Current DNA forensics techniques rely upon allele sizing of short tandem repeats by capillary electrophoresis. High throughput DNA sequencing enables characterizations of trace DNA samples for large numbers of DNA loci. DNA Sequence barcode tagging of samples for multiplexing of samples is used for increased throughput and decreased cost per sample. Advanced variant analysis algorithms enable improved kinship identification, biogeographic ancestry prediction, analysis of complex DNA mixtures, prediction of externally visible traits, and more. The slowest computational component of the DNA forensics analysis methods is the characterization of raw sequences to variant calls. The elapsed time from sample to results is critical in many forensic scenarios.
 
SNP panels are designed with multiple pairs of oligonucleotide primers that each amplifies target location(s) in the genome for characterization of SNP alleles. Each HTS sequence should contain the following components: multiplexing barcodes on the 5′ and sometimes 3′ end of each sequence, 5′ and 3′ primers, and the SNP surrounded by flanking DNA sequences ( FIG.  1   ). HTS DNA datasets also contain other sequences arising from sequencing or polymerase chain reaction (PCR) amplification artifacts; these other sequences are ignored. For Ion Torrent Proton HTS SNP sequences, the 5′ barcode starts at the first or second base pair position in ˜94% of the valid SNP sequences.
 
The original Scala SNP caller was developed leveraging the Actors model for efficient parallel processing on symmetric multiprocessing (SMP) or remote actors on distributed systems. With a SNP dataset of N millions of sequences (length L) for a panel of M amplification loci is an order O(N×M×L) scale problem. Each sequence is compared against the specified set of barcodes used for the dataset. Reference sequences for each locus from dbSNP (http://www.ncbi.nlm.nih.gov/SNP/) are used as comparison references. For efficient processing, each sequence is compared against the 10 base pairs immediately flanking each reference SNP to identify target loci and SNP position, O(N×M). A minimum of 19 of the 20 flanking bases are required to be identical for correct positioning of called SNP (or STR).
 
In some embodiments, an enhanced Scala SNP caller was developed to implement various embodiments. A hash lookup table was added that uses a 12 base pair (k-mer) lookup tag using the sequences starting 4 bases after the end of the barcode and skipping over the linker bases (GAT) that follow immediately after the 5′ barcode. A lookup table of tags to loci is added as an input file that is loci panel specific. When a 5′ barcode is identified, the lookup tag can reduce the complexity of the analysis of the sequence from O(M) to O(1) speeding up the data analysis.
 
Results
 
Timing results on the AMD Operon 64 and Intel 64 (32 cores with hyperthreads) (Table 37) is shown for panels of 1,598 loci (Table 38), 5,396 loci (Table 39), and 14,942 loci (Table 40). For the Scala SNP caller, the timing results scale with the SpecInt of the two platforms with the Intel 64 having roughly 2X performance over the older AMD 64 SMP system. Performance on both of these platforms is scaling in time by both the number of sequences (N) and the panel size (M) for runtime complexity of O(N×M). The timing of the enhanced Scala SNP caller with the sequence tag lookup for loci identification scales linearly with number of sequences O(N) with no impact of panel size.
 
     
       
         
           
               
             
               
                 TABLE 37 
               
             
            
               
                   
               
               
                 SMP computers used for timing benchmarks 
               
            
           
           
               
               
               
               
            
               
                 Server 
                 CPU/GPU Cores 
                 Storage 
                 Memory 
               
               
                   
               
               
                 AMD 64 
                 AMD Opteron 6282 
                 7200 RPM HDs 
                 512 GB 
               
               
                   
                 (64-cores: 32-cores x 2 CPUs) 
                   
                   
               
               
                 I64 
                 Intel Xeon 2698 v3 
                 10 K RPM HDs 
                 512 GB 
               
               
                   
                 (32-cores/64 threads) 
                 (718162-B21) 
                   
               
               
                   
                 (16-cores/32-threads x 2 CPUs) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 38 
               
             
            
               
                   
               
               
                 Timing results for DNA panel of 1,598 loci 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Scala SNP 
                 Scala SNP 
                 Implementation 
               
               
                   
                   
                 caller 
                 caller 
                 version 
               
               
                   
                 Sequences 
                 AMD 64 
                 Intel 64 
                 Intel 64 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 25 
                 million 
                 20  
                 min 
                 9 
                 min 
                 2 
                 min 
               
               
                   
                 50 
                 million 
                 34  
                 min 
                 18 
                 min 
                 4 
                 min 
               
               
                   
                 100 
                 million 
                 65  
                 min 
                 35 
                 min 
                 9 
                 min 
               
               
                   
                 250 
                 million 
                 153  
                 min 
                 86 
                 min 
                 26 
                 min 
               
               
                   
                 500 
                 million 
                 303  
                 min 
                 172 
                 min 
                 65 
                 min 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 39 
               
             
            
               
                   
               
               
                 Timing results for DNA panel of 5,396 loci 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Scala SNP 
                 Scala SNP 
                 Implementation 
               
               
                   
                   
                   
                 caller 
                 caller 
                 version 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Sequences 
                 AMD 64 
                 Intel 64 
                 Intel 64 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 25 
                 million 
                 55 
                 min 
                 27 
                 min 
                 2 
                 min 
               
               
                   
                 50 
                 million 
                 107 
                 min 
                 53 
                 min 
                 5 
                 min 
               
               
                   
                 100 
                 million 
                 216 
                 min 
                 103 
                 min 
                 9 
                 min 
               
               
                   
                 250 
                 million 
                 505 
                 min 
                 271 
                 min 
                 23 
                 min 
               
               
                   
                 500 
                 million 
                 1098 
                 min 
                 532 
                 min 
                 65 
                 min 
               
               
                   
                   
               
            
           
         
       
     
                     TABLE 40                  Timing results for DNA panel of 14,942 loci                                 Scala SNP   Implementation   Implementation           caller   version   on WL       Sequences   Intel 64   Intel 64   Intel 64 + WL                                                     25   million   79   min   2   min   0.7   min       50   million   137   min   5   min   1.3   min       100   million   274   min   11   min   2.6   min                    
Performance engineering of HTS SNP calling indicates that the problem remains compute bound on SMP computers. Increasing the number of cores or moving towards processors with higher SpecInt scores will reduce runtimes. The GrigoraSNPs out performs the original version substantially with linear runtime with respect to the number of FITS sequences. This method applies equally for both SNPs and STRs for HTS DNA sequence analysis. Runtimes are reduced by ˜75% with faster reads on HP workload accelerator.
 
HTS sequencing enables characterization of forensics trace DNA samples. In DNA forensics, being able to go from sample to profile is fundamental. In some scenarios, being able to quickly characterize samples is essential for generating leads in a case.
 
Genetic Chain Rule for Probabilistic Kinship Estimation
 
Kinship prediction for DNA forensic samples has been limited to first degree relatives. High throughput sequencing will revolutionize DNA forensics with advanced mixture analysis capabilities and push the state of the art in kinship identification for forensic samples. Beyond predicting first degree relatives, current kinship identification models rely on statistics that do not adequately model the biology, or rely on machine learning algorithms that are prone to over optimization while requiring highly similar and extensive training data to ensure generalizability. This work presents an alternative approach using Bayesian statistics to model inheritance of single nucleotide polymorphism (SNPs) based on a given relationship between persons. The impact of panel size on predictions is visualized in terms of distribution of allelic differences between individuals. Confidence of predictions is made using the log likelihood. With a panel of 39108 SNPs evaluated on an in silico dataset, this method can resolve parents from siblings and distinguish 1st, 2nd, 3rd, and 4th degree relatives from each other and unrelated individuals, providing greater potential performance than current state of the art algorithms. First degree relatives can also be partially resolved but results overlap both 4th degree relatives and unrelated individuals.
 
High throughput sequencing (FITS) is revolutionizing capabilities in the fields of forensics, biology, and medicine. DNA forensics is evolving from sizing short tandem repeats (STRs) to sequencing STRs and single nucleotide polymorphisms (SNPs). Currently, DNA forensics currently uses STRs sized by capillary electrophoresis to per-form both identity and familial searching. Familial searching is a method in which STR matching requirements are relaxed to obtain a more expansive list of potentially related suspects. These additional matches are then filtered using statistical method such as identity by state (IBS) and/or kinship index (KI). Lineage testing is then per-formed using mitochondrial DNA or Y chromosome STRs to confirm paternal relationships. Familial searches are limited to First degree relatives due to the small number of STRs used (20 loci for US Combined DNA Index System—CODIS), and the large number of STR matches when matching parameters are set too low[4]. Familial searching and other kinship prediction methods rely on IBD/identity by state (IBS), and KI calculations. Ancestry prediction companies use DNA SNP microarrays and the aforementioned methods to predict close and distant relatives. These DNA SNP microarrays require a lot more DNA than is typically available for forensic samples. Machine learning and forensic HTS SNP panels have been used to predict familial relationships across a set of three families. This work trained a support vector ma-chine based on features including the KING coefficient, IBS, and IBD. While machine learning models have the potential for accurate performance, they are highly dependent on the consistency of the training data, and are prone to over-optimization.
 
Enhanced kinship prediction capabilities can be obtained by incorporating Bayes&#39; Theorem with high throughput sequencing (FITS). This discussion formalizes the expected relationship between any two individuals using Bayesian statistics with applications to FITS forensic SNP panels. As discussed, a Genetic Chain Rule for Probabilistic Kinship Estimation provides a mathematical model that can predict likely relationship between two individuals. This model does not require training data, thereby increasing generalizability. Furthermore, this work reflects the biological underpinnings of inheritance allowing for further extensions based on improved understanding of the biology.
 
Methods
 
Input Data
 
All results were tested on an in silico dataset that simulated millions Of individuals across four ethnic groups. The minor allele frequencies for 39,108 SNPs were taken the Allele Frequency Database (ALFRED) for SNPs well characterized across African Americans, Estonians, Koreans, and Palestinians. The data were simulated across 9 generations with an intermarriage and marriage rate set to reflect public census data. Four generations of data were used to simulate individuals with relationships spanning first through fifth degree and strangers.
 
Data Representation
 
All data are represented as a series of SNPs, with each locus having a minor allele, coupled with a minor allele frequency (mAF). The probability of the major allele occurring across a population is represented as p, while the probability of the minor allele occurring across a population is represented as q. As the SNPs analyzed have one major, and one minor allele, p, and q are set such that:
 
 p+q= 1  (1)
 
This follows Hardy-Weinberg equilibrium and leads to the number of people with a homozygous major genotype to occur with a frequency of p 2 , the number of individuals with a heterozygous genotype to occur with a frequency of 2pq, and the number of homozygous recessive genotypes to occur with a frequency of q 2 . By satisfying Eq. 1, it is ensured that
 
 p 2+2 pq+q 2=1  (2)
 
Using this information, we set out to derive the conditional probability of any genotype occurring, given another individual of a known relationship having a certain genotype.
 
Parent Child Relationships
 
Child Given Known Parent
 
The first relationship calculated is the probability of a child having a particular genotype Gc, given that their parent has a genotype Gp. Given that you know one parent&#39;s genotype, you know the possible alleles that they could pass on to their child. For instance, if a parent is homozygous major (AA), then you know that they will inevitably pass a major allele on to their children.
 
Thus, the probability that any individual child will be homozygous major, is the probability that the other parent passes on a major allele, which is p, and the child will be heterozygous with probability q.
 
Parent Given Known Child
 
Leveraging the information presented in Table 41, it is possible to calculate the probability of a parent having a particular genotype Gp, given that the child has a known genotype Ge. This is formulated through an application of Bayes&#39; rule.
 
                     Pr   ⁡   (       G   p     ❘     G   c       )     =         Pr   ⁡   (       G   c     ❘     G   p       )     *     Pr   ⁡   (     G   p     )           ∑     G   i               Pr   ⁡   (         G   c     ❘     G   p       =     G   i       )     ⁢     Pr   ⁡   (       G   p     =     G   i       )                   (   3   )               
In the above and subsequent equations, Gi, is used to represent all possible allelic combinations. As a result, Gi can be expressed as
 
Gi∈(AA, Aa, aa)  (4)
 
Where A is a major allele, and a is a minor allele.
 
Sibling Relationships
 
It is possible to use this information to further compute the probability that a child will have a genotype Gc 1  given that a sibling of theirs has an observed genotype Gc 2 . In order to properly compute the probability of genotype Gel occurring, it is essential to factor in genotypes of the two parents Gp 1 , and Gp 2 . Using this information, the desired sibling-sibling conditional probability is computed as the probability of Child  1  having a genotype Gel given the possible genotypes that their parents could have, multiplied by the probability of the two parents having genotypes Gp 1  and Gp 2  given the known genotype of Child  2 .
 
                           Pr   ⁡   (       G     c   ⁢   1       ❘     G     c   ⁢   2         )     =       ∑     G     i   ⁢   1             ∑     G     i   ⁢   2             Pr   ⁡   (           G     c   ⁢   1       ❘     G     p   ⁢   1         =     G     i   ⁢   1         ,       G     p   ⁢   2       =     G     i   ⁢   2           )     *     Pr   ⁡   (         G     p   ⁢   1       =     G     i   ⁢   1         ,       G     p   ⁢   2       =       G     i   ⁢   2       ❘     G     c   ⁢   2             )                     (   5   )               
Bayesian Chain Rule of Kinship
 
The above framework can be generalized to compute the probability of a particular genotype given any relationship between two people. We define this formulation as the Bayesian Chain Rule of Kinship. The Bayesian Chain Rule of Kinship expresses any relationship between individuals as the product of a series of relationships. For instance, if we wished to compute the cousin relationship between M 31  and F 33  as shown in  FIG.  73   , we would represent this as the relationship between child and parent, parent and sibling, and the parent&#39;s sibling and their child. As can be noted, all components of the chain rule take the form of child given parent to move up the tree, sibling given sibling to move across the tree, and parent given child to move down the tree. These operations allow for complete navigation between any two individuals. Expressed another way:
 
     
       
         
           
             
               
                 
                     
                   
                     
                       Pr 
                       ⁡ 
                       ( 
                       
                         
                           G 
                           
                             c 
                             ⁢ 
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                     TABLE 41                  Probability of the event (e) an individual with a given genotype (Inde), conditioned (c) on another individual (Indc) having a given genotype.                                                  Pr(Ind e  = Grandchild|Ind e  = Grandparent 1 )               Pr(Ind e  = Child|Ind e  = Parent 1 )   Pr(Ind e  = Parent 1 |Ind e  = Child)   Parent 1 : p 1 , q 1 , Parent 2 : p 2 , q 2 ,       Ind e     Ind c     Parent 1 : p 1 , q 1  Parent 2 : p 2 , q 2     Parent 1 : p 1 , q 1  Parent 2 : p 2 , q 2     Grandparent 1 : p 3 , q 3 , Grandparent 2 : p 4 , q 4                 AA   AA   p 2                   p   2     *     p   1   2             p   2     *     p   1   2       +     0.5     p   2     *   2   ⁢     p   1     ⁢     q   1           =     p   1             p 2 p 4  + 0.5p 2 q 4                 AA   Aa   q 2                 0.5     p   2     *   2   ⁢     p   1     ⁢     q   1             p   2     *     p   1   2       +     0.5     p   2     *   2   ⁢     p   1     ⁢     q   1           =     q   1             q 2 p 4  + 0.5q 4                 AA   aa   0   0   0.5q 2 q 4                 Aa   AA   0.5p 2                   q   2     *     q   1   2           0.5     q   2     *   2   ⁢     p   1     ⁢     q   1       +       q   2     *     q   1   2           =     q   1             0.5p 2 p 4  + 0.25p 2                 Aa   Aa   0.5p 2  + 0.5q 2  = 0.5               q   2     *     p   1   2             q   2     *     p   1   2       +       (       0.5     p   2       +     0.5     q   2         )     *   2   ⁢     p   1     ⁢     q   1       +       p   2     *     q   1   2                 0.5p2q 4  + 0.25 + 0.5q 2 p 4                 Aa   aa   0.5q 2                 (       0.5     p   2       +     0.5     q   2         )     *   2   ⁢     p   1     ⁢     q   1             q   2     *     p   1   2       +       (       0.5     p   2       +     0.5     q   2         )     *   2   ⁢     p   1     ⁢     q   1       +       p   2     *     q   1   2                 0.25q 2  + 0.5q 2 q 4                 aa   AA   0   0   0.5p 2 p 4                 aa   Aa   p 2                 p   2     *     q   1   2             q   2     *     p   1   2       +       (       0.5     p   2       +     0.5     q   2         )     *   2   ⁢     p   1     ⁢     q   1       +       p   2     *     q   1   2                 0.5p 4  + p 2 q 4                 aa   aa   q 2                 0.5     q   2     *   2   ⁢     p   1     ⁢     q   1           0.5     q   2     *   2   ⁢     p   1     ⁢     q   1       +       q   2     *     q   1   2           =     p   1             0.5p 2 q 4  + q 2 q 4                 The genotype letter (A) represents the major allele with population frequency pi for individual i, while genotype letter (a) represents the minor allele with population frequency qi; this allows individuals to have different ethnicities.            
This takes the product of all people between two individuals, and uses the Bayesian Chain Rule of Kinship to compute a probability of a genotype given a particular relationship.
 
Extended Relationships
 
Extended relationships can be computed using the previously defined Bayesian Chain Rule of Kinship.
 
 FIG.  1    shows a family tree where each individual is identified as male (M) or female (F), and with two indices identifying their generation, along with a unique identifier for that individual within the generation. For instance F 23  represents the third unique woman appearing in the second generation.
 
Grandchild Given Grandparent
 
The probability of a child (M 31 ) having a given genotype Gc, given their grandparent (M 11 ) has a known genotype Gg can easily be computed using the Markov and chain rule assumptions to model the child (M 31 ) as dependent on their parent (F 21 ), and the parent (F 21 ) to be dependent on the grandparent (M 11 ).
 
                     Pr   ⁢     (       G   c     ❘     G   g       )       =       ∑     G   i           Pr   ⁡   (         G   c     ❘     G   p       =     G   i       )     *     Pr   ⁡   (       G   p     =       G   i     ❘     G   g         )                 (   7   )               
As the child is assumed to inherit grandparental DNA from only one parent, the probability equation decomposes into the child being directly dependent on their parent, and the parent being directly dependent on the grandparent. It is unnecessary to condition the child&#39;s genotype on the grandparent&#39;s genotype, as that is already factored into the parent&#39;s genotype. Given that the parent has an unknown genotype, Gi is used to marginalize over all possible genotypes for that parent.
 
Child Given Aunt/Uncle
 
The same principles apply to identify the likelihood that a child will have a genotype given that their aunt/uncle have a known genotype Gau. In this case, the probability of the child&#39;s genotype is decomposed into the relationship between child and parent, and parent and sibling.
 
                     Pr   ⁡   (       G   c     ❘     G   au       )     =       ∑     G     i   ⁢   1             ∑     G     i   ⁢   2             Pr   ⁡   (           G     c   ⁢   1       ❘     G     p   ⁢   1         =     G     i   ⁢   1         ,       G     p   ⁢   2       =     G     i   ⁢   2           )     *     Pr   ⁡   (       G     p   ⁢   1       =       G     i   ⁢   1       ❘     G     c   ⁢   2           )     *     Pr   ⁡   (       G     p   ⁢   2       =       G     i   ⁢   2       ❘     G     c   ⁢   2           )                   (   8   )               
Log Likelihood Calculation
 
All of the above formulation can be further used to calculate the log likelihood of two individuals having a particular relationship given the observed data. The log likelihood is defined as the probability of data (D) given a hypothesis (H).
 
 L =log( Pr ( D|H ))  (9)
 
In the case of familial identification, this is computed by taking the product of all conditional probabilities across SNPs. This allows for the computation of the likelihood of any relationship given the observed genotypes of two individuals.
 
Current Limitations
 
The current calculations rely on the independence of inheritance of all alleles. This simplifies the calculation; however, it does not account for haploblocks, or sex chromosomes. As a result of this, it is not possible to distinguish between different relationships that are two or more generations apart, or the directionality of the relationship (e.g. Parent given child, versus child given parent). However, this framework is generalizable, and fully capable of incorporating this information.
 
Results
 
The previously defined mathematical relationships are validated using an in silico database of ten million individuals that are separated across nine generations. The data are further subdivided into four different ethnic groups which have separate mAF values across the 39,108 sampled SNPs.
 
Data Relationship Separability
 
The relationship separability was examined as a function of the number of differences across SNPs. A difference was defined as the number of discordant alleles at each locus with a value between zero and two. The number of discrepancies was summed across all SNPs for a single pairwise relationship. This was then done for one thousand examples of each relationship. A kernel density estimate was fitted to this distribution and then shown in the figure below.
 
The number of differences across degree was plotted while varying the number of SNPs used in the comparison.  FIG.  74    plots differences across distributions using the full panel of 39k SNP loci. The level of separation is then plotted for half this panel, utilizing 20k SNPs as shown in  FIG.  75   , and finally the number of differences is examined with the panel reduced to only 2k SNPs, as shown in  FIG.  76   .
 
                     TABLE 42                  Confusion matrix for degree prediction                                                 Parent-   Sib-   Degree    Degree    Degree    Degree    Un-           Child   ling   2   3   4   5   related                                                     Parent-   2000   0   0   0   0   0   0       Child                                   Sibling   0   1000   0   0   0   0   0       Degree 2   0   0   4000   0   0   0   0       Degree 3   0   0   0   4997   3   0   0       Degree 4   0   0   0   1   949   50   0       Degree 5   0   0   0   0   53   903   44       Stranger   0   0   0   0   0   46   954                    
Log Likelihood Prediction
 
After examining differences between individuals, the log likelihood was then used to predict the degree of relation across pairs of individuals. At each pair, the algorithm identifies if it is a parent-child relationship, a sibling-sibling relationship, 2nd to 5th degree relationship, or two unrelated individuals. The performance for this assessment is shown in the Table 42.
 
As discussed, in silico data may be used to identify the degree of relatedness between individuals spanning four generations.  FIG.  2    demonstrated a clear separability between parent-child relationships and siblings, as well as between individuals with second, third, and unrelated levels of relationship. This was reflected through the log likelihood being able to fully and correctly identify the difference between individuals of these different degrees. As the degree increases, the curves become closer together. The upper tail of the 4th degree relatives is near the lower tail of unrelated individuals. For the 39k SNP panel, the distribution for 5th degree relatives overlap the distributions for 4th degree relatives and unrelated individuals. Larger SNP panels are required to separate 5th degree relatives from 4th degree relatives and unrelated individuals. The confusion matrix shown in Table 42 for this method illustrates the high accuracy on these in silico pedigrees. The impact of reducing the SNP panel size is illustrated in  FIG.  75    for 20k SNPs and  FIG.  76    for 2k SNPs. For the 2k SNPs panel, the different relationships become much less separable. The curves also become wider as a function of racial heterogeneity/admixture. As the amount of mixed ancestry increased the standard deviation of the distributions also increases. This also increases the difficulty of distinguishing levels of relationship in less related individuals.
 
In conclusion, a Bayesian framework may be used for identifying the level of relation between different individuals. This framework builds on the biology of inheritance, along with Bayesian statistics to predict degree of relation with-out requiring a training database or parameter optimization. This allows for further improvement by incorporating more biological properties into the model.
 
Equivalents
 
     While several inventive embodiments have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the function and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the inventive embodiments described herein. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the inventive teachings is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific inventive embodiments described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described and claimed. Inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the inventive scope of the present disclosure. 
     All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and/or ordinary meanings of the defined terms. 
     All references, patents and patent applications disclosed herein are incorporated by reference with respect to the subject matter for which each is cited, which in some cases may encompass the entirety of the document. 
     The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.” 
     The phrase “and/or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Multiple elements listed with “and/or” should be construed in the same fashion, i.e., “one or more” of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the “and/or” clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to “A and/or B”, when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc. 
     As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and/or” as defined above. For example, when separating items in a list, “or” or “and/or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of” or “exactly one of,” or, when used in the claims, “consisting of,” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of.” “Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law. 
     As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc. 
     It should also be understood that, unless clearly indicated to the contrary, in any methods claimed herein that include more than one step or act, the order of the steps or acts of the method is not necessarily limited to the order in which the steps or acts of the method are recited. 
     In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” “composed of,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of” shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03. It should be appreciated that embodiments described in this document using an open-ended transitional phrase (e.g., “comprising”) are also contemplated, in alternative embodiments, as “consisting of” and “consisting essentially of” the feature described by the open-ended transitional phrase. For example, if the disclosure describes “a composition comprising A and B”, the disclosure also contemplates the alternative embodiments “a composition consisting of A and B” and “a composition consisting essentially of A and B”. 
     Based on the foregoing disclosure, it should be apparent to one of ordinary skill in the art that the embodiments disclosed herein are not limited to a particular computer system platform, processor, operating system, network, or communication protocol. Also, it should be apparent that the embodiments disclosed herein are not limited to a specific architecture or programming language. 
     It is to be appreciated that embodiments of the methods and apparatuses discussed herein are not limited in application to the details of construction and the arrangement of components set forth in the following description or illustrated in the accompanying drawings. The methods and apparatuses are capable of implementation in other embodiments and of being practiced or of being carried out in various ways. Examples of specific implementations are provided herein for illustrative purposes only and are not intended to be limiting. In particular, acts, elements and features discussed in connection with any one or more embodiments are not intended to be excluded from a similar role in any other embodiments. 
     Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. Any references to embodiments or elements or acts of the systems and methods herein referred to in the singular may also embrace embodiments including a plurality of these elements, and any references in plural to any embodiment or element or act herein may also embrace embodiments including only a single element. References in the singular or plural form are not intended to limit the presently disclosed systems or methods, their components, acts, or elements. The use herein of “including,” “comprising,” “having,” “containing,” “involving,” and variations thereof is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. References to “or” may be construed as inclusive so that any terms described using “or” may indicate any of a single, more than one, and all of the described terms. Use of at least one of and a list of elements (e.g., A, B, C) is intended to cover one selection from A, B, C (e.g., A), two selections from A, B, C (e.g., A and B), three selections (e.g., A, B, C), and multiples of each selection. 
     Having thus described several aspects of at least one embodiment of this invention, it is to be appreciated that various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and scope of the invention. Accordingly, the foregoing description and drawings are by way of example only.