# Deciphering the genetic diversity of landraces with high-throughput SNP genotyping of DNA bulks: methodology and application to the maize 50k array Mariangela Arca

Mariangela Arca, Tristan Mary-Huard, Cyril Bauland, Brigitte Gouesnard, Aurélie Berard, Valérie Combes, Delphine Madur, Alain Charcosset, Stephane Nicolas

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Mariangela Arca, Tristan Mary-Huard, Cyril Bauland, Brigitte Gouesnard, Aurélie Berard, et al. Deciphering the genetic diversity of landraces with high-throughput SNP genotyping of DNA bulks: methodology and application to the maize 50k array Mariangela Arca. 2020. hal-02965048

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Deciphering the genetic diversity of landraces with high-
throughput SNP genotyping of DNA bulks: methodology and
application to the maize 50k array

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Mariangela Arca¹, Tristan Mary-Huard ¹, Brigitte Gouesnard², Aurélie Bérard³, Cyril

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Bauland¹, Valérie Combes¹, Delphine Madur¹, Alain Charcosset¹, Stéphane D. Nicolas¹

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Author's affiliations :

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1 Université Paris-Saclay, INRAE, CNRS, AgroParisTech, GQE - Le Moulon, 91190,

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Gif-sur-Yvette, France

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2 Amélioration Génétique et Adaptation des Plantes méditéranéennes et tropicales, Univ

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Montpellier, CIRAD, INRAE, Institut Agro, F-34090 Montpellier, France

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3 Université Paris-Saclay, INRAE, Etude du Polymorphisme des Génomes Végétaux,

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91000, Evry-Courcrounnes, France

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Corresponding authors: stephane.nicolas@inrae.fr

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**ABSTRACT**

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Genebanks harbor original landraces carrying many original favorable alleles for mitigating biotic and abiotic stresses. Their genetic diversity remains however poorly characterized due to their large within genetic diversity. We developed a high-throughput, cheap and labor saving DNA bulk approach based on SNP Illumina Infinium HD array to genotype landraces. Samples were gathered for each landrace by mixing equal weights from young leaves, from which DNA was extracted. We then estimated allelic frequencies in each DNA bulk based on fluorescent intensity ratio (FIR) between two alleles at each SNP using a two step-approach. We first tested either whether the DNA bulk was monomorphic or polymorphic according to the two FIR distributions of individuals homozygous for allele A or B, respectively. If the DNA bulk was polymorphic, we estimated its allelic frequency by using a predictive equation calibrated on FIR from DNA bulks with known allelic frequencies. Our approach: (i) gives accurate allelic frequency estimations that are highly reproducible across laboratories, (ii) protects against false detection of allele fixation within landraces. We estimated allelic frequencies of 23,412 SNPs in 156 landraces representing American and European maize diversity. Modified Roger's genetic Distance between 156 landraces estimated from 23,412 SNPs and 17 SSRs using the same DNA bulks were highly correlated, suggesting that the ascertainment bias is low. Our approach is affordable, easy to implement and does not require specific bioinformatics support and laboratory equipment, and therefore should be highly relevant for large-scale characterization of genebanks for a wide range of species.

Keywords: Landraces, DNA pooling, Genetic diversity, 50K Illumina Infinium HD Zea mays L., Allelotyping, genebanks
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# INTRODUCTION

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Genetic resources maintained *in situ* or *ex situ* in genebanks represent a vast reservoir of traits/alleles for future genetic progress and an insurance against unforeseen threats to agricultural production (Tanksley 1997; Hoisington et al. 1999; Kilian and Graner 2012; McCouch et al. 2012). Due to their local adaptation to various agro-climatic conditions and human uses, landraces are particularly relevant to address climate change and the requirements of low input agriculture (Fernie et al. 2006; McCouch et al. 2012; Mascher et al. 2019). For instance, maize displays considerable genetic variability, but less than 5 % of this variability has been exploited in elite breeding pools, according to (Hoisington et al. 1999). However, landraces are used to a very limited extent, if any, in modern plant breeding programs, because they are poorly characterized, genetically heterogeneous and exhibit poor agronomic performance compared to elite material (Kilian and Graner 2012; Strigens et al. 2013; Brauner et al. 2019; Mascher et al. 2019; Hölker et al. 2019). Use of molecular techniques for characterizing genetic diversity of landraces and their relation with the elite germplasm is essential for a better management and preservation of genetic resources and for a more efficient use of these germplasms in breeding programs (Hoisington et al. 1999; Mascher et al. 2019).

The genetic diversity of landraces conserved *ex situ* or *in situ* has been extensively studied using various types of molecular markers such as restriction fragment length polymorphism (RFLP) or simple sequence repeat (SSR) in maize (Dubreuil and Charcosset 1998; Dubreuil et al. 1999; Rebourg et al. 1999, 2001; Gauthier et al. 2002; Rebourg et al. 2003; Reif et al. 2005b; Vigouroux et al. 2005; Reif et al. 2005a; Camus-Kulandaivelu 2006; Dubreuil et al. 2006; Eschholz et al. 2010; Mir et al. 2013), in Pearl Millet (Bhattacharjee et al. 2002), cabbage (Dias et al. 1991; Divaret et al. 1999), Barley (Parzies et al. 2000; Backes et al. 2003; Hagenblad et al. 2012), pea (Hagenblad et al. 2012), oat (Hagenblad et al. 2012), rice (Ford-Lloyd et al. 2001; McCouch et al. 2012), Alfalfa (Pupilli et al. 2000; Segovia-Lerma et al. 2003) and fonio millet (Adoukonou-Sagbadja et al. 2007). SSRs have proven to be markers of choice for analyzing diversity in different plant species and breeding research, because of their variability, ease of use, accessibility of detection and reproducibility (Liu et al. 2003; Reif et al. 2006; Yang et al. 2011). Nevertheless, the development of SSR markers requires a substantial investment of time and money. Allele coding is also difficult to standardize across genotyping platforms and laboratories, a major drawback in a genetic resources characterization context. SNPs have become the marker of choice for various crop species such as maize (Ganal et al. 2011), rice (McCouch et al. 2010), barley (Moragues et al. 2010) and soybean (Lam et al. 2010). They are
the most abundant class of sequence variation in the genome, co-dominantly inherited, genetically stable and appropriate to high-throughput automated analysis (Rafalski 2002). For instance, maize arrays with approx. 50,000 and 600,000 SNP markers are available since 2010 (Illumina MaizeSNP50 array, Ganal et al. 2011) and 2013 (600K Affymetrix Axiom, Unterseer et al., 2013), respectively. SNP arrays may however lead to some ascertainment bias notably when diversity analysis was performed on a plant germplasm distantly related from those that have been used to discover SNP put on the array (Nielsen 2004; Clark et al. 2005; Hamblin et al. 2007; Inghelandt et al. 2011; Frascaroli et al. 2013). Properties of SNP array regarding diversity analysis have to be carefully investigated to evaluate ascertainment bias. For maize 50K Infinium SNP array, only “PZE” prefixed SNPs (so called later PZE SNPs in this study) give consistent results for diversity analysis as compared with previous studies based on SSR markers and are therefore suitable for assessing genetic variability (Inghelandt et al. 2011; Ganal et al. 2011; Bouchet et al. 2013; Frascaroli et al. 2013). 50K Infinium SNP array has been used successfully to decipher genetic diversity of inbred lines (van Heerwaarden et al. 2011; Bouchet et al. 2013; Frascaroli et al. 2013; Rincent et al. 2014), landraces using either doubled haploids (Strigens et al. 2013) or a single individual per accession (van Heerwaarden et al. 2011; Arteaga et al. 2016), or teosinte with few individuals per accession (Aguirre-Liguori et al. 2017).

Due to high diversity within accessions, characterization of landraces from allogamous species such as maize or alfalfa should be performed based on representative sets of individuals (Reyes-Valdés et al. 2013, Segovia-Lerma et al., 2002, Dubreuil and Charcosset., 1998). Despite the recent technical advances, genotyping large numbers of individuals remains very expensive for many research groups. To bring costs down, estimating allele frequencies from pooled genomic DNA (also called “allelotyping”) has been suggested as a convenient alternative to individual genotyping using high-throughput SNP arrays (Sham et al. 2002; Teumer et al. 2013) or using Next Generation Sequencing (Schlötterer et al. 2014). It was successfully used to decipher global genetic diversity within maize landraces using RFLPs (Dubreuil and Charcosset 1998; Dubreuil et al. 1999; Rebourg et al. 2001, 2003; Gauthier et al. 2002) and SSR markers (Reif et al. 2005a; Camus-Kulandaivelu 2006; Dubreuil et al. 2006; Yao et al. 2007; Mir et al. 2013). Various methods for estimating gene frequencies in pooled DNA have been developed for RFLP (Dubreuil and Charcosset 1998), SSR (LeDuc et al. 1995; Perlin et al. 1995; Daniels et al. 1998; Lipkin et al. 1998; Breen et al. 1999) and SNP marker arrays in human and animal species (Hoogendoorn et al. 2000; Craig et al. 2005; Brohede 2005;
Teumer et al. 2013; Gautier et al. 2013). These methods have been successfully used to detect QTL (Lipkin et al. 1998), to decipher genetic diversity (Segovia-Lerma et al. 2003; Dubreuil et al. 2006; Pervaiz et al. 2010; Johnston et al. 2013; Ozerov et al. 2013), to perform genome wide association studies (Barcellos et al. 1997; Sham et al. 2002; Baum et al. 2007), to identify selective sweep (Elferink et al. 2012) or to identify causal mutation in tilling bank (Abe et al. 2012). Genotyping DNA bulks of individuals from landraces with SNP arrays could therefore be interesting to characterize and manage genetic diversity in plant germplasm. SNP arrays could be notably a valuable tool to identify selective sweep between landraces depending on their origin, to manage plant germplasm collection at worldwide level (e.g. identify duplicate), to identify landraces poorly used so far in breeding programs or to identify genomic regions where diversity has been lost during the transition from landraces to inbred lines (Arca et al., in prep).

In this study, we developed a new DNA bulk method to estimate allelic frequencies at SNPs based on Fluorescent Intensity data produced by the maize 50K Illumina SNP array (Ganal et al. 2011). Contrary to previous methods that have been mostly developed for QTL detection purposes, our approach is dedicated to genome-wide diversity analysis in plant germplasm since it protects against false detection of alleles. Additionally, calibration of equations for predicting allelic frequencies of DNA bulks for each SNP is based on controlled pools with variable allelic frequencies rather than only heterozygous genotypes as in previous methods (Hoogendoorn et al. 2000; Brohede 2005; Peiris et al. 2011; Teumer et al. 2013). As a proof of concept, we applied our new approach to maize by estimating allelic frequencies of 23,412 SNPs in 156 maize landraces representative of European and American diversity present in genebanks (Arca et al., in prep). To our knowledge, it is the first time that a DNA bulk approach was used on 50K maize high-throughput SNP array to study genetic diversity within maize landraces germplasm.

## RESULTS

We developed a new method to estimate allelic frequencies of SNPs within pools of individuals using the fluorescent intensity ratio (FIR) between A and B alleles from Illumina MaizeSNP50 array. Briefly, allelic frequencies at SNPs belonging to MaizeSNP50 array were estimated within 156 maize landraces by pooling randomly 15 individuals per population and by calibrating a predictive two-step model (Figure 1). We considered only the subsample of 32,788 prefixed PZE markers (so called PZE SNPs) that have proven suitable for diversity
analyses (Ganal *et al.* 2011). Among these SNPs, we selected 23,412 SNPs that passed weighted
deviation (wd) quality criteria (wd>50). This removed SNPs for which estimated allelic
frequency deviated strongly from expected allelic frequency (Figure. S1 A, B, C, D, E, F and
G for the threshold choice and validation).

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**Accuracy of allelic frequency prediction and detection of allele fixation**

In order to prevent erroneous detection of alleles within landraces, we first tested for each
landrace whether allele A or allele B was fixed at a given SNP locus (Figure 1). We tested for
SNP whether the FIR of the landrace was included within one of the two Gaussian
distributions drawn from mean and variance of FIR of genotypes AA and BB within the inbred
line panel (Figure 1). For landraces that were considered polymorphic after this first step (allele
fixation rejected for both alleles), we estimated allelic frequency based on FIR by using a unique
logistic regression model for the 23,412 SNPs, calibrated with a sample of 1,000 SNPs (Figure
1). Parameters of the logistic model were adjusted on these 1,000 SNPs using FIR of two series
of controlled pools whose allelic frequencies were known (Figure S2). We obtained these pools
by mixing various proportion of two series of three inbred lines with known genotypes (Table
1). The 1,000 SNPs were selected to maximize the allelic frequency range within controlled
pools (Table 1). The logistic regression was calibrated on 1,000 SNPs taken together rather than
for each SNP individually to avoid the ascertainment bias that would be generated by selecting
only SNPs polymorphic in the controlled pools (Figure S3) and to reduce loss of accuracy in
prediction for SNPs displaying limited allelic frequency range in two controlled pools (Figure
S4). To investigate the loss of accuracy of the prediction curve due to a reduction in allelic
frequency ranges in controlled pool, we progressively removed at random from one to 15
samples from the calibration set of the 1000 above described SNPs. The mean absolute error
(MAE) between 1000 replications increased significantly from 4.14 % to 8.54 % when
removing more samples (Table 2). For comparison, MAE was 7.19 % using a cross-validation
approach in which the predictive equation was calibrated with a random subsample of 800 out
of 1000 SNPs, and then applied to estimate allelic frequencies for the remaining 200 SNPs
(Table S1). Calibrating the logistic regression between FIR and allelic frequency in controlled
pool based on 1000 SNPs therefore appears well adapted to prevent ascertainment bias while
increasing globally prediction accuracy (Figure S4). Finally, we observed that MAE was higher
for balanced allelic frequencies than for almost fixed allelic frequencies (Figure 2 and Tables
S2). Accordingly, the dispersion of predicted frequencies were larger for expected allelic
frequencies near 0.5 than for fixed alleles (Table S2).
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## Reproducibility of frequency across laboratories and samples

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We evaluated the reproducibility of the method across laboratories by comparing FIR of one series of controlled pools from two different laboratories using all PZE SNPs or 23,412 SNPs selected using *wd* criterion (Figure 3). The correlation between the two different laboratories for controlled pools was very high (r²>0.98) whether we selected the SNPs based on *wd* criterion or not. Beyond reproducibility across laboratories, the precision of frequency estimation depends on the sampling of individuals within landraces (Table 3). The precision of frequency estimation was addressed both by numerical calculation and by the independent sampling of 15 different individuals (30 different gametes) within 10 landraces (biological replicate). For both numerical calculations and biological replicates, the sampling error was higher for loci with balanced allelic frequencies than for loci that are close to fixation (Table 3, Figure 4). Sampling error also decreased as the number of sampled individuals increased (Table 3). Considering a true frequency of 50% within landraces, we expect that 95% of frequency estimates lie between 31.30% and 68.70% when sampling 15 individuals per landrace and 42.9 to 57.13% when sampling 100 individuals per landrace (Table 3). Considering biological replicates, allelic frequencies of the two biological replicates over 23,412 SNPs were highly correlated except for population Pol3 (Table S3). When excluding Pol3, 94.5% of points were located within the 95% confidence limits accounting for the effect of sampling alone, suggesting that the error inherent to the frequency estimation for DNA pools was very low compared to the sampling error (Figure 4). Over nine populations with replicates (excluding Pol3), we observed only four situations among 23,412 loci where two different alleles were fixed in the two replicates (Figure 4). Loci for which an allele was fixed in one replicate was either fixed or displayed a high frequency (above 88%) for the same allele in the other replicate in 98% of cases. Moreover, we estimated pairwise roger's genetic distance (MRD) based on 23,412 SNPs between the two independent pools from the same landraces. Excluding Population Pol3 (MRD = 0.208), this distance ranged from 0.087 to 0.120 (Table S3). These values provide a reference to decide whether two populations can be considered different or not.

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## Effect of SNP number and *wd* on the relationship of genetic distance estimated with SNP and SSR

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Finally, we evaluated the possible ascertainment bias due to SNP selection with our filtering based on *wd* criterion. MRD obtained with 17 SSR markers (MRD<sub>SSR</sub>) and MRD based on
different set of SNP markers (MRD<sub>SNP</sub>) were highly correlated (Figure 5), indicating a low ascertainment bias. The selection of SNPs based on *wd* quality criterion strongly increased the coefficient of determination (r<sup>2</sup>) between MRD<sub>SNP</sub> and MRD<sub>SSR</sub>, from 0.587 to 0.639 (Figure S6). We attempted to define the minimal SNP number required to correctly describe the relationship between maize landraces. While increasing the number of SNPs from 500 to 2500 slightly increased r<sup>2</sup> between MRD<sub>SNP</sub> and MRD<sub>SSR</sub> from 0.606 to 0.638 (Figure S6 D,E,F), we observed no further increase beyond 2500 SNPs (Figure S6 A, B, C) suggesting that 2,500 SNPs are enough to obtain a correct picture of landrace relationships.
209 **DISCUSSION**

210 A molecular approach for diversity analysis of landraces needs to answer several criteria
211 (i) an accurate estimation of allelic frequency in each population, (ii) a robust and reproducible
212 measurement of allelic frequency across laboratories in order to facilitate comparison of genetic
213 diversity of accessions across genebanks, (iii) a reliable estimate of genetic distance between
214 landraces with no or little ascertainment bias (iv) an affordable, high-throughput and labor
215 efficient method, due to both strong financial and human constraints in plant genebanks. Four
216 main sources of errors affect the accuracy of allelic frequency estimation of a locus in a
217 population using a DNA pooling approach: (i) the sampling of individuals (so called “sampling”
218 errors), (ii) the procedure to mix DNA from individuals (so called “DNA mixing” errors) (iii)
219 the imprecision of quantitative measurement used by the model for the prediction (so called
220 “experimental” errors) and (iv) the predictive equation used to predict allelic frequency in a
221 population (so called “approximation” errors).

222 **A two-step model to protect against erroneous detection of**
223 **polymorphism and predict accurately allelic frequencies in DNA bulk**

224 Approximation errors due to predictive equation depend on (i) the model used to predict
225 allelic frequencies and (ii) the set of individuals and SNPs used to calibrate the predictive
226 equation. In this study, we used a two-step modeling using inbred lines and controlled pools as
227 sets of calibration to test for polymorphism and then predict allelic frequency for polymorphic
228 markers. Detection of allele fixation in a population is an important issue for deciphering
229 and managing genetic diversity within plant and animal germplasm. We used two Student
230 tests based on fluorescent intensity ratio (FIR) distribution of lines homozygous for allele
231 A and B to determine polymorphism of a SNP in a given landrace (Figure 1). In this first
232 step, we preferred a method based on FIR distribution rather than the clustering
233 approach implemented in genome studio because it is possible to control the type I risk
234 of false allele detection (at 5% in our study). Using this two-step approach reduces
235 strongly the erroneous detection of polymorphisms in a population compared to previous
236 methods: MAE for fixed locus <0.1% in our approach (Table S2) vs ~2-3% using PPC
237 method (Brohede 2005) or ~2-8% using different k correction from (Peiris et al. 2011).
238 This is not surprising as previous methods focused on an accurate estimation of the
239 difference in allele frequencies between DNA bulks of individuals contrasted for a
240 quantitative trait of interest (Sham et al. 2002; Craig et al. 2005; Kirov et al. 2006; Teumer et al. 2013) and did not focus specifically on protecting again false detection of alleles.

242 For loci that were detected as polymorphic, we predicted allelic frequencies from 243 FIR in landrace DNA pools by using a unique logistic regression for 23,412 SNPs passing 244 wd quality criterion. The relationship between FIR and allelic frequency was modelled 245 using a quasi-logistic regression for different reasons. First, the logistic function ensures 246 that the predicted frequencies take value in (0,1), a property that is not satisfied by 247 polynomial regression (PPC) or tan transformation (Brohede 2005; Teumer et al. 2013). 248 Second, one could observe that the relationship between the fluorescent intensity ratio 249 and allelic frequencies within controlled pools was not linear (Figure S2).

250 This two-step approach led to a low global error rate in allelic frequency prediction 251 (MAE = 3% for polymorphic and monomorphic loci considered jointly; Figure 2, Table S2). 252 It is comparable to the most accurate previous pooling DNA methods for SNP array that 253 used a specific model for each SNP: (i) MAE ranging from 3 to 8% (Peiris et al., 2011) or 254 5-8% (Brohede et al., 2005) depending on k-correction applied (ii) MAE ~ 3% for PPC 255 correction (Brohede et al., 2005; Teumer et al., 2013) (iii) MAE ~ 1% for tan-correction 256 (Teumer et al., 2013). Several factors can explain this relative good global accuracy of our 257 approach. First, almost half of the loci were fixed on average in each landrace, which 258 contributed positively to global accuracy since our method over-performed previous 259 methods for fixed locus (see above). Second, wd quality criterion removed SNPs for which 260 allelic frequencies were poorly predicted using FIR. We observed indeed that increasing 261 the threshold for wd quality criterion led to a global increase in accuracy at both steps 262 (Figure S1). While 90% of SNPs have a MAE<2% for wd criterion >10, only 50% of SNPs 263 have a MAE<2% for wd criterion <10. Taking into account differential hybridization by 264 using a specific logistic regression for each SNP could be a promising way to further 265 improve the accuracy of allelic frequencies prediction, notably for balanced allelic 266 frequencies (Brohede et al., 2005, Peiris et al., 2011, Teumer et al., 2013). To limit possible 267 ascertainment bias and errors in allelic frequency estimation, it requires however to 268 genotype additional series of controlled pools for SNPs for which current controlled pools 269 were monomorphic or have a limited range of allelic frequency (Figure S3 and S4).
To estimate the parameters of the logistic regression, we used two series of controlled pools rather than heterozygous individuals for both technical and practical reasons. Controlled pools cover more homogenously the frequency variation range than heterozygous and homozygous individuals only, which therefore limits the risk of inaccurate estimation of logistic model parameters. Different studies showed that accuracy of allelic frequency estimation strongly depends on accuracy of FIR estimation for heterozygous individual and therefore the number of heterozygous individuals (Le Hellard et al. 2002; Simpson 2005; Jawaid and Sham 2009). Between 8 and 16 heterozygous individuals are recommended to correctly estimate FIR mean for heterozygous individuals, depending on FIR variance (Le Hellard et al. 2002). In maize, we can obtain heterozygote genotypes either by crossing inbred lines to produce F1 hybrids, by planting seeds from maize landraces, or by using residual heterozygosity of inbred lines. Using residual heterozygosity to calibrate model is not possible since half SNPs show no heterozygous genotype in the 327 inbred lines of our study. Obtaining at least 16 heterozygous individuals for each SNP therefore requires to genotype a few dozens of F1 hybrids or individuals from landraces considering that expected heterozygosity in a landrace is comprised between 3 and 28% (Arca et al., in prep). This represents additional costs since maize researchers and breeders genotyped preferentially inbred lines to access directly haplotypes without phasing and because genotypes of F1 hybrids can be deduced of that of their parental inbred lines. Beyond allogamous species as maize, genotyping heterozygous individuals could be time demanding and very costly in autogamous cultivated plant species for which genotyped individuals are mostly homozygotes (wheat, tomato, rapeseed). On the contrary, one can easily produce controlled pools whatever the reproductive system, either by mixing DNA or equal mass of plant materials, which allows producing a wide range of allelic frequencies.

## Effect of DNA mixing procedure on accuracy of allelic frequency estimation

There are two main errors coming from DNA mixing procedure: (i) the “sampling error” that is directly connected to the number of individuals sampled in each population (Table 3), and (ii) the “bulking error” associated with the laboratory procedure to mix equal DNA amounts of sampled individuals.
We evaluated sampling and bulking errors by comparing 10 independent biological replicates from 10 different landraces obtained by independently sampling and mixing equal leaf areas of young leaves of 15 individuals. Allelic frequencies estimated for both biological replicates from a same landrace were highly correlated. Excluding Pol3, 94.5% of difference of allelic frequencies between replicates was of included within 95% confidence limits originated from sampling effect only Figure 4). This suggests that the "bulking error" is low compared to the "sampling error". Consistently, Dubreuil et al., (1999) observed a low "bulking error" for RFLP markers using the same DNA pooling method, with a coefficient of determination of 0.99 between allelic frequencies based on individual genotyping of plants and those predicted using DNA bulks. Several studies also showed that the effect of bulking errors on allelic frequencies measured by comparing DNA pool and individual genotyping of plant of this DNA pool is very low compared with other sources of errors (Le Hellard et al. 2002; Jawaid and Sham 2009). Additionally, the mixing procedure starting from leaf samples strongly reduced the number of DNA extractions for each DNA bulk as compared to first extracting DNA from each individual, and then mixing by pipetting each DNA samples to obtain an equimolar DNA mix ("post-extraction" approach). Since the cost of DNA extraction becomes non-negligible when the number of individual increases, mixing plant material based on their mass before extraction is highly relevant to save time and money. This can be done without losing accuracy as shown in this study for SNP array and previously for RFLP by Dubreuil et al., (1999).

We highlighted the critical importance of the number of individuals sampled per landrace on allelic frequency estimation (Table 3). By using DNA pooling, accuracy can be gained with very little additional cost by increasing number of sampled individuals. Whereas a high accuracy of allelic frequency estimation within landraces is required to scan genome for selective sweeps, it is less important to estimate global genetic distance, due to the large number of SNPs analyzed. Sampling fifteen plants per population (30 gametes) appears convenient to obtain an accurate estimation of frequencies in a population and analyze genetic diversity (Reyes-Valdés et al. 2013).

**A low ascertainment bias to estimate genetic distance between landraces**
There are two possible sources of ascertainment bias using a DNA pooling approach on a SNP array. The first one relates to the design of array because the set of lines to discover SNPs may not well represent genetic diversity and a threshold in allelic frequency was possibly applied to select SNPs. The second one relates to the selection of a subset of SNPs from the array regarding the genetic diversity of samples in calibration set used to predict allelic frequencies.

To avoid risk of ascertainment bias due to selection of markers genotyped by the array, the logistic regression model was adjusted on 1,000 SNPs with the largest allelic frequency range rather than for each of the 23,412 PZE SNPs individually. Using a specific model for each SNP would indeed conduct to discard markers monomorphic in controlled pools and therefore select only markers polymorphic between parents of controlled pool. Note that the same issue would be raised by using heterozygous individuals since 8 to 16 heterozygotes were recommended to adjust a logistic regression. Using heterozygous individuals and SNP specific equations could lead to systematically counter-select SNPs with low diversity. It could also lead to systematically remove SNPs that are differentially fixed between isolated genetic groups, because no or very few heterozygote individuals are available.

We also evaluated ascertainment bias by comparing Modified Roger's Distance (MRD) between the 156 landraces obtained using SNPs (MRD<sub>SNP</sub>) and SSRs (MRD<sub>SSR</sub>) (Camus-Kulandaivelu 2006; Mir *et al.* 2013), which display no or limited ascertainment bias. MRD<sub>SNP</sub> was highly correlated with MRD<sub>SSR</sub> (r<sup>2</sup> = 0.64; Figure 5). This correlation is high considering that SSR and SNP markers evolve very differently (mutation rate higher for SSRs than SNPs, multiallelic vs biallelic), that the number of SSR markers used to estimate genetic distance is low and that errors in allelic frequency prediction occur for both SNPs and SSRs. For comparison, correlation was lower than between Identity By State estimated with 94 SSRs and 30k SNPs in a diversity panel of 337 inbred lines (r<sup>2</sup> = 0.41), although very few genotyping errors are expected in inbred lines (Bouchet *et al.* 2013). Using the *wd* criterion significantly increased the correlation between MRD<sub>SNP</sub> and MRD<sub>SSR</sub> markers for 156 landraces (Figure S5). It suggests that the *wd* criterion removes SNP markers that blurred the relationships between landraces. We can therefore define a subset of 23,412 SNPs to analyze global genetic diversity in landraces. This is in
agreement with previous studies in inbred lines showing that PZE SNPs are suitable to
analyze the genetic diversity in inbred lines (Inghelandt et al. 2011; Ganal et al. 2011;
Bouchet et al. 2013; Frascaroli et al. 2013). These studies showed that diversity analysis
based on PZE SNPs give consistent results with previous studies based on SSR markers
(Inghelandt et al. 2011; Bouchet et al. 2013; Frascaroli et al. 2013).

The DNA pooled-sampling approach therefore provides a reliable picture of the
genetic relatedness among populations that display a large range of genetic divergence
and opens a way to explore genome-wide diversity along the genome.

An affordable, high-throughput, labor-efficient and robust method
compared to SSR / RFLP markers and sequencing approaches

Using SNP arrays instead of SSR/RFLP marker systems or sequencing approaches
has several advantages. First, SNP genotyping using arrays is very affordable compared
to SSR/RFLP or resequencing approaches because it is highly automatable, high-
throughput, labor-efficient and cost effective (currently 30-80€ / individual depending of
array). Obtaining accurate estimations of allelic frequencies using a whole genome
sequencing (WGS) approach requires high depth and coverage for each individual
because of the need of counting reads (Schlötterer et al. 2014). To estimate allelic
frequency in DNA bulks, WGS remains costly compared to SNP arrays for large and
complex genomes of plant species as maize. Different sequencing approaches based either
on restriction enzyme or sequence capture make it possible to target some genomic
regions and multiplex individuals, reducing the cost of library preparation and
sequencing while increasing the depth for the selected regions (Glaubitz et al. 2014).
However, these sequencing approaches remain more expensive than SNP arrays and
require laboratory equipment to prepare DNA libraries and strong bioinformatics skills
to analyze sequencing data. These skills are not always available in all genebanks. With
the maize 50K array, FIR measurement used to predict allelic frequencies were highly
reproducible both across laboratories and batches (r2 = 0.987; Figure 3). We can
therefore consistently predict allelic frequencies using 50K array in new DNA pools
genotyped in other laboratories, by applying the same parameters of presence /absence
test and logistic regression as in this study. This will greatly facilitate the comparison of
accessions across collections and laboratories. This is a strong advantage over SSRs for
which a strong laboratory effect has been observed for the definition of alleles, leading to difficulties for comparing genetic diversity across seedbanks and laboratories (Mir et al. 2013). Similarly, one can expect some laboratory effect for sequencing approaches due to preparation of library and bioinformatics analysis. However, there is some disadvantage to use SNP arrays instead of SSR markers or sequencing approach. First, SNP marker are bi-allelic whereas SSRs are multi-allelic. At a constant number of markers, using SNPs rather than SSRs therefore leads to less discriminative power (Laval et al. 2002; Hamblin et al. 2007). This disadvantage is largely compensated by the higher number of SNPs and the fact that SNPs are more frequent and more regularly spread along the genome than SSR/RFLP, allowing genome wide diversity analyses. Second, contrary to SSR / RFLP markers and sequencing approach, SNP array does not allow one to discover new polymorphisms, which may lead to ascertainment bias for diversity analysis of new genetic groups (Nielsen 2004; Clark et al. 2005; Hamblin et al. 2007; Inghelandt et al. 2011; Frascaroli et al. 2013). Comparison with SSRs results showed that PZE SNPs provide reliable genetic distances between landraces, suggesting a low ascertainment bias for a global portrayal of genetic diversity (see above). Sequencing techniques may be interesting in a second step to identify, among preselected accessions, those which show an enrichment in new alleles.

The number of SNPs affects the estimates of relationship between landraces and population structure (Moragues et al. 2010). In our study, the correlation coefficient between MRD<sub>SNP</sub> and MRD<sub>SSR</sub> increased with increasing number of SNPs and reached a plateau for 2,500 SNPs (Figure S6). This suggests that increasing the number of SNPs above 2,500 does not provide further improvement in precision to estimate relationships between landraces as compared to 17 SSRs. Our approach could therefore be made further cost efficient by selecting less loci for studying global genetic relationships and genetic diversity. For maize, a customizable 15K Illumina genotyping array has been developed that includes 3,000 PZE SNPs selected for studying essential derivation (Rousselle et al. 2015) and 12,000 others selected for genetic applications such as genomic selection. Alternatively, the same approach could be applied to other genotyping arrays with higher density as the 600K Affymetrix Axiom Array (Unterseer et al., 2013) to gain precision in detection of selective footprints.
424 **CONCLUSION**

425 The DNA pooling approach we propose overcomes specific issues for genetic diversity
426 analysis and plant germplasm management purposes that were not or partially addressed by
427 previous methods which were mostly focused on QTL analysis and genome wide association
428 studies (Hoogendoorn et al. 2000; Craig et al. 2005; Brohede 2005; Teumer et al. 2013). As
429 proof of concept, we used the DNA pooling approach to estimate allelic frequencies in maize
430 landraces in order to identify original maize landraces in germplasm for pre-breeding
431 purposes and selective footprints between geographic and/or admixture groups of
432 landraces cultivated in contrasted agro-climatic conditions (Arca et al., in prep). Our
433 approach could be very interesting for studying plant germplasm since time, money and
434 molecular skills can be limiting factors to study and compare large collections of landraces
435 maintained in seedbank (Mir et al. 2013). Applications could be expanded to QTL
436 identification in pools (Gallais et al. 2007), detecting signatures of selection in multi-generation
437 experiments, or detection of illegitimate seed-lots during multiplication in genebanks. The DNA
438 pooling approach could be easily applied to decipher organization of genetic diversity in
439 other plant germplasm since Infinium Illumina HD array have been developed for several
440 cultivated plant species, including soybean, grapevine, potato, sweet cherry, tomato,
441 sunflower, wheat, oat, brassica crops but also animal species.

442 **MATERIALS AND METHODS**

443 **Plant material**

444 **Landraces**

445 A total of 156 landrace populations (Table S4) were sampled among a panel of 413
446 landraces capturing a large proportion of European and American diversity and analyzed in
447 previous studies using RFLP (Dubreuil and Charcosset 1998; Rebourg *et al.* 1999, 2001, 2003;
448 Gauthier *et al.* 2002) and SSR markers (Camus-Kulandaivelu 2006; Dubreuil *et al.* 2006; Mir
449 *et al.* 2013).

450 Each population were represented by a bulk of DNA from 15 individual plants, mixed in
451 equal amounts as described in Reif *et al.* (2005) and Dubreuil *et al.* (2006). In order to analyze
452 the effect of individual sampling on allelic frequency estimation (see below), ten populations
453 were represented by two DNA bulks of 15 plants sampled independently (Table 3).

454 Controlled DNA Pools

455 To calibrate a prediction model for SNP allelic frequencies in populations, we considered
456 two series of nine controlled pools derived from the mixing of two sets of three parental inbred
457 lines: EP1 – F2 – LO3 (European Flint inbred lines) and NYS302– EA1433 – M37W (Tropical
458 inbred lines).

459 For each set of three parental lines, we prepared nine controlled pools by varying the
460 proportion of each line in the mix (Table 1), measured as the number of leaf disks with equal
461 size according to Dubreuil et al., (1999). The proportion of lines 2 and 3 (EA1433 and M37W
462 or F2 and LO3) varies similarly whereas line 1 (EP1 or NYS302) varies inversely. The genotype
463 of the inbred lines and the proportion of each inbred line in each pool give the expected allelic
464 frequencies as shown in Table 1. Combination of genotypes in parental lines can conduct either
465 to monomorphic or polymorphic controlled pools if the genotypes of 3 parental lines are the
466 same or not, respectively. If we exclude monomorphic controlled pools and heterozygote SNPs
467 in parental lines, these different combinations conduct to four different polymorphic
468 configurations in the 9 controlled pools, corresponding to four ranges of allelic frequencies: 1-
469 33% (R1), 33-50% (R2), 51-67% (R3), 67-99% (R4), (Table 1). Combination of R1 and R4
470 configurations in two series of controlled pools displayed the largest allelic frequencies range
471 (1% to 99%) while combination of R2 and R3 displayed a more reduced allelic frequency range
472 (33% to 67%).

473 Inbred lines

474 To test for allele fixation within landraces, we used a panel of 333 inbred maize lines
475 representing the worldwide diversity well characterized in previous studies (Camus-
476 Kulandaivelu 2006; Bouchet et al. 2013) (Table S5). This panel includes the six inbred lines
477 used to build two series of controlled pools.

478 Genotyping

479 We used the 50K Illumina Infinium HD array (Ganal *et al.* 2011) to genotype (i) 166 DNA
480 bulks representing 156 landraces (ii) 18 DNA bulks representing 2 series of controlled DNA
481 pools (iii) 333 inbred lines. 50K genotyping was performed according to the manufacturer's
482 instructions using the MaizeSNP50 array (IlluminaInc, San Diego, CA). The genotype results
483 were produced with GenomeStudio Genotyping Module software (v2010.2, IlluminaInc) using 484 the cluster file MaizeSNP50_B.egt available from Illumina. The array contains 49,585 SNPs 485 passing quality criteria defined in (Ganal et al. 2011).

486 We also used 17 SSRs genotyping data from 145 and 11 landraces analyzed by Camus et 487 al. (2006) and Mir et al. (2013), respectively.

488 **Measurement variable: fluorescence intensities ratio**

489 The MaizeSNP50 array has been developed into allele-specific single base extension using 490 two colors labeling with the Cy3 and Cy5 fluorescent dyes. The fluorescent signal on each spot 491 is digitized using GenomeStudio software. Data consist of two normalized intensity values (x, 492 y) for each SNP, with one intensity for each of the fluorescent dyes associated with the two 493 alleles of the SNP. The alleles measured by the x intensity value (Cy5 dye) are arbitrary, with 494 respect to haplotypes, are called the A alleles, whereas the alleles measured by the y intensity 495 value (Cy3 dye) are called the B alleles.

496 We assumed that the strength of the fluorescent signal of each spot is representative of the 497 amount of labeled probe associated with that spot. The amount of labeled probes at each spot 498 relies upon the frequency of the corresponding alleles of PCR product immobilized on it. Based 499 on this assumption, the fluorescent intensity ratio (FIR) of each spot (y/(x+y)) can be employed 500 to estimate the allele frequency of DNA bulk immobilized on it.

501 To test the reproducibility of the measurement the controlled pool of European lines was 502 genotyped twice in two platforms, at CNG Genotyping National Center, Evry 91, France, and 503 at Trait Genetics.

504 **SNP filtering and quality control**

505 For the purpose of this study, we used only the subset of 32,788 markers contributed by the 506 Panzea project (http://www.panzea.org/), so called PZE SNPs, developed on the basis of US 507 NAM founders (Zhao 2006). These SNPs represent a comprehensive sample of the maize 508 germplasm and are therefore suitable for diversity analysis (Ganal et al. 2011).

509 The following equation (1) was then used to create a rank score (weighted deviation, wd) 510 for each SNP in order to identify and remove those of poor quality,

$$511 \quad wd = \frac{|\mu_{AA} - \mu_{BB}|}{\sqrt{\frac{N_{AA} \cdot \sigma_{AA}^2 + N_{BB} \cdot \sigma_{BB}^2}{N_{AA} + N_{BB}}}} \quad (1)$$
where $\mu_{AA}$ and $\sigma_{AA}$ and $\mu_{BB}$ and $\sigma_{BB}$ are the mean and the standard deviation for the fluorescence intensity ratios of AA and BB genotypes for the 327 inbred lines panel and $N_{AA}$ and $N_{BB}$ is the number of inbred lines with genotype AA or genotype BB respectively. To avoid selection bias, loci which were monomorphic within the reference inbred lines population were selected using the $wd$ equations (1), assuming $\mu_{AA}=0$ and $\sigma_{AA}=0$ for monomorphic BB SNPs or assuming $\mu_{BB}=1$ and $\sigma_{BB}=0$ for monomorphic AA SNPs.

This criterion removes from analysis those SNPs for which distributions of fluorescence signal ratios for AA and BB genotypes of 327 inbred lines panel overlap or have large variances. To analyze genetic diversity, we first selected 23,656 with $wd$ above 50 among 32,788 PZE SNPs. This threshold removed SNPs displaying high error rate in allelic frequency prediction (Figure S1). In addition, we removed 244 SNPs that were heterozygous in one of parental lines of controlled pools and that displayed high error rate in allelic frequency prediction (data not shown).

## Alleles detection and allele frequency estimation

Allele frequency estimation within DNA pools was implemented as a two-step process. We first determined the fixation of alleles A and/or B by comparing the fluorescent ratio of DNA pools at a given SNP locus with the distribution of the fluorescent signal of inbred lines (see above) which have AA or BB genotypes at the same locus. We assumed Gaussian distributions for the fluorescent intensities and tested for fixation using a Student's t-tests with a 5% type I nominal level.

In second step, for each SNP for which alleles A and B were both declared present, the allelic frequency $fB$ of allele B was inferred using the following generalized linear model:

$$g(fB) = \alpha + \beta \frac{y}{x+y} (2)$$

where $x$ and $y$ are the fluorescent intensities at SNP for alleles A and B respectively, $\alpha$ and $\beta$ are the parameters of a logistic curve, calibrated on fluorescent ratio data from controlled pools for 1000 SNPs and $\varepsilon_i$ is a noise term. As allele B frequency is a binomial variable, GLM was set with a logit link function (R, version 3.0.3).

The calibration sample of 1,000 SNPs consists in 250 randomly selected SNPs for each possible configuration (R1, R2, R3, R4 defined in Table 1). It was preferred to a calibration sample of all SNPs or to a specific prediction curve for each SNPs, in order to have a homogeneous distribution of observations into each class of expected frequency. Calibrating
the model for each SNP would lead to high error in allelic frequency prediction, notably for monomorphic controlled pools as exemplified by Figure S3 and S4. Calibrating model for all SNPs would give strong weight to fixed allele in calibration due to large number of monomorphic controlled pools that are homozygous either for allele A or B.

## 547 Accuracy of allelic frequency estimation

We assessed the accuracy of allele frequency estimates from pooled DNA samples by calculating the absolute difference between allelic frequencies of the B allele predicted by our two-step model and those expected for controlled pools from the genotype of their six parental lines. We obtained expected allelic frequencies for two series of controlled pools by weighting the allelic frequency of each parental line (0 or 1) by their relative mass in the mix (Table 1). We obtained genotypes of inbred lines from clustering by genome studio. This absolute difference was averaged over SNPs and samples in order to obtain mean absolute error (MAE).

We first evaluated the mean absolute error for 23,412 SNPs in the two series of controlled pools (Table S2, Figure 2). In order to estimate the effect of the calibration set of individuals and SNPs on the accuracy of allelic frequency prediction, we applied two cross-validation approaches on the 1000 SNPs and the two series of controlled pools and six parental inbred lines (24 samples) used to calibrate parameters of the common logistic regression. In order to evaluate the effect of SNP calibration set (Table S1), we repeated five time a K-fold approach in which 1000 SNPs were split randomly in a training set of 800 SNPs on which we calibrated our two-step model and a validation set of 200 SNPs on which we predicted allelic frequency using this model in same two series controlled pools and estimated MAE. In order to evaluate the effect calibration samples (Table 2), we repeated 1000 times a K-fold approach on 1000 SNPs in which 1, 3, 5, 8, 10, 15 samples among 18 from controlled pools were randomly removed from the calibration set. We used the remaining samples to estimate parameters of the logistic regression, and then predicted allelic frequencies using this predictive equation in these K removed samples (Table 2).

To estimate sampling error (Table 3), we estimated the 95% confidence interval of the allelic frequency in the population considering various observed allelic frequency obtained by sampling either 15, 30, 100 or 200 individuals from this population. To obtain the lower and upper bound of the 95% confidence interval for allelic frequency in the population, we considered the binomial probability to obtain various number of allele B in 15, 30, 100, 200 individuals (estimated allelic frequencies) from a population (true allelic frequencies) by using
575 binom.confint function implemented in R package "binom". We used the following parameters:
576 binom.confint(x = number of alleles observed, n = 2\*number of individuals, conf.level=95%,
577 methods = exact) with x = number of successes and n = number of trial in the binomial
578 experiment.

579
**Comparison of genetic distance between SNP and SSR markers**

580 We calculated the modified Roger's distance (MRD) (Rogers 1972) based on allelic
581 frequency data between landraces using different sets of markers to analyze the effect of the *wd*
582 criterion (Figure S5) and of the number of markers (Figure S6) on the estimation of relatedness.
583 To analyze the effect of *wd* criterion, we selected four random sets of 2,000 SNPs with different
584 *wd* ranges (0-20, 20-40, 40-60, 60-80) among 32,788 PZE SNPs. To analyze the effect of SNP
585 number, we selected six random sets of SNPs with various number of SNPs (15,000, 10,000,
586 5000, 2500, 1000, 500) among 23,412 SNPs with *wd* above 50. In order to test if the genetic
587 distance is robust when changing the type and the number of markers, we compared MRD
588 between landraces estimated with different SNP datasets with that estimated with 17 SSR
589 markers (Figure 5, Figure S5 and Figure S6). Missing allele frequencies within accession were
590 replaced by corresponding average frequencies within the whole set of accessions before
591 running this analysis. Allelic frequencies of two samples for replicated landraces were averaged
592 before estimating MRD distance except for Pol3 for which one of two samples was removed
593 (WG0109808-DNAH04).

594
Coefficient of determination between the distance matrices based on different subsets of
595
SNP (MRD<sub>SNP</sub>) and 17 SSR markers (MRD<sub>SSR</sub>) was determined by using linear regression.
597 Acknowledgements

598 This study was funded by l'Association pour l'étude et l'amélioration du mais (PROmais) in
599 the project "Diversity Zea" and French National Research Agencies in project Investissement
600 d'Avenir Amaizing, (ANR-10-BTBR-01). We acknowledge greatly the French maize
601 Biological Ressources Center, PROmais, and INRAE experimental units of St Martin de Hinx
602 and Mauguio for collecting and maintaining Landraces and Inbred lines collection. We greatly
603 acknowledge the colleagues who initially collected these landraces and André Gallais for
604 having initiated these research programs. We also greatly acknowledge Pierre Dubreuil, Letizia
605 Camus-Kulandaivelu, Cecile Rebourg, Céline Mir, Domenica Maniccaci that conducted
606 previous study on these landraces using DNA pooling approach with SSR and RFLP markers.
607 The Infinium genotyping work was supported by CEA-CNG, by giving the INRAE-EPGV
608 group access to its DNA and cell bank service for DNA quality control and to their Illumina
609 genotyping platform. Thanks respectively to Anne Boland and Marie-Thérèse Bihoreau and
610 their staff. We acknowledge the EPGV group, Dominique Brunel, Marie-Christine Le Paslier,
611 Aurélie Chauveau for the discussion and management of the Illumina genotyping.

612 Author's contribution

613 S.D.N, A.C and B.G designed and supervised the study and selected the plant material

614 M.A, S.D.N, A.C drafted and corrected the manuscript

615 D.M, V.C and A.B extracted DNA and managed genotyping of landraces and inbred lines

616 C.B, B.G and A.C collected, maintained landraces, and inbred lines collection

617 S.D.N, M.A, A.C and T.M-H developed the statistical methods and scripts for predicting
618 allelic frequency from fluorescent data

619 M.A, B.G and S.D.N analyzed genetic diversity of landraces panel.

620 All authors read and approved the manuscript.

621 Data availability
R scripts and fluorescent intensity data of 327 inbred lines and two series of controlled pools used for predicting allelic frequency in DNA bulks of maize landraces by our two-step approaches are available at https://doi.org/10.15454/GANJ7J. Fluorescent Intensity data and allelic frequencies of 20 samples corresponding to 10 duplicated landraces were also available at https://doi.org/10.15454/GANJ7J. Allelic frequencies of new DNA bulks for new maize populations genotyped by maize 50K array could be predicted by using these datasets with R scripts. Note that these datasets and R scripts will become available when the publication would be accepted in a peer review journal.

Conflicts of interest

No

632
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<table><caption>Table 1: Expected frequencies of allele B for the nine controlled pools obtained by varying the proportions of leaf weights of three inbred lines (L1, L2, L3) according to their genotypes at a bi-allelic SNP coded A/B. Heterozygous genotypes for inbred lines were not considered in this table.</caption><thead><tr><th colspan="4">Proportion of leaf weights</th><th colspan="6">Genotypes of parental lines L1, L2, L3 in controlled pools</th></tr><tr><th rowspan="2">Pools</th><th rowspan="2">L1</th><th rowspan="2">L1</th><th rowspan="2">L3</th><th colspan="2">AA,AA,BB</th><th colspan="2">BB,AA,BB</th><th rowspan="2">AA,BB,BB</th><th rowspan="2">BB,BB,BB</th></tr><tr><th>AA,AA,AA</th><th>BB,AA,AA</th><th>OR</th><th>or</th></tr><tr><th></th><th></th><th></th><th></th><th></th><th colspan="2">AA,BB,AA</th><th colspan="2">BB,BB,AA</th><th></th><th></th></tr></thead><tbody><tr><td>#1</td><td>0.01</td><td>0.495</td><td>0.495</td><td>0%</td><td>1%</td><td>50%</td><td>51%</td><td>99%</td><td>100%</td></tr><tr><td>#2</td><td>0.02</td><td>0.49</td><td>0.49</td><td>0%</td><td>2%</td><td>49%</td><td>51%</td><td>98%</td><td>100%</td></tr><tr><td>#3</td><td>0.03</td><td>0.485</td><td>0.485</td><td>0%</td><td>3%</td><td>49%</td><td>52%</td><td>97%</td><td>100%</td></tr><tr><td>#4</td><td>0.05</td><td>0.475</td><td>0.475</td><td>0%</td><td>5%</td><td>48%</td><td>53%</td><td>95%</td><td>100%</td></tr><tr><td>#5</td><td>0.07</td><td>0.465</td><td>0.465</td><td>0%</td><td>7%</td><td>47%</td><td>54%</td><td>93%</td><td>100%</td></tr><tr><td>#6</td><td>0.1</td><td>0.45</td><td>0.45</td><td>0%</td><td>10%</td><td>45%</td><td>55%</td><td>90%</td><td>100%</td></tr><tr><td>#7</td><td>0.15</td><td>0.425</td><td>0.425</td><td>0%</td><td>15%</td><td>43%</td><td>58%</td><td>85%</td><td>100%</td></tr><tr><td>#8</td><td>0.2</td><td>0.4</td><td>0.4</td><td>0%</td><td>20%</td><td>40%</td><td>60%</td><td>80%</td><td>100%</td></tr><tr><td>#9</td><td>0.333</td><td>0.333</td><td>0.333</td><td>0%</td><td>33%</td><td>33%</td><td>67%</td><td>67%</td><td>100%</td></tr></tbody><tfoot><tr><td colspan="10">Configuration of controlled pools</td></tr><tr><td colspan="2">Monomorphic</td><td>R1</td><td>R2</td><td>R3</td><td>R4</td><td>Monomorphic</td><td></td><td></td><td></td></tr></tfoot></table>
<table><caption>Table 2: Mean absolute error (MAE) in frequency estimation for 1,000 SNPs used to calibrate logistic regression equations. MAE is estimated by a cross-validation procedure in which a number of pools comprised between 1 and 15 among 18 is removed at random from the calibration set. This procedure was repeated 1,000 times for each SNP.</caption><thead><tr><th rowspan="2"># of samples</th><th rowspan="2"># of removed repetitions</th><th rowspan="2">Mean absolute error (MAE)</th><th colspan="2">Mean</th><th colspan="2">SD*</th></tr><tr><th>Mean</th><th>SD*</th><th>Mean</th><th>SD*</th></tr></thead><tbody><tr><td>1</td><td>1000</td><td>0.0414</td><td>0.0414</td><td>0.0219</td><td>0.0219</td></tr><tr><td>3</td><td>1000</td><td>0.0428</td><td>0.0428</td><td>0.0226</td><td>0.0226</td></tr><tr><td>5</td><td>1000</td><td>0.0447</td><td>0.0447</td><td>0.0232</td><td>0.0232</td></tr><tr><td>8</td><td>1000</td><td>0.0484</td><td>0.0484</td><td>0.0245</td><td>0.0245</td></tr><tr><td>10</td><td>1000</td><td>0.0522</td><td>0.0522</td><td>0.0257</td><td>0.0257</td></tr><tr><td>12</td><td>1000</td><td>0.0582</td><td>0.0582</td><td>0.0274</td><td>0.0274</td></tr><tr><td>15</td><td>1000</td><td>0.0854</td><td>0.0854</td><td>0.0309</td><td>0.0309</td></tr></tbody></table>

<footnote>* SD = Standard deviation</footnote>
<table><caption>Table 3: Sampling error estimated by numerical calculation for one or two biological replicates with independent sampling of 15 or 100 individuals within landraces. Lower and upper bounds indicate the 95% confidence interval for the allelic frequency in the population, based on the binomial probability of the frequency estimated with the corresponding sample size.</caption><thead><tr><th rowspan="3">Allelic Frequency</th><th colspan="6">15 individuals</th><th colspan="6">100 individuals</th></tr><tr><th colspan="3">One biological replicate</th><th colspan="3">Two biological replicates</th><th colspan="3">One biological replicate</th><th colspan="3">Two biological replicates</th></tr><tr><th># Alleles</th><th>Lower bound</th><th>Upper bound</th><th># Alleles</th><th>Lower bound</th><th>Upper bound</th><th># Alleles</th><th>Lower bound</th><th>Upper bound</th><th># Alleles</th><th>Lower bound</th><th>Upper bound</th></tr></thead><tbody><tr><td>0</td><td>0</td><td>0</td><td>0.116</td><td>0</td><td>0</td><td>0.06</td><td>0</td><td>0</td><td>0.018</td><td>0</td><td>0</td><td>0.009</td></tr><tr><td>0.03</td><td>1</td><td>0.001</td><td>0.172</td><td>2</td><td>0.004</td><td>0.115</td><td>6</td><td>0.011</td><td>0.064</td><td>13</td><td>0.017</td><td>0.055</td></tr><tr><td>0.1</td><td>3</td><td>0.021</td><td>0.265</td><td>6</td><td>0.038</td><td>0.205</td><td>20</td><td>0.062</td><td>0.15</td><td>40</td><td>0.072</td><td>0.134</td></tr><tr><td>0.2</td><td>6</td><td>0.077</td><td>0.386</td><td>12</td><td>0.108</td><td>0.323</td><td>40</td><td>0.147</td><td>0.262</td><td>80</td><td>0.162</td><td>0.243</td></tr><tr><td>0.3</td><td>9</td><td>0.147</td><td>0.494</td><td>18</td><td>0.189</td><td>0.432</td><td>60</td><td>0.237</td><td>0.369</td><td>120</td><td>0.256</td><td>0.348</td></tr><tr><td>0.4</td><td>12</td><td>0.227</td><td>0.594</td><td>24</td><td>0.276</td><td>0.535</td><td>80</td><td>0.332</td><td>0.472</td><td>160</td><td>0.352</td><td>0.45</td></tr><tr><td>0.5</td><td>15</td><td>0.313</td><td>0.687</td><td>30</td><td>0.368</td><td>0.632</td><td>100</td><td>0.429</td><td>0.571</td><td>200</td><td>0.45</td><td>0.55</td></tr><tr><td>0.6</td><td>18</td><td>0.406</td><td>0.773</td><td>36</td><td>0.465</td><td>0.724</td><td>120</td><td>0.529</td><td>0.669</td><td>240</td><td>0.55</td><td>0.648</td></tr><tr><td>0.7</td><td>21</td><td>0.506</td><td>0.853</td><td>42</td><td>0.568</td><td>0.812</td><td>140</td><td>0.631</td><td>0.763</td><td>280</td><td>0.653</td><td>0.745</td></tr><tr><td>0.8</td><td>24</td><td>0.614</td><td>0.923</td><td>48</td><td>0.677</td><td>0.892</td><td>160</td><td>0.738</td><td>0.853</td><td>320</td><td>0.757</td><td>0.838</td></tr><tr><td>0.9</td><td>27</td><td>0.735</td><td>0.979</td><td>54</td><td>0.795</td><td>0.962</td><td>180</td><td>0.85</td><td>0.938</td><td>360</td><td>0.866</td><td>0.928</td></tr><tr><td>1</td><td>30</td><td>0.884</td><td>1</td><td>60</td><td>0.94</td><td>1</td><td>200</td><td>0.982</td><td>1</td><td>400</td><td>0.991</td><td>1</td></tr></tbody></table>
PZE-101005765

<figure><img src="image_2.png" /></figure>

Figure 1: Two-step approach for estimating allelic frequency in DNA pools, exemplified by marker PZE-101005765. Red and green histograms correspond to the fluorescent intensity ratio (FIR) distribution for inbred lines homozygote for allele A (AA) and B (BB), respectively. Red and green curves indicate the corresponding Gaussian distributions. Red, Blue, and Green areas correspond to the FIR for which landraces are declared homozygous for allele A, polymorphic and homozygous for allele B after testing for fixation of alleles A and B. Dotted blue line corresponds to the curve of the logistic regression adjusted on 1,000 SNPs and two series of controlled pools. Blue cross corresponds to a landrace represented by a DNA bulk of 15 individuals, with its observed FIR on X axis and predicted frequency on Y axis.
<figure><img src="image_3.png" /><figcaption>Figure 2: Mean absolute error (MAE) according to the known allelic frequency in two series of controlled pools. MAE measured the absolute difference between allelic frequencies predicted by the two-step approach and those expected from the genotypes of parental lines in two series of controlled pools for 23,412 SNPs. MAE is averaged for each interval of expected allelic frequency across all SNPs.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 3: Relationship between fluorescent intensity ratio of European Flint controlled pools genotyped in two different laboratories: CNG and Consortium. Each dot represents the combination of one out of 9 controlled pools and one out of 23,412 PZE SNPs. Coefficient of determination (r²) between FIR of two laboratories is 0.987.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 4: Relationship between allele frequencies predicted for two biological replicates of 9 landraces over 23,412 selected SNPs. Each dot represents one landrace and one SNP, with allele frequency of replicates 1 and 2 on X and Y axes, respectively. Blue line indicates linear regression. 94.5% of points are included in the red ellipse that represents the 95% confidence limit accounting for the effect of sampling alone. r² between replicates is 0.93</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 5: Relationship between Modified Roger's Distances (MRD) obtained with 17 SSRs and 23,412 SNPs for 156 landraces. Each dot represents one pair of landraces. Red dotted lines represents linear regression between MRD<sub>SSR</sub> and MRD<sub>SNP</sub>. Coefficient of determination (r<sup>2</sup>) is reported on the plot.</figcaption></figure>