BACKGROUND
genetic linkage maps permit the elucidation of genome structure and organization and enable the identification of molecular markers linked to traits in an experimental segregating progeny, leading ultimately to the elucidation of the genetic basis of the trait of interest.
as a result, maps have been developed for many diverse plant species  <cit> .
traditionally, transferable linkage map development has been achieved through the scoring of restriction fragment length polymorphisms   <cit> , microsatellites  and gene specific markers  <cit>  in a segregating progeny.
using such markers, saturated reference linkage maps for many plant species have been developed.
reference maps inform the selection of markers for mapping in other progenies  <cit>  and have been used to anchor, order and orientate physical map bac contigs, and genome sequencing scaffolds for the assignment of pseudo-chromosomes for whole genome sequence initiatives  <cit> .
single nucleotide polymorphisms  are the most abundant mutations between related dna molecules.
the advent of affordable second generation sequencing technologies in recent years has led to the release of whole genome reference sequences for many plant species  <cit> , and the identification of abundant snps throughout the genomes of these organisms  <cit> .
thus, snps are becoming increasingly important as markers for both fundamental and applied genetics research in plants.
relatively low throughput methods have been developed for the analysis and mapping of snps.
these include high resolution melting   <cit> , and the cleaved amplified polymorphic dna  assay  <cit> .
additionally, medium and high throughput genotyping assays have been developed that permit hundreds of thousands of snps to be interrogated simultaneously on a single multiplexed array.
platforms for genotyping in this way include snplex, golden gate, infinium and axiom, which have been employed successfully for genotyping in many plant species including apple, peach, grape and purple false brome  <cit> .
genotyping arrays have many advantages over other techniques for genetic analysis, however an essential prerequisite for array development is a predetermined set of snps, preferably located at known positions on a reference genome sequence.
additionally, the transferability of heterozygous snps between species has been shown to be low  <cit>  and as such, in many genera, arrays must be developed specifically for the species under investigation.
thus for minor crops and for genotyping interspecific progenies or species complexes, the development of arrays is currently not a viable experimental solution.
despite the second generation sequencing ‘revolution’ in the biological sciences, many crops of significant economic importance remain without a reference genome sequence, or an abundance of snp data in public repositories.
high throughput snp genotyping for these organisms using array-based technologies is not economically viable, yet rapid, high-throughput snp genotyping would be immensely advantageous for the progression of classical mapping and qtl analyses, for genome-wide association studies and pedigree-based analyses, genomic selection and for the development and implementation of marker-assisted breeding and selection.
second generation sequencing has offered the possibility to genotype sequence variation in the genome of an organism for use in mapping experiments through whole genome re-sequencing.
whole genome re-sequencing has been employed for mapping in eukaryotic species with a relatively small genome size and on a selective mapping populations such as for the fungus venturia inequalis <cit> .
however, for the majority of organisms, even those with relatively small genomes such as the diploid strawberry fragaria vesca <cit>  a complexity reduction step must be performed prior to sequencing to enable sufficient depth of coverage of the same regions in all genomes of a segregating progeny to permit segregation to be scored.
genotyping through the sequencing of reduced representation genomic libraries developed through restriction digestion of genomic dna  was initially proposed by miller   <cit>  and adapted to incorporate barcoding for multiplexing with illumina sequencing technology by baird et al.
<cit> .
the rad procedure has been used successfully to identify snps in a number of plant species including eggplant, barley, and globe artichoke  <cit>  and its utility to linkage map development and qtl analysis in a large mapping population was demonstrated recently by pfender et al.
<cit> .
subsequently, elshire et al.
<cit>  proposed a method for the construction of highly multiplexed reduced complexity genotyping by sequencing  libraries.
the procedure is based on a similar restriction digestion technique to rad, however it is substantially less complicated, resulting in time and cost savings in library preparation, but the resultant data contains a larger number of missing genotype calls.
rubus is a genus in the rosaceae family containing more than  <dig> species, some of which, such as r. idaeus subsp.
idaeus l.  and rubus l. subgenus rubus watson  are of economic importance as cultivated fruit crops.
breeding methods for these species have remained largely unchanged since the first empirical breeding programs were initiated.
however, changes in cultural practices, the withdrawl of soil fumigants, and demands for increased fruit quality, shelf-life and for the extension of the traditional cultivation season, have necessitated novel breeding techniques to satisfy the demand for new cultivars.
the development and application of molecular tools for rubus would increase the speed and precision of the breeding process, particularly for traits that are difficult to characterize phenotypically, such as pyramided resistances to pests or pathogens.
looking further forward, rubus breeding would greatly benefit from genomic selection approaches that have recently become popular in crops such as maize, barley, and wheat  <cit>  because even modest gains from genomic selection could save years of in-field evaluation.
an essential precursor to the development of such tools is the characterization of an abundance of informative molecular markers with which to perform marker-trait association analyses.
in rubus, the majority of molecular markers that have been developed and mapped in the genus to date are ssrs  <cit> .
more recently, low throughput methods were employed for mapping snp markers in an interspecific rubus mapping progeny  <cit> , but high throughput methods for the identification and mapping of molecular markers have yet to be reported for the genus.
in this investigation, we have exploited the recent advances in low-cost sequencing and multiplexed library preparation  <cit>  to generate segregation data for snp markers distributed throughout the r. idaeus genome.
we used these markers for linkage map construction in a red raspberry progeny from the cross ‘heritage’×‘tulameen’ .
the segregation data was generated using multiplexed sequencing on the illumina hiseq sequencing-by-synthesis platform.
shallow genome sampling resulted in a data set containing a large proportion of missing values, and thus we developed a pipeline which includes a novel imputation algorithm  to deal with the missing and putatively erroneous data through comparison of genotypes in internal genotype bins following initial co-segregation analysis.
the challenges and solutions to generating and handling segregation data from thousands of loci for linkage mapping are discussed.
RESULTS
genotyping by sequencing
sequencing resulted in  <dig> , <dig> reads including deeper coverage of parents.
there were  <dig> , <dig> reads for ‘heritage’ and  <dig> , <dig> for ‘tulameen’.
within the population the mean number of reads was  <dig> , <dig> and the median was  <dig>  per individual.
forty-two individuals from the progeny were sequenced in library one and  <dig> individuals were sequenced in library two although each individual within a library was part of a 96-plex reaction in a single sequencing lane at two different sequencing centers.
sequence quality differed between the two sequencing lanes with a mean phred score at base  <dig> of  <dig>  in library one and a mean phred score at base  <dig> of  <dig>  in library two.
overall, library one had lower per base quality scores and a greater per base interquartile range compared to library two .
however, on a per read basis both libraries had quality scores greater than  <dig> for most reads .
in library one approximately  <dig>  percent of reads contained n’s  compared to only  <dig>  percent of reads in library two.
further differences in the error rate between the lanes is illustrated by the percentage of unique reads in each library because as coverage increases additional unique reads are likely to result from sequencing errors rather than new sequences .
overrepresented sequences in the libraries had high sequence similarity to the fragaria vesca chloroplast genome and accounted for approximately  <dig>  percent of library one and approximately  <dig>  percent of library two  as determined by alignment with bowtie .
the percent missing data was also a clear function of sequencing depth .
number of segregating snps identified
a total of  <dig> segregating snps were identified in the progeny following analysis of raw data using stacks  <cit> .
of these,  <dig> were present in the parental configuration ab×aa ,  <dig> in the configuration aa×ab , and the remaining  <dig> in the configuration ab×ab .
to simplify the process of imputation, and subsequent analysis using maximum likelihood implemented in joinmap  <dig>  , only snps segregating in a uni-parental configuration, i.e.
ab×aa or aa×ab were used for further analysis.
segregating ssrs identified in the h × t progeny
in total,  <dig> rubus ssr loci, distributed throughout the seven linkage groups of previously published rubus linkage maps were tested and identified as heterozygous in the ‘heritage’ parental genotype.
of these loci,  <dig> were also heterozygous in the ‘tulameen’ parental genotype.
the  <dig> markers were scored and mapped in the h×t progeny.
no heterozygous markers were found to define linkage group lg <dig> of the ‘tulameen’ map, however the other six linkage groups were all assigned numbers based on the ssrs which were located to each group, and thus lg <dig> was defined by default.
the positions of the ssrs on the ‘heritage’ linkage map were compared to their positions on the previously published ‘latham’ × ‘glen moy’  linkage maps of graham et al.
.
the version of the l×gm linkage groups containing the greatest number of common markers were compared to the ‘heritage’ linkage map.
the comparison of common markers  demonstrated a high degree of colinearity in marker order between the ‘heritage’ and l×gm linkage maps.
in all but one linkage group , marker order was maintained between the two populations, however, in the l×gm linkage map, genetic distances between markers were uniformly greater than on the ‘heritage’ linkage map.
total number of snps mapped and percentage of missing values
following initial co-segregation analysis a total of  <dig> snps displaying the parental configuration ab × aa , along with the  <dig> ssr markers scored in the progeny, coalesced into seven linkage groups associated with the haploid chromosome number for the species at a minimum lod score of  <dig> .
a further  <dig> snps, along with  <dig> ssr loci displaying the parental configuration aa × ab , coalesced into seven linkage groups at a minimum lod score of  <dig> .
the total number of data-points analysed in the initial phase of mapping was  <dig>  in  <dig> seedlings in the ‘heritage’ data set and  <dig>  in  <dig> seedlings in the ‘tulameen’ data set, containing a total of  <dig>   and  <dig>   missing values respectively.
the average number of perceived recombination events per individual was  <dig>  in ‘heritage’ and  <dig>  in ‘tulameen’, indicating a large number of double recombination events due to erroneous marker genotypes.
imputation
following imputation of missing values and removal of suspected erroneous genotypes using maskov, an average of  <dig>  and  <dig>  recombination events per individual were observed in the ‘heritage’ and ‘tulameen’ maps; a reduction in recombination of  <dig> % and 67% respectively, whilst the total map length was reduced by  <dig> % and  <dig> % respectively.
the  <dig> and  <dig> markers, including ssrs that mapped to the seven ‘heritage’ and ‘tulameen’ linkage groups were contained in  <dig> genotype bins on the ‘heritage’ linkage map and  <dig> on the ‘tulameen’ linkage map.
following co-segregation analysis using joinmap  <dig>   implementing the kosambi mapping function, the linkage maps presented in figure  <dig> were resolved.
the ‘heritage’ linkage map spanned a total of  <dig>  cm, with a maximum and minimum linkage group length of  <dig>  cm  and  <dig>  cm  respectively, an average length of  <dig>  cm and an average marker density of  <dig>  cm per marker, or  <dig>  cm per marker based on the genotyping bins .
the ‘tulameen’ map spanned a total of  <dig>  cm with a maximum and minimum linkage group length of  <dig>  cm  and  <dig>  cm , an average length of  <dig>  cm and an average marker density of  <dig>  cm per marker, or  <dig>  cm per marker based on the number of genotyping bins, rather than the total number of markers mapped.
tables  <dig> and  <dig> detail the marker composition and lengths of the seven ‘heritage’ and ‘tulameen’ lgs.
recombination ‘cold-spots’ were observed on six ‘heritage’  and one ‘tulameen’  linkage groups at which marker density was significantly higher than across the rest of the linkage group.
the markers mapped to the two parental maps, along with the linkage group and map position to which they were located, the snp type and the nucleotide sequence flanking each side of each snp are detailed in additional file 6: table s <dig>  comparison of data imputed manually and that imputed using maskov revealed that the two methods produced very similar datasets .
imputation using maskov tended to be more conservative due to the stringent parameters used in the pipeline.
the maps produced using both methods were colinear, however, those produced using maskov had fewer genotyping bins, containing relatively more markers, and thus had lower overall resolution than those produced manually.
segregation distortion
genome wide patterns of segregation distortion for ‘heritage’ and ‘tulameen’ are presented in figures  <dig> and  <dig>  a total of  <dig>  snps mapped on the ‘heritage’ and  <dig>  snps mapped on the ‘tulameen’ linkage maps displayed significant  segregation distortion.
segregation distortion was non-random across the two linkage maps, with similar localized regions of distortion observed on lg <dig>   <dig>   <dig> and  <dig> of both maps.
the most significant distortion was observed on lg <dig> of the ‘tulameen’ linkage map, where all markers displayed highly significant segregation distortion  and the lg length was significantly shorter than the other six lgs.
discussion
using a recently reported method of multiplexed, reduced representation library construction  <cit>  and massively parallel sequencing using the illumina hiseq platform, gbs was successfully employed to produce a high density, saturated linkage map for a red raspberry  mapping population.
problems of missing data and false negative genotyping calls were overcome by relying on data from snp genotyping bins to perform imputation of missing and erroneous data points within the segregation data matrix using maskov.
the ‘heritage’ and ‘tulameen’ linkage maps produced were of a comparable length to previously-published linkage maps of the species  <cit>  and to the linkage maps of closely-related genera such as diploid fragaria <cit>  and diploid rosa <cit> , but shorter than the l×gm rubus linkage maps published by graham et al.
<cit> .
a comparison of common ssr markers revealed almost complete colinearity between the ‘heritage’ and l×gm maps, but a reduction in genetic distance on the ‘heritage’ map.
since the process of imputation employed tended towards conservatively placing markers into genotypic bins and thus eliminating the occurrence of spurious double recombination events within the data, the process would also tend to reduce the overall length of the linkage maps produced.
however, positioning of common markers has demonstrated that the imputation process employed results in accurate marker placement, albeit at the expense of precise marker ordering within genotyping bins.
despite the calculation of relatively low inbreeding coefficients for both ‘heritage’ and ‘tulameen’  by dale et al.
<cit> , in this investigation we observed almost twice the level of heterozygous snps in the genome of ’heritage’ than in the genome of ‘tulameen’.
relatively high levels of genome differentiation and heterozygosity is a feature of red raspberry germplasm, despite the majority of modern varieties being derived from a narrow genetic base  <cit> .
the genome of ‘heritage’, the more heterozygous of the two parental genotypes, is currently being sequenced by an international consortium  <cit> , and thus data from the relative positions of snps mapped in this investigation within sequence scaffolds of the ‘heritage’ genome sequence will help to validate the snp positioning on the h×t linkage maps and will increase the precision of snp positions within genotype blocks.
additionally, the genetic positions of the snps on the h×t linkage maps will permit anchoring of sequencing scaffolds and the development of pseudochromosomes for the rubus genome sequence, as had been performed for other highly heterozygous genome sequences  <cit> .
the gbs approach used in this investigation enabled the identification and mapping of an unprecedented number of sequence characterized markers in rubus and to produce the most saturated linkage map for a species within the rosaceae family to date, at a fraction of the time and cost of developing maps for rubus using traditional marker technologies such as ssrs  <cit>  and gene specific and est-based markers  <cit> .
indeed, the methods employed here are more cost-effective than the array-based methods of snp detection and scoring, such as the irsc infinium whole genome genotyping array recently developed and used for linkage map construction in malus <cit> .
however, gbs as used in this investigation yielded data containing large amounts of missing values.
splitting the library preparations between two lanes of sequencing allowed examination of the effect that varied quality in sequencing has on the outcome.
one sequencing center provided data with nearly twice as many uncalled bases and in the current implementation of stacks reads containing uncalled bases are discarded.
increasing depth of coverage by sequencing each individual in multiple lanes would likely resolve the issue of missing values, but it is also expected that starting with dna of increased quality and purity would result in a more uniform restriction digestion and adapter ligation.
therefore performing manual dna extraction or preparing multiple libraries with independent automated dna extractions may result in more uniform sequencing and fewer missing values when the gbs method of elshire et al.
<cit>  is applied to linkage map construction.
the most robust method is likely to be one in which two independent library preparations are conducted and sequenced for each progeny individual in separate lanes.
choosing an enzyme that cuts less frequently could also reduce the number of missing values by increasing coverage per restriction fragment.
using a more rare cutting enzyme could also potentially reduce the amount of sequenced chloroplast dna.
however, the use of rare cutting enzymes in pseudo-testcross progenies that are less heterozygous would also dramatically decrease the number of markers detected in the aa × ab and ab × aa configuration.
as sequencing yield and quality continues to increase and costs continue to decrease, the desire to conduct larger and more highly multiplexed experiments may propagate the problem of missing data further.
the maskov imputation program that we present here can be used to overcome the challenges of missing data through map-based imputation.
on previously reported rubus linkage maps, regions of significant segregation distortion have been observed  <cit> .
similar regions of segregation distortion were observed in this investigation, however, the depth of marker saturation of the linkage maps presented here allowed us to plot the occurrence of segregation distortion along each linkage group with a high degree of precision.
a number of well-defined regions of the ‘heritage’ and ‘tulameen’ linkage maps exhibited significant segregation distortion and in many cases these regions were conserved between the two parental linkage maps, indicating the presence of lethal or sub-lethal genes that are conserved in heterozygous form in both parental genotypes.
jennings   <cit>  reported on the genetics of two loci, h conferring the presence of cane pubescence, and t conferring the presence of red pigmentation, and observed that they are rarely present in the homozygous forms hh and tt which was postulated to be due to lethal or sub-lethal genes linked in coupling to the dominant allele of each gene.
later, a gene affecting the viability of seeds in raspberry progenies and determining the presence or absence of cotyledonary glands was also described by jennings   <cit> .
graham et al.
<cit>  reported a genetic map position for gene h on lg <dig> of the ‘latham’ × ‘glen moy’ genetic linkage map, which is within the region of one of the defined areas of segregation distortion on the ‘heritage’ linkage map, as well as on the linkage map of sargent et al.
<cit> , but not on the ‘tulameen’ map.
both ‘heritage’ and ‘tulameen’ present the glabrous recessive phenotypes for gene h  however, the maps presented here suggest that there are a number of genes distributed throughout the seven r. idaeus chromosomes that exhibit a lethal or highly detrimental sub-lethal effects which are conserved in heterozygous form in the ‘heritage’ and ‘tulameen’ genotypes, presumably due to advantages associated with pleiotrpic effects of the recessive lethal or sub-lethal alleles.
these genes are most likely a factor in the high degree of heterozygosity that is maintained in rubus despite the breakdown of the self-incompatibility system in the species  <cit> .
whilst segregation distortion has previously been observed on genetic linkage maps of rubus <cit> , in this investigation, we have mapped markers in sufficient numbers to permit the identification of a number of conserved genetic regions between linkage maps putatively responsible for biased transmission of alleles.
the availability of a genome sequence for rubus would potentially allow the identification of candidate genes creating the segregation distortion apparent on the h×t linkage maps.
CONCLUSIONS
using gbs followed by imputation of missing data guided by marker membership to genotyping bins using maskov, we have identified and mapped a total of  <dig> snps in rubus and developed a comprehensive snp reference map for red raspberry.
as the flanking sequences of each of the snps presented here have been defined and are available in table s <dig>  marker positions from this investigation can be used to inform studies in other rubus populations.
fine mapping of regions of interest could be performed either through development of caps markers  <cit> , or hrm assays  <cit>  from snps within regions of interest to saturate existing rubus linkage maps, or by first identifying heterozygous snps from gbs of parental lines of genetically undefined mapping populations.
this could be followed by design of assays for selected heterozygous snps distributed throughout the seven rubus linkage groups.
the approach described here is suitable for the rapid and reliable development of saturated linkage mapping resources for any organism, whether or not it has been previously genetically characterized, or has an available genome sequence, and provides a wealth of genetic information that can serve as the starting point for downstream genetic investigations such as qtl analyses, positional cloning of genes controlling traits of interest, the anchoring of genome sequence contigs and the development of genomic selection strategies.

 genetic linkage maps permit the elucidation of genome structure and organization and enable the identification of molecular markers linked to traits in an experimental segregating progeny, leading ultimately to the elucidation of the genetic basis of the trait of interest. as a result, maps have been developed for many diverse plant species. traditionally, transferable linkage map development has been achieved through the scoring of restriction fragment length polymorphisms, microsatellites and gene specific markers in a segregating progeny. using such markers, saturated reference linkage maps for many plant species have been developed. reference maps inform the selection of markers for mapping in other progenies and have been used to anchor, order and orientate physical map bac contigs, and genome sequencing scaffolds for the assignment of pseudo-chromosomes for whole genome sequence initiatives. single nucleotide polymorphisms are the most abundant mutations between related dna molecules. the advent of affordable second generation sequencing technologies in recent years has led to the release of whole genome reference sequences for many plant species, and the identification of abundant snps throughout the genomes of these organisms. thus, snps are becoming increasingly important as markers for both fundamental and applied genetics research in plants. relatively low throughput methods have been developed for the analysis and mapping of snps. these include high resolution melting, and the cleaved amplified polymorphic dna assay. additionally, medium and high throughput genotyping assays have been developed that permit hundreds of thousands of snps to be interrogated simultaneously on a single multiplexed array. platforms for genotyping in this way include snplex, golden gate, infinium and axiom, which have been employed successfully for genotyping in many plant species including apple, peach, grape and purple false brome. genotyping arrays have many advantages over other techniques for genetic analysis, however an essential prerequisite for array development is a predetermined set of snps, preferably located at known positions on a reference genome sequence. additionally, the transferability of heterozygous snps between species has been shown to be low and as such, in many genera, arrays must be developed specifically for the species under investigation. thus for minor crops and for genotyping interspecific progenies or species complexes, the development of arrays is currently not a viable experimental solution. despite the second generation sequencing ‘revolution’ in the biological sciences, many crops of significant economic importance remain without a reference genome sequence, or an abundance of snp data in public repositories. high throughput snp genotyping for these organisms using array-based technologies is not economically viable, yet rapid, high-throughput snp genotyping would be immensely advantageous for the progression of classical mapping and qtl analyses, for genome-wide association studies and pedigree-based analyses, genomic selection and for the development and implementation of marker-assisted breeding and selection. second generation sequencing has offered the possibility to genotype sequence variation in the genome of an organism for use in mapping experiments through whole genome re-sequencing. whole genome re-sequencing has been employed for mapping in eukaryotic species with a relatively small genome size and on a selective mapping populations such as for the fungus venturia inequalis. however, for the majority of organisms, even those with relatively small genomes such as the diploid strawberry fragaria vesca a complexity reduction step must be performed prior to sequencing to enable sufficient depth of coverage of the same regions in all genomes of a segregating progeny to permit segregation to be scored. genotyping through the sequencing of reduced representation genomic libraries developed through restriction digestion of genomic dna was initially proposed by miller and adapted to incorporate barcoding for multiplexing with illumina sequencing technology by baird et al.. the rad procedure has been used successfully to identify snps in a number of plant species including eggplant, barley, and globe artichoke and its utility to linkage map development and qtl analysis in a large mapping population was demonstrated recently by pfender et al.. subsequently, elshire et al. proposed a method for the construction of highly multiplexed reduced complexity genotyping by sequencing libraries. the procedure is based on a similar restriction digestion technique to rad, however it is substantially less complicated, resulting in time and cost savings in library preparation, but the resultant data contains a larger number of missing genotype calls. rubus is a genus in the rosaceae family containing more than species, some of which, such as r. idaeus subsp. idaeus l. and rubus l. subgenus rubus watson are of economic importance as cultivated fruit crops. breeding methods for these species have remained largely unchanged since the first empirical breeding programs were initiated. however, changes in cultural practices, the withdrawl of soil fumigants, and demands for increased fruit quality, shelf-life and for the extension of the traditional cultivation season, have necessitated novel breeding techniques to satisfy the demand for new cultivars. the development and application of molecular tools for rubus would increase the speed and precision of the breeding process, particularly for traits that are difficult to characterize phenotypically, such as pyramided resistances to pests or pathogens. looking further forward, rubus breeding would greatly benefit from genomic selection approaches that have recently become popular in crops such as maize, barley, and wheat because even modest gains from genomic selection could save years of in-field evaluation. an essential precursor to the development of such tools is the characterization of an abundance of informative molecular markers with which to perform marker-trait association analyses. in rubus, the majority of molecular markers that have been developed and mapped in the genus to date are ssrs. more recently, low throughput methods were employed for mapping snp markers in an interspecific rubus mapping progeny, but high throughput methods for the identification and mapping of molecular markers have yet to be reported for the genus. in this investigation, we have exploited the recent advances in low-cost sequencing and multiplexed library preparation to generate segregation data for snp markers distributed throughout the r. idaeus genome. we used these markers for linkage map construction in a red raspberry progeny from the cross ‘heritage’×‘tulameen’. the segregation data was generated using multiplexed sequencing on the illumina hiseq sequencing-by-synthesis platform. shallow genome sampling resulted in a data set containing a large proportion of missing values, and thus we developed a pipeline which includes a novel imputation algorithm to deal with the missing and putatively erroneous data through comparison of genotypes in internal genotype bins following initial co-segregation analysis. the challenges and solutions to generating and handling segregation data from thousands of loci for linkage mapping are discussed.  genotyping by sequencing sequencing resulted in, reads including deeper coverage of parents. there were, reads for ‘heritage’ and, for ‘tulameen’. within the population the mean number of reads was, and the median was per individual. forty-two individuals from the progeny were sequenced in library one and individuals were sequenced in library two although each individual within a library was part of a 96-plex reaction in a single sequencing lane at two different sequencing centers. sequence quality differed between the two sequencing lanes with a mean phred score at base of in library one and a mean phred score at base of in library two. overall, library one had lower per base quality scores and a greater per base interquartile range compared to library two. however, on a per read basis both libraries had quality scores greater than for most reads. in library one approximately percent of reads contained n’s compared to only percent of reads in library two. further differences in the error rate between the lanes is illustrated by the percentage of unique reads in each library because as coverage increases additional unique reads are likely to result from sequencing errors rather than new sequences. overrepresented sequences in the libraries had high sequence similarity to the fragaria vesca chloroplast genome and accounted for approximately percent of library one and approximately percent of library two as determined by alignment with bowtie. the percent missing data was also a clear function of sequencing depth. number of segregating snps identified a total of segregating snps were identified in the progeny following analysis of raw data using stacks. of these, were present in the parental configuration ab×aa, in the configuration aa×ab, and the remaining in the configuration ab×ab. to simplify the process of imputation, and subsequent analysis using maximum likelihood implemented in joinmap, only snps segregating in a uni-parental configuration, i.e. ab×aa or aa×ab were used for further analysis. segregating ssrs identified in the h × t progeny in total, rubus ssr loci, distributed throughout the seven linkage groups of previously published rubus linkage maps were tested and identified as heterozygous in the ‘heritage’ parental genotype. of these loci, were also heterozygous in the ‘tulameen’ parental genotype. the markers were scored and mapped in the h×t progeny. no heterozygous markers were found to define linkage group lg of the ‘tulameen’ map, however the other six linkage groups were all assigned numbers based on the ssrs which were located to each group, and thus lg was defined by default. the positions of the ssrs on the ‘heritage’ linkage map were compared to their positions on the previously published ‘latham’ × ‘glen moy’ linkage maps of graham et al.. the version of the l×gm linkage groups containing the greatest number of common markers were compared to the ‘heritage’ linkage map. the comparison of common markers demonstrated a high degree of colinearity in marker order between the ‘heritage’ and l×gm linkage maps. in all but one linkage group, marker order was maintained between the two populations, however, in the l×gm linkage map, genetic distances between markers were uniformly greater than on the ‘heritage’ linkage map. total number of snps mapped and percentage of missing values following initial co-segregation analysis a total of snps displaying the parental configuration ab × aa, along with the ssr markers scored in the progeny, coalesced into seven linkage groups associated with the haploid chromosome number for the species at a minimum lod score of. a further snps, along with ssr loci displaying the parental configuration aa × ab, coalesced into seven linkage groups at a minimum lod score of. the total number of data-points analysed in the initial phase of mapping was in seedlings in the ‘heritage’ data set and in seedlings in the ‘tulameen’ data set, containing a total of and missing values respectively. the average number of perceived recombination events per individual was in ‘heritage’ and in ‘tulameen’, indicating a large number of double recombination events due to erroneous marker genotypes. imputation following imputation of missing values and removal of suspected erroneous genotypes using maskov, an average of and recombination events per individual were observed in the ‘heritage’ and ‘tulameen’ maps; a reduction in recombination of % and 67% respectively, whilst the total map length was reduced by % and % respectively. the and markers, including ssrs that mapped to the seven ‘heritage’ and ‘tulameen’ linkage groups were contained in genotype bins on the ‘heritage’ linkage map and on the ‘tulameen’ linkage map. following co-segregation analysis using joinmap implementing the kosambi mapping function, the linkage maps presented in figure were resolved. the ‘heritage’ linkage map spanned a total of cm, with a maximum and minimum linkage group length of cm and cm respectively, an average length of cm and an average marker density of cm per marker, or cm per marker based on the genotyping bins. the ‘tulameen’ map spanned a total of cm with a maximum and minimum linkage group length of cm and cm, an average length of cm and an average marker density of cm per marker, or cm per marker based on the number of genotyping bins, rather than the total number of markers mapped. tables and detail the marker composition and lengths of the seven ‘heritage’ and ‘tulameen’ lgs. recombination ‘cold-spots’ were observed on six ‘heritage’ and one ‘tulameen’ linkage groups at which marker density was significantly higher than across the rest of the linkage group. the markers mapped to the two parental maps, along with the linkage group and map position to which they were located, the snp type and the nucleotide sequence flanking each side of each snp are detailed in additional file 6: table s comparison of data imputed manually and that imputed using maskov revealed that the two methods produced very similar datasets. imputation using maskov tended to be more conservative due to the stringent parameters used in the pipeline. the maps produced using both methods were colinear, however, those produced using maskov had fewer genotyping bins, containing relatively more markers, and thus had lower overall resolution than those produced manually. segregation distortion genome wide patterns of segregation distortion for ‘heritage’ and ‘tulameen’ are presented in figures and a total of snps mapped on the ‘heritage’ and snps mapped on the ‘tulameen’ linkage maps displayed significant segregation distortion. segregation distortion was non-random across the two linkage maps, with similar localized regions of distortion observed on lg and of both maps. the most significant distortion was observed on lg of the ‘tulameen’ linkage map, where all markers displayed highly significant segregation distortion and the lg length was significantly shorter than the other six lgs. discussion using a recently reported method of multiplexed, reduced representation library construction and massively parallel sequencing using the illumina hiseq platform, gbs was successfully employed to produce a high density, saturated linkage map for a red raspberry mapping population. problems of missing data and false negative genotyping calls were overcome by relying on data from snp genotyping bins to perform imputation of missing and erroneous data points within the segregation data matrix using maskov. the ‘heritage’ and ‘tulameen’ linkage maps produced were of a comparable length to previously-published linkage maps of the species and to the linkage maps of closely-related genera such as diploid fragaria and diploid rosa, but shorter than the l×gm rubus linkage maps published by graham et al.. a comparison of common ssr markers revealed almost complete colinearity between the ‘heritage’ and l×gm maps, but a reduction in genetic distance on the ‘heritage’ map. since the process of imputation employed tended towards conservatively placing markers into genotypic bins and thus eliminating the occurrence of spurious double recombination events within the data, the process would also tend to reduce the overall length of the linkage maps produced. however, positioning of common markers has demonstrated that the imputation process employed results in accurate marker placement, albeit at the expense of precise marker ordering within genotyping bins. despite the calculation of relatively low inbreeding coefficients for both ‘heritage’ and ‘tulameen’ by dale et al., in this investigation we observed almost twice the level of heterozygous snps in the genome of ’heritage’ than in the genome of ‘tulameen’. relatively high levels of genome differentiation and heterozygosity is a feature of red raspberry germplasm, despite the majority of modern varieties being derived from a narrow genetic base. the genome of ‘heritage’, the more heterozygous of the two parental genotypes, is currently being sequenced by an international consortium, and thus data from the relative positions of snps mapped in this investigation within sequence scaffolds of the ‘heritage’ genome sequence will help to validate the snp positioning on the h×t linkage maps and will increase the precision of snp positions within genotype blocks. additionally, the genetic positions of the snps on the h×t linkage maps will permit anchoring of sequencing scaffolds and the development of pseudochromosomes for the rubus genome sequence, as had been performed for other highly heterozygous genome sequences. the gbs approach used in this investigation enabled the identification and mapping of an unprecedented number of sequence characterized markers in rubus and to produce the most saturated linkage map for a species within the rosaceae family to date, at a fraction of the time and cost of developing maps for rubus using traditional marker technologies such as ssrs and gene specific and est-based markers. indeed, the methods employed here are more cost-effective than the array-based methods of snp detection and scoring, such as the irsc infinium whole genome genotyping array recently developed and used for linkage map construction in malus. however, gbs as used in this investigation yielded data containing large amounts of missing values. splitting the library preparations between two lanes of sequencing allowed examination of the effect that varied quality in sequencing has on the outcome. one sequencing center provided data with nearly twice as many uncalled bases and in the current implementation of stacks reads containing uncalled bases are discarded. increasing depth of coverage by sequencing each individual in multiple lanes would likely resolve the issue of missing values, but it is also expected that starting with dna of increased quality and purity would result in a more uniform restriction digestion and adapter ligation. therefore performing manual dna extraction or preparing multiple libraries with independent automated dna extractions may result in more uniform sequencing and fewer missing values when the gbs method of elshire et al. is applied to linkage map construction. the most robust method is likely to be one in which two independent library preparations are conducted and sequenced for each progeny individual in separate lanes. choosing an enzyme that cuts less frequently could also reduce the number of missing values by increasing coverage per restriction fragment. using a more rare cutting enzyme could also potentially reduce the amount of sequenced chloroplast dna. however, the use of rare cutting enzymes in pseudo-testcross progenies that are less heterozygous would also dramatically decrease the number of markers detected in the aa × ab and ab × aa configuration. as sequencing yield and quality continues to increase and costs continue to decrease, the desire to conduct larger and more highly multiplexed experiments may propagate the problem of missing data further. the maskov imputation program that we present here can be used to overcome the challenges of missing data through map-based imputation. on previously reported rubus linkage maps, regions of significant segregation distortion have been observed. similar regions of segregation distortion were observed in this investigation, however, the depth of marker saturation of the linkage maps presented here allowed us to plot the occurrence of segregation distortion along each linkage group with a high degree of precision. a number of well-defined regions of the ‘heritage’ and ‘tulameen’ linkage maps exhibited significant segregation distortion and in many cases these regions were conserved between the two parental linkage maps, indicating the presence of lethal or sub-lethal genes that are conserved in heterozygous form in both parental genotypes. jennings reported on the genetics of two loci, h conferring the presence of cane pubescence, and t conferring the presence of red pigmentation, and observed that they are rarely present in the homozygous forms hh and tt which was postulated to be due to lethal or sub-lethal genes linked in coupling to the dominant allele of each gene. later, a gene affecting the viability of seeds in raspberry progenies and determining the presence or absence of cotyledonary glands was also described by jennings. graham et al. reported a genetic map position for gene h on lg of the ‘latham’ × ‘glen moy’ genetic linkage map, which is within the region of one of the defined areas of segregation distortion on the ‘heritage’ linkage map, as well as on the linkage map of sargent et al., but not on the ‘tulameen’ map. both ‘heritage’ and ‘tulameen’ present the glabrous recessive phenotypes for gene h however, the maps presented here suggest that there are a number of genes distributed throughout the seven r. idaeus chromosomes that exhibit a lethal or highly detrimental sub-lethal effects which are conserved in heterozygous form in the ‘heritage’ and ‘tulameen’ genotypes, presumably due to advantages associated with pleiotrpic effects of the recessive lethal or sub-lethal alleles. these genes are most likely a factor in the high degree of heterozygosity that is maintained in rubus despite the breakdown of the self-incompatibility system in the species. whilst segregation distortion has previously been observed on genetic linkage maps of rubus, in this investigation, we have mapped markers in sufficient numbers to permit the identification of a number of conserved genetic regions between linkage maps putatively responsible for biased transmission of alleles. the availability of a genome sequence for rubus would potentially allow the identification of candidate genes creating the segregation distortion apparent on the h×t linkage maps.  using gbs followed by imputation of missing data guided by marker membership to genotyping bins using maskov, we have identified and mapped a total of snps in rubus and developed a comprehensive snp reference map for red raspberry. as the flanking sequences of each of the snps presented here have been defined and are available in table s marker positions from this investigation can be used to inform studies in other rubus populations. fine mapping of regions of interest could be performed either through development of caps markers, or hrm assays from snps within regions of interest to saturate existing rubus linkage maps, or by first identifying heterozygous snps from gbs of parental lines of genetically undefined mapping populations. this could be followed by design of assays for selected heterozygous snps distributed throughout the seven rubus linkage groups. the approach described here is suitable for the rapid and reliable development of saturated linkage mapping resources for any organism, whether or not it has been previously genetically characterized, or has an available genome sequence, and provides a wealth of genetic information that can serve as the starting point for downstream genetic investigations such as qtl analyses, positional cloning of genes controlling traits of interest, the anchoring of genome sequence contigs and the development of genomic selection strategies. 
recently, robust genotyping methods based on high-throughput sequencing were developed, which provide high marker density, but result in some genotype errors and a large number of missing genotype values. the high marker density allowed identification of genomic regions with segregation distortion in r. idaeus, which may help to identify deleterious alleles that are the basis of inbreeding depression in the species. comparison of ssrs to published r. idaeus maps showed that the linkage maps constructed with gbs and our method of imputation were robust, and marker positioning reliable. genotyping by sequencinggbsradseqimputationraspberryrubus idaeuspsuedotestcrosslinkage mapsegregation distortion microsatellites linked these results to published maps for cross-validation and map comparison. detection of precise genomic regions with segregation distortion was possible because of map saturation. while low coverage and high variance in sequencing resulted in a large number of missing values for some individuals, a novel method of imputation based on maximum likelihood marker ordering from initial marker segregation overcame the challenge of missing values, and made map construction computationally tractable. the two resulting parental maps contained and molecular markers spanning and cm respectively over seven linkage groups.
 rapid development of highly saturated genetic maps aids molecular breeding, which can accelerate gain per breeding cycle in woody perennial plants such as rubus idaeus. recently, robust genotyping methods based on high-throughput sequencing were developed, which provide high marker density, but result in some genotype errors and a large number of missing genotype values. imputation can reduce the number of missing values and can correct genotyping errors, but current methods of imputation require a reference genome and thus are not an option for most species.  genotyping by sequencing was used to produce highly saturated maps for a r. idaeus pseudo-testcross progeny. while low coverage and high variance in sequencing resulted in a large number of missing values for some individuals, a novel method of imputation based on maximum likelihood marker ordering from initial marker segregation overcame the challenge of missing values, and made map construction computationally tractable. the two resulting parental maps contained and molecular markers spanning and cm respectively over seven linkage groups. detection of precise genomic regions with segregation distortion was possible because of map saturation. microsatellites linked these results to published maps for cross-validation and map comparison.  gbs together with genome-independent imputation provides a rapid method for genetic map construction in any pseudo-testcross progeny. our method of imputation estimates the correct genotype call of missing values and corrects genotyping errors that lead to inflated map size and reduced precision in marker placement. comparison of ssrs to published r. idaeus maps showed that the linkage maps constructed with gbs and our method of imputation were robust, and marker positioning reliable. the high marker density allowed identification of genomic regions with segregation distortion in r. idaeus, which may help to identify deleterious alleles that are the basis of inbreeding depression in the species. genotyping by sequencinggbsradseqimputationraspberryrubus idaeuspsuedotestcrosslinkage mapsegregation distortion 