Phaseolus vulgaris L.) is an important worldwide legume crop with low to moderate levels of resistance to common bacterial blight (CBB) caused by Xanthomonas axonopodis pv. phaseoli. A total of 852 genotypes  from the North Dakota State University dry bean breeding program were tested for their effectiveness as populations for genome-wide association studies (GWAS) to identify genomic regions associated with resistance to CBB, to exploit the associated markers for marker-assisted breeding (MAB), and to identify candidate genes. The genotypes were evaluated in a growth chamber for disease resistance at both the unifoliate and trifoliate stages. At the unifoliate stage, 35% of genotypes were resistant, while 25% of genotypes were resistant at the trifoliate stage. Libraries generated from each genotype were sequenced using the Illumina platform. After filtering for sequence quality, read depth, and minor allele frequency, 41,998 single-nucleotide polymorphisms (SNPs) and 30,285 SNPs were used in GWAS for the Middle American and Andean gene pools, respectively. One region near the distal end of Pv10 near the SAP6 molecular marker from the Andean gene pool explained 26.7–36.4% of the resistance variation. Three to seven regions from the Middle American gene pool contributed to 25.8–27.7% of the resistance, with the most significant peak also near the SAP6 marker. Six of the eight total regions associated with CBB resistance are likely the physical locations of quantitative trait loci identified from previous genetic studies. The two new locations associated with CBB resistance are located at Pv10:22.91–23.36 and Pv11:52.4. A lipoxgenase-1 ortholog on Pv10 emerged as a candidate gene for CBB resistance. The state of one SNP on Pv07 was associated with susceptibility. Its subsequent use in MAB would reduce the current number of lines in preliminary and advanced field yield trial by up to 14% and eliminate only susceptible genotypes. These results provide a foundational SNP data set, improve our understanding of CBB resistance in dry bean, and impact resource allocation within breeding programs as breeding populations may be used for dual purposes: cultivar development as well as genetic studies.Dry bean ( Phaseolus vulgaris L.) is the most important grain legume directly consumed by humans  germplasm panels as mapping populations will not identify important QTL found within an existing breeding program. Therefore, using advanced-generation genotypes selected during cultivar development as an association population for genetic mapping will identify SNPs relevant to the breeding program which can be converted to easily distinguishable markers in a MAB program. Toward this goal, Xanthomonas axonopodis pv. phaseoli (Xap), the causal agent of CBB, causes necrotic lesions sometimes encircled by chlorosis as well as wilting and rot with severe infection , tnfection . The bacachinery . Up to 5achinery . CBB is Common bacterial blight resistance is inherited as both minor- and major-effect QTL and is highly variable depending on disease pressure, environmental conditions, genetic background, and plant maturity . Direct The objective of this study was to determine if lines across various stages of the breeding program could serve a dual purpose for both cultivar development and GWAS, thereby not dividing limited resources between selection/cultivar development and genetic mapping. The CBB resistance phenotype was used as a test case for both the Andean and Middle American gene pools since both major and minor QTLs have been previously described.1 were selected for genotyping and CBB phenotyping under controlled conditions in a growth chamber. These genotypes included 32 cultivars, 137 genotypes at the advanced stage, and 683 genotypes at the preliminary stage  using the KingFisher Flex (ThermoScientific) for bead washing. DNA was quantified using a nanodrop, diluted to 50 ng/μl, and checked for quality TaqI and MseI; The breeding line SNP data set was obtained by low-pass sequencing of libraries generated using a two-enzyme protocol . Read groups including library ID, platform, and platform unit were added to each alignment within the BAM files using Picard4. Alignments for each breeding line were divided to generate gene pool-specific SNP data sets. Each gene pool has undergone separate domestication bottlenecks and selection pressure; thus, the SNP data sets were generated separately (via hard filtering when variants contained more than 25% missing data (50% in the MA SNP data set), more than one nucleotide, and more than two alleles or the minor allele was less than 5% (<1% in the MA SNP data set). The minor allele frequency (MAF) was reduced to less than 5% to allow the detection of rare alleles in the breeding population. The MAF was set to the equivalent of five individuals in each population as the presence of the allele in five genotypes suggests the presence of a true allele. The data set may be filtered to remove additional SNP with MAF below 5% for future use. Genotypes with more than 90% missing data were removed. SNPs with less than 25% (50% in MA SNP data set) of missing data were imputed in fastPHASE  of the peak SNP.The physical location of 11 polymerase chain reaction-based markers previously associated with CBB resistance QTL on chromosomes identified as associated with CBB resistance in these GWAS was located on the sequence . Legume Xap isolate from Minnesota, United States. The median scores for both unifoliate and trifoliate resistance were normally distributed. At the unifoliate stage, 35% of genotypes were resistant, 55% intermediate, and 10% susceptible. At the trifoliate stage, 25% of genotypes were resistant, 69% intermediate, and 6% susceptible. Resistance was not always consistent across growth stages  to highly susceptible (8) under growth chamber conditions using a highly virulent h stages . ApproxiThe number of sequencing reads obtained from each breeding genotype ranged from 118,208 to over 11 million. The total number of variants in the MA data set before filtering ranged from 210,000 variants on Pv06 to over 420,000 variants on Pv08. After filtering and combining the SNP data sets from each chromosome, 41,998 SNP variants were discovered for the Middle American population. Pv09 had the fewest number of SNPs with 1,467, and Pv08 had the most with 6,006. Only SNPs with less than 50% missing data underwent imputation. Of those SNPs undergoing imputation, 58% were found in 80% of the genotypes.The initial count of sequence variants in the Andean population was over 1.3 million SNPs. After filtering for read depth, MAF, and missing data, 30,285 SNPs remained in the data set. The SNPs were dispersed across all 11 chromosomes ranging from 1,007 on Pv10 in the Andean population to 7,075 on Pv11, indicating that little genetic diversity was found on Pv10 and a much higher level on Pv11. The marker density was higher in the Middle American data set with one SNP marker per 14.4 kb when compared with the Andean data set at one SNP marker per 24.8 kb. In the Andean population, only SNPs with less than 25% missing data underwent imputation. Of the SNPs undergoing imputation, 54% were found in 80% of the genotypes.The relationship matrix was calculated using the center-relatedness algorithm in GEMMA, and a heat map was generated . The brelipoxygenase (LOX) 1-like genes. It lies 11 kb downstream of gene model Phvul.010G135151, a LOX 1-like gene, and 246 bp upstream of gene model Phvul.010G135200, which putatively encodes a protein belonging to the calcium-binding endonuclease/exonuclease/phosphatase family. Besides the location on Pv10, two additional locations with significant SNPs were identified at Pv07:28.50–28.84 and Pv11:52.40 . The locations on Pv05, Pv07, Pv08, and Pv10 identified in the univariate analysis were confirmed in the multivariate analysis.Multivariate mixed model analyses provided further evidence for six of the CBB resistance-associated locations identified in the two univariate mixed model analyses . Two locThe one-way ANOVA analyses for each nucleotide state indicated that the means for the two homozygous states were statistically different for each of the six significant SNPs confirmed by the multivariate analysis . The lacTwo association analyses, unifoliate and trifoliate, were performed on the phenotypic data using a univariate mixed model. Both analyses identified a single significant genomic location on Pv10 . The sigp = 8.8), was 120 kb distal of the most significant SNP found in the unifoliate analysis and 34 bp proximal of the most significant SNP found in the trifoliate analysis . Phenotyping all lines in the NDSU breeding program provided a snapshot of the status of CBB resistance as well as the identification of adapted sources of resistance for further use within the breeding program. The results indicate that over 40% of genotypes within the program have CBB resistance at either the unifoliate or trifoliate stages, or both, and can be advanced and/or used as parents in subsequent crosses. A high frequency and number of resistant small red  lines indicate that this market class is well positioned in regard to CBB resistance going forward. The frequency of CBB resistance in light red kidney  is high, but the number of genotypes evaluated was relatively low. The frequency of CBB resistance for pinto , great northern , and dark red kidney  beans is somewhat low, but a relatively high number of genotypes were screened, resulting in resistance being identified in numerous genotypes. The number of CBB-resistant genotypes identified is particularly low for black (six genotypes), pink (three genotypes), navy (two genotypes), and white kidney (six genotypes) beans, suggesting that crosses made with the CBB-resistant genotypes identified here should be increased, particularly with black and navy, which represent a moderate level of the market share in the region. Several VAX germplasm lines .Field testing within the North Dakota State University dry bean breeding program consists of two stages (see footnote 1). Initially, many genotypes, generally at the F5 stage of inbreeding, are grown at a few locations over several years . A subset of genotypes demonstrating good agronomic performance in preliminary yield trials was grown in advanced yield trials across multiple locations and years. Each trial is specific to a single dry bean market class  centered at 41.78 Mb on Pv10 amidst a family of LOX genes. This region consisted of only 16 identifiable genes, of which 13 were LOX-1 orthologs. The LOX pathway is important in plant–pathogen interactions. Various compounds synthesized in the LOX pathway are signaling molecules, antimicrobials, and cytotoxic molecules , and SU91 was moderately correlated with S08_62399301 (correlation coefficient = 0.56).Uromyces appendiculatus), anthracnose (Colletotrichum lindemuthianum), and bean common mosaic necrotic virus to identify SNPs within the breeding population. Other traits of interest can be evaluated in these populations, including resistance to other pathogens and abiotic stresses. The genome-wide association studies provide valuable information in identifying the physical locations of resistance. Useful MAB SNPs identified for these other traits can be combined with the Pv07 SNP, S07_28,772,508, to generate a panel of markers used to reduce the number of genotypes with unacceptable phenotypes undergoing field testing.The SNP data set generated in this study is being further exploited. Agronomic traits including seed yield and size, flowering date, and maturity date are undergoing association mapping to identify associated SNPs in order to confirm the previous findings from Dry bean breeding populations can be used for GWAS studies to identify previous linkage-mapped QTL, new genomic regions associated with traits of interest, candidate genes, and SNPs to target for future marker development. The CBB resistance test case using breeding populations in GWAS successfully identified genotypes with high levels of resistance and identified eight regions associated with resistance, including six previously discovered using biparental mapping and two new regions, one each on Pv11 and Pv10 in the Middle American population. The more diverse Middle American population led to the identification of several candidate genes for CBB disease resistance, including LOX orthologs as well as several SNPs to validate for MAB. Identification of haplotypes containing significant levels of CBB resistance and utilizing them during selection can provide a powerful strategy for dry bean improvement. Breeding population utilization for genetic studies allows the overlapping use of developed plant resources instead of generating usage-specific plant resources.https://hdl.handle.net/10365/31610, 2015 Snapshot.The datasets presented in this study can be found in online repositories. The names of the repository/repositories can be found below: KS, JO, PM, and JP conceived the original research plans, analyzed the data, and wrote the manuscript. KS, RL, and M performed the phenotyping experiments. KS generated the SNP data sets. AO performed the GEMMA analysis. All the authors read and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


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 single-nucleotide polymorphism (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 simple sequence repeats 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. Due to oduction . For insoduction . Use of oduction .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  quality criteria (wd > 50). This removed SNPs for which estimated allelic frequency deviated strongly from expected allelic frequency  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 . We consIn 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 . We testwd criterion (r2> 0.99) 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  and MRD based on different set of SNP markers (MRDSNP) were highly correlated  between MRDSNP and MRDSSR, from 0.587 to 0.639  an accurate estimation of allelic frequency in each population, (ii) a robust and reproducible measurement of allelic frequency across laboratories in order to facilitate comparison of genetic diversity of accessions across genebanks, (iii) a reliable estimate of genetic distance between landraces with no or little ascertainment bias, and (iv) an affordable, high-throughput and labor efficient method, due to both strong financial and human constraints in plant genebanks. Four main sources of errors affect the accuracy of allelic frequency estimation of a locus in a population using a DNA pooling approach: (i) the sampling of individuals , (ii) the procedure to mix DNA from individuals  (iii) the imprecision of quantitative measurement used by the model for the prediction , and (iv) the predictive equation used to predict allelic frequency in a population .Approximation errors due to predictive equation depend on (i) the model used to predict allelic frequencies and (ii) the set of individuals and SNPs used to calibrate the predictive equation. In this study, we used a two-step modeling using inbred lines and controlled pools as sets of calibration to test for polymorphism and then predict allelic frequency for polymorphic markers. Detection of allele fixation in a population is an important issue for deciphering and managing genetic diversity within plant and animal germplasm. We used two Student tests based on FIR distribution of lines homozygous for allele A and B to determine polymorphism of a SNP in a given landrace . In thiswd quality criterion. The relationship between FIR and allelic frequency was modeled using a quasi-logistic regression for different reasons. First, the logistic function ensures that the predicted frequencies take value in , a property that is not satisfied by polynomial regression (PPC) or tan transformation  the “sampling error” that is directly connected to the number of individuals sampled in each population , and  and SSRs (MRDSSR) , although very few genotyping errors are expected in inbred lines  between the 156 landraces obtained using SNPs (MRD(MRDSSR) , which ded lines . Using tandraces . It sugged lines . These sed lines .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.r2 = 0.99; 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 . 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 . To estiSNP and MRDSSR increased with increasing number of SNPs and reached a plateau for 2,500 SNPs  and NYS302– EA1433 – M37W .For each set of three parental lines, we prepared nine controlled pools by varying the proportion of each line in the mix , measureTo test for allele fixation within landraces, we used a panel of 333 inbred maize lines representing the worldwide diversity well characterized in previous studies . This paWe used the 50K Illumina Infinium HD array  to genotWe also used 17 SSRs genotyping data from 145 and 11 landraces analyzed by The MaizeSNP50 array has been developed into allele-specific single base extension using two colors labeling with the Cy3 and Cy5 fluorescent dyes. The fluorescent signal on each spot is digitized using GenomeStudio software. Data consist of two normalized intensity values  for each SNP, with one intensity for each of the fluorescent dyes associated with the two alleles of the SNP. The alleles measured by the x intensity value (Cy5 dye) are arbitrary, with respect to haplotypes, are called the A alleles, whereas the alleles measured by the y intensity value (Cy3 dye) are called the B alleles.We assumed that the strength of the fluorescent signal of each spot is representative of the amount of labeled probe associated with that spot. The amount of labeled probes at each spot relies upon the frequency of the corresponding alleles of PCR product immobilized on it. Based on this assumption, the FIR of each spot (y/(x+y)) can be employed to estimate the allele frequency of DNA bulk immobilized on it.To test the reproducibility of the measurement the controlled pool of European lines was genotyped twice in two platforms, at CNG Genotyping National Center, Evry 91, France, and at Trait Genetics.1 so called PZE SNPs, developed on the basis of US NAM founders  for each SNP in order to identify and remove those of poor quality,The following Eq (1) was then used to create a rank score , assuming μAA = 0 and σAA = 0 for monomorphic BB SNPs or assuming μBB = 1 and σBB = 0 for monomorphic AA SNPs.where μwd above 50 among 32,788 PZE SNPs. This threshold removed SNPs displaying high error rate in allelic frequency prediction  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 fB) was inferred using the following generalized linear model:In second step, for each SNP for which alleles A and B were both declared present, the allelic frequency of allele B .where The calibration sample of 1,000 SNPs consists in 250 randomly selected SNPs for each possible configuration  by their relative mass in the mix . We obtaWe first evaluated the MAE for 23,412 SNPs in the two series of controlled pools . In ordex = number of alleles observed, n = 2∗number of individuals, conf.level = 95%, methods = exact) with x = number of successes and n = number of trial in the binomial experiment.To estimate sampling error , we estiwd criterion  among 32,788 PZE SNPs. To analyze the effect of SNP number, we selected six random sets of SNPs with various number of SNPs  among 23,412 SNPs with wd above 50. In order to test if the genetic distance is robust when changing the type and the number of markers, we compared MRD between landraces estimated with different SNP datasets with that estimated with 17 SSR markers  and 17 SSR markers (MRDSSR) was determined by using linear regression.Coefficient of determination between the distance matrices based on different subsets of SNP (MRDhttps://data.inrae.fr/) with the following doi: https://doi.org/10.15454/GANJ7J.The datasets as well as R scripts to predict allelic frequency in maize DNA bulk presented in this study can be found in online repositories (SN, AC, and BG designed and supervised the study and selected the plant material. MA, SN, and AC drafted and corrected the manuscript. DM, VC, and AB extracted DNA and managed genotyping of landraces and inbred lines. CB, BG, and AC collected, maintained landraces, and inbred lines collection. SN, MA, AC, and TM-H developed the statistical methods and scripts for predicting allelic frequency from fluorescent data. MA, BG, and SN analyzed genetic diversity of landraces panel. All authors read and approved the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The irruption of Next-generation sequencing (NGS) and restriction site-associated DNA sequencing (RAD-seq) in the last decade has led to the identification of thousands of molecular markers and their genotyping for refined genomic screening. This approach has been especially useful for non-model organisms with limited genomic resources. Many building-loci pipelines have been developed to obtain robust single nucleotide polymorphism (SNPs) genotyping datasets using a de novo RAD-seq approach, i.e. without reference genomes. Here, the performances of two building-loci pipelines, STACKS 2 and Meyer’s 2b-RAD v2.1 pipeline, were compared using a diverse set of aquatic species representing different genomic and/or population structure scenarios. Two bivalve species (Manila clam and common edible cockle) and three fish species  were studied. Four SNP panels were evaluated in each species to test both different building-loci pipelines and criteria for SNP selection. Furthermore, for Manila clam and brown trout, a reference genome approach was used as control..Despite different outcomes were observed between pipelines and species with the diverse SNP calling and filtering steps tested, no remarkable differences were found on genetic diversity and differentiation within species with the SNP panels obtained with a de novo approach. The main differences were found in brown trout between the de novo and reference genome approaches. Genotyped vs missing data mismatches were the main genotyping difference detected between the two building-loci pipelines or between the de novo and reference genome comparisonsTested building-loci pipelines for selection of SNP panels seem to have low influence on population genetics inference across the diverse case-study scenarios here studied. However, preliminary trials with different bioinformatic pipelines are suggested to evaluate their influence on population parameters according with the specific goals of each study.The online version contains supplementary material available at 10.1186/s12864-021-07465-w. Next-generation sequencing (NGS) technologies have represented a breakthrough for genomic studies  due to thttps://www.ncbi.nlm.nih.gov/datasets/). Nevertheless, there are about 9200 species within the 1260 bivalve genera [https://www.earthbiogenome.org/). For this reason, one of the strengths of a RAD-based method is its applicability without a reference genome [Genomic laboratory protocols have been set up and optimized through years by introducing modifications on the original RAD-seq methodology to get better results using different laboratory protocols for different scenarios . Similae genera  and 35,6e genera . Althouge genome .There are different bioinformatic pipelines to identify a high number of SNPs and achieve confident genotypes using a RAD-seq approach. The most popular one is STACKS , 16  with SNPs obtained from three pipelines  using two species with reference genome. Results showed remarkable differences in some population parameters (e.g. Hardy Weinberg Equilibrium) across bioinformatic approaches. Considering this information, a main issue that should be clarified on RAD-seq methodologies is the impact of building-loci pipelines on population genetics parameter estimations and derived conclusions using a de novo approach on different biological scenarios and to some extent, to be compared to a reference genome approach.Studies comparing bioinformatic pipelines and strategies already exist. Some comparisons between de novo and reference-based approaches are available , 22, andhttp://catchenlab.life.illinois.edu/stacks/) and ii) Meyer’s 2b-RAD v2.1 pipeline were tested using a de novo approach on different genomics and population genetics scenarios by using five aquatic species: (i) Manila clam (Ruditapes philippinarum), (ii) common edible cockle (Cerastoderma edule), (iii) brown trout , (iv) silver catfish (Rhamdia quelen) and (v) small-spotted catshark (Scyliorhinus canicula). A range of population parameters were compared in the five species applying similar parameter settings for each pipeline (description of pipelines in Methods). The two marine bivalve species from the Order Veneroida show high polymorphism and low population structure [In this work, two building-loci pipelines for SNP calling and genotyping: i) STACKS 2.0  and brotructure ). There tructure  such as tructure ). AnywayWang and Guo  hypothesFor the five species, population parameters, structure pattern and outlier loci detection were estimated as an essential outcome to evaluate the performance of four SNP panels after different filtering steps. From two building-loci pipelines, STACKS (STA panel onwards) and Meyer’s 2b-RAD v2.1 pipeline (ALT panel onwards), and two criteria for SNP selection, common SNPs  and merged SNP  panels. When available, the results from reference genome approach were used to compare the results of population parameters evaluated with the de novo approach. In this case three additional SNP panels were obtained: the former with the reference genome approach using STACKS and the two remaining with the shared SNPs (i.e. STACKS de novo and 2b-RAD v2.1). Our main goal was to assess the influence of the genomic architecture and population structure on the biological conclusions obtained with the different bioinformatic pipelines, and accordingly, to propose methodological recommendations for future studies using a de novo approach.The number of filtered reads loaded into building-loci pipelines using the reference genome approach was lower than with the de novo approach. A percentage of 22.1 and 25.4% were finally used in Manila clam and in brown trout, respectively. This reduction mostly due to those reads aligning to more than one place  that were filtered out (i.e. -m 1 in Bowtie 1.1.2), the remaining reads failed to align with the mismatch criteria applied .P < 0.01) at ALT panel on average (28.74 ± 15.24) as compared to STA panel (21.07 ± 17.54). The two species with the lowest median coverage at this step were small-spotted catshark (median = 10x for ALT and STA panels), brown trout  and Manila clam (21x for the STA panel).The number of initial SNPs, after the building-loci step with the de novo approach, ranged from 56,074 in brown trout (STA) and 125,823 in silver catfish (ALT) to 356,389 (STA) and 426,317 (ALT) in common cockle Tables . These ftotal COM genotypes  = Nsamples (21) x NCOM SNP ) was missing data, ranging from 2.6% in common cockle to 14.8% at small-spotted catshark . The main source of missing genotype differences between pipelines was related to COM SNPs from STA pipeline that passed the minimum coverage filter (Min coverage 8x), but not were genotyped by ALT pipeline due to having a coverage lower than 3x. Both pipelines never genotyped with a coverage lower than 3x with the used configuration. This situation was found in most species, causing from 46.8% of the total missing genotype differences between ALT and STA genotypes in shared SNPs (COM panel) in brown trout to 63.2% in small-spotted catshark. Nevertheless, the main source of missing data differences in Manila clam was genotypes removed by coverage filter (Min coverage 8x) in ALT but not in STA (53.5% of the missing genotype differences). The percentage of the genotyping differences caused by homozygous-heterozygous differences between pipelines at the same SNP and individual ranged from 0.5% in brown trout to 2.6% in small-spotted catshark with respect to the whole COM genotype panel  and 956 (ALT) in Manila clam to 21,468 (STA) and 22,481 (ALT) in silver catfish. These figures were always higher with the ALT pipeline for all species. The number of SNPs in COM panels, those from STA panel shared with ALT panel, ranged from 206 in Manila clam to 17,459 SNPs in silver catfish, while the percentage of SNPs called in STA that were found in ALT ranged from 23.9% in small-spotted catshark to 81.3% in silver catfish. The main source of variation when considering the whole COM panels genotype dataset  were roughly similar when using the different SNP panels in each species, showing higher differences in FIS values  greatly differed between both approaches. The structure patterns obtained using STRUCTURE and DAPC analyses (see “Methods” section) were similar between both approaches  and the uniqueness of RAD loci should be tested . For instance, in Manila clam was predicted that the percentage of the genome constituted by repetitive elements and combined transposable elements could exceed 70% [In the last decade, the binomial NGS / RAD-seq has been the choice for genomic screening in many studies due to the vast number of genetic markers identified and genotyped in a single step. In this context, species with low genomic information have been targeted for population genomics and evolutionary studies broadening the opportunities for more refined approaches regarding conservation genetics and breeding programs. Nevertheless, the effect of genomic architecture, genetic diversity, and population structure into the outcomes of these techniques  in the target species are essential issues to be addressed using both with simulation and real data approaches. These issues are not only important for the wet-lab protocols, but also for the bioinformatic pipelines to be used to analyse the huge amount of data produced. Technical decisions on the reduced-representation method and restriction enzymes selection to be applied when constructing libraries are critical. When a reference genome is available the number of potential loci obtained with different restriction enzymes (e.g. using ExtractSites.pl ceed 70% . This geceed 70% ), to impST, allelic richness). Nevertheless, the results obtained in our study within species using the four de novo panels  were roughly similar for all the population parameters evaluated. Accordingly, biological inferences would hardly change. Minor differences were found in the number of suggestive outliers detected in common cockle. In this case, the number of suggestive outliers detected could be related to the total number of SNPs of each panel. But beyond this observation, our results suggest that whatever the pipeline chosen similar results are obtained with a de novo approach. The number of initial and final SNPs obtained with reference genome was lower than obtained with a de novo approach. This would be related to the high number of input reads removed by duplicate or multiple alignment to the reference genomes due to the short length of 2b-RAD reads before going to the building-loci pipeline. Some population parameters between both approaches showed relevant differences  data is to assay trials with a small subset of data and check for their results using a meaningful set of population parameters, previously selected according to the objectives of the study. Indeed, using the number of SNPs obtained as the main criterion  to decidIS SNP filtering step when paralogs or null alleles can be a problem to avoid misinterpretations); this is the case of HWE deviations in brown trout caused by potential paralogs whose impact can be reduced using a reference genome.After the building-loci pipeline, it is important to adjust filtering (criteria and order ) accordiGlycine max L.) data [ST estimation using reduced SNPs subsets was tested and similar values regarding the full panel were obtained. Moreover, estimated genotyping accuracy may be higher with SNPs shared by more than one building-loci pipeline according to Torkamaneh et al. [Attention should be paid to the order of the different filtering steps because this can alter the final SNP panel. When adjusting the filtering parameters, it would be advisable to consider not exclusively the number of removed SNPs at each step separately, since they could result from the interaction among filtering steps. For instance, the coverage filter determines the increase of missing data which influences the percentage of SNPs eliminated by MAC and population representation filters, according to the stringency of the coverage threshold used. Furthermore, missing data may be due to a lower coverage than the selected threshold or for not being genotyped by the building-loci software with the genotyping options selected (e.g. previously selected nucleotide frequencies range to genotype in ALT pipeline). We found that the last could be the main source of COM SNPs genotyping differences between both building-loci pipelines excluding Manila clam. This means that the ALT pipeline genotyping parameter should be improved by choosing appropriate ranges for each species. The objective of any filtering strategy is removing SNPs that are not reliable without losing informative SNPs. Different factors can influence the filtering criteria, e.g. to achieve the number of SNPs required to meet the research goals. In this sense, a panel made up with markers found by two different pipelines should ensure reliability. It was found that 67% of SNPs from STACKS panel were common with UNEAK panel, using a de novo approach in soybean (L.) data . With reL.) data . Using aL.) data . The lowL.) data  the possh et al. . The imph et al. .Summarizing, the results obtained suggest that both building-loci pipelines are adequate and provide more confident results adjusting parameters and SNP filtering steps to the research context. Despite the differences observed in the number of SNPs among de novo approach panels, this seems not to affect dramatically the conclusions, at least in the biological scenarios managed in this study. When there is no reference genome, a COM panel could be interesting in terms of SNP panel consistency with species with high genomic complexity. In a general way for some population parameters, to have less SNPs do not imply loss of biological information and a COM panel could increase data reliability in these cases. In the case of choosing this option differences in genotyping between pipelines should be checked, although in this study genotyping differences between pipelines were infrequent. The main source of genotyping differences in COM SNP panels was missing data and had different sources. On one hand, different genotypes can be obtained due to the different building-loci pipeline parameters to call genotypes  and the different alignment strategies . For missing genotype differences, it should be considered that even RAD loci showing high coverage, might have missing data if building-loci pipeline parameters involved in genotyping are not properly set up. Furthermore, small differences in the building-loci pipeline could have more influence in the number of missing genotypes when working with low coverage loci. Anyway, it would be advisable to use a few intra-library and inter-library sample-replicates to estimate genotyping errors  to increThe results here obtained on the diverse case studies analysed show that selected building-loci pipeline did not have a substantial influence on the estimation of population parameters and derived biological interpretations. The slight differences in the results here obtained between some de novo and reference genome derived panels could be solved by improving SNP filtering steps. Anyway, our results cannot be generalized and users should contextualise building-loci pipelines to their particular species and population genomics scenarios. One recommendation would be to test building-loci parameters and filtering SNP steps with subset of samples to save hardware resources and computation time. The best parameter set would be those leading to consistent results obtained across different replicates and should be taken using population parameters consistent with the research goals of the study. Despite being time-consuming, this preliminary testing could enhance the robustness of results through improving the bioinformatic tools applied.R. philippinarum) localities, three from the Adriatic Sea  localities from the European Atlantic area  were used from regions with extractive cockle activities [Salmo trutta) from Duero River basin in the Iberian Peninsula , two of them representing different mitochondrial pure native lineages , a Neotropical freshwater species distributed from the Northeast of Los Andes to the centre of Argentina and living in fluvial and coastal lagoon environments [S. canicula) from North Sea (N = 13) and Irish Sea (N = 15) were analysed [All datasets used in the present study are own resources obtained from previous research carried out by the authors. Four Manila clam  andd Duero, ;), were ronments , were ananalysed . All infDNA extraction and 2b-RAD libraries preparation using AlfI IIB RE followed the same protocol except for small-spotted catshark  where CsSTACKS 2.0 and Meyer’s 2b-RAD v2.1 were the building-loci pipelines chosen for comparing their performances using a de novo approach within the broad genome and population genetics species scenarios selected. Meyer’s 2b-RAD v2.1 pipeline and STACKS building-loci pipelines have some similarities on their strategy; roughly, both are based on stacking reads into putative loci by sequence similarity, assuming that each locus corresponds to a single place in the species genome. Nevertheless, there are many differences on how loci are built and how the user can control the existing options and genotyping strategies. STACKS, with a de novo approach, works firstly at the individual level demanding a number of identical reads to build a locus (i.e –m parameter in ustacks), while the 2b-RAD v2.1 pipeline works with a combined subset of samples to build a global reference panel to which align every read. For genotyping, STACKS uses a chi square test to call a heterozygote or a homozygote , whereas nucleotide frequencies based on allele read depth at each position and sample are used for genotyping in the 2b-RAD v2.1 pipeline. Accordingly, huge differences in the raw SNP number were obtained in preliminary analysis in our study. Anyway, we tried to apply the highest number of common parameters in both pipelines to be consistent among comparisons.STACKS 2.0 pipeline can be summarized as follows: (1) Raw sequence reads were demultiplexed and filtered according to different criteria such as quality, uncalled bases and read length (process_radtags); (2) reads from each individual were clustered into putative loci, and polymorphic nucleotide sites identified (ustacks); (3) putative loci were grouped across individuals and catalogues of RAD-loci, SNPs and alleles were constructed (cstacks); (4) putative loci from each individual were matched against the catalogue (sstacks); (5) the data were transposed to be oriented by locus, instead of by sample (tsv2bam); (6) all individuals were genotyped at each called SNP (gstacks); and (7) SNPs were finally subjected to population genetics filters (populations) and results written in different output files  and earlier versions on request.The de novo approach used for the 2b-RAD v2.1 pipeline can be summarized as follows: (1) from a subset of high quality reads  from all samples, a global de novo reference catalogue was built by clustering these reads with the BuildRef.pl script and cd-hit 4.6.8 , 56, (2)A reference genome-based pipeline was used for Manila clam and brown trout, the species with chromosome assembly level reference genomes. In this case, the differences in the pipelines of STACKS 2 and Meyer’s 2b-RAD v2.1 are lower. For instance, STACKS 2 reduces the number of modules necessary from six to two when using reference genome and the building of putative loci is conditioned by the step using a short-read aligner. Our goal was not to compare this option between pipelines, but to take as reference the genome-based approach to be compared with the de novo approach as a gold standard within each pipeline.After demultiplexing raw data, several filtering criteria were applied: (1) all reads were trimmed and filtered by the RE recognition site to retain only those sequences of 36 bp (or 32 bp from CII RE catshark) centred on the RE recognition site using our own Perl scripts and Trimmomatic 0.38 ; and (2)At the building-loci pipeline step, the parameters considered were: (1) minimum number of identical reads to create a stack ; (2) maximum number of mismatches between RAD loci within and between individuals ; (3) indels were discarded (i.e. --disable-gapped at different modules); (4) SNP calling model and alpha cut-off: their default values were used in the STA pipeline (STACKS 2.0), while in the ALT pipeline (Meyer’s 2b-RAD v2.1) we considered a range of 0.1–0.2 to determine the genotype at each position ; to say, when the frequency of the less frequent allele was lower than 0.1 the genotype was called as homozygous while frequencies higher than 0.2 were called as heterozygous; intermediate allele frequencies for the less frequent allele were called as uncertain . The same parameter values were used in STACKS modules shared between reference-based genome and de novo approaches (i.e. gstacks and populations modules).P < 0.01) in more than half of the populations analysed (HW filter); and vii) only the first SNP per RAD-locus was retained when several SNPs were called in the same RAD-locus to avoid redundant information.The raw SNP panels of the STA and ALT pipelines were filtered using the same parameters for consistency, retaining only a set of markers and alleles represented across the individuals genotyped. Filters were applied in the same order for each dataset Fig. , as recoAccording to the aforementioned criteria, four SNP panels were tested and compared: 1) STA and (2) ALT SNP panels were further used to obtain 3) common (COM) and (4) merged (MER) panels. When reference genome was available three additional SNP panels were obtained . RAD-loci of these panels from both pipelines were compared to identify shared and private RAD-loci. In order to do this, cd-hit-est was used to cluster similar RAD-loci taken from the two pipeline catalogues with the same threshold of similarity (−c) used in the clustering steps of building-loci pipelines . Furthermore, we used a -g value of 1 when clustering sequences to meet the established similarity threshold and a band alignment width (−b) of 1 to avoid previously separated sequences due to indels at specific clusters. This procedure rendered COM and MER SNP panels created using a customized Perl script . SNPs at shared RAD-loci between STA and ALT panels were selected after the sixth filtering step, since the first SNP at shared RAD-loci could be different after the full filtering pipeline  and population genomics metrics. Filtered GENEPOP files were obtained using customized Perl scripts. These files were transformed for subsequent analyses using the PGDSPIDER 2.1.1.5 software . Firstlyo and He, respectively), inbreeding coefficient  and allelic richness were calculated per population using R’s package diveRsity [ST calculation and HW tests were performed with GENEPOP R package [ParallelStructure [, was used to define the most likely number of population units (K) present with LOCPRIOR model with correlated allele frequencies model, testing K values from 1 to the number of sampling localities in the species dataset + 1 with 10 replicates composed by 100,000 Markov chain Monte Carlo (MCMC) replicates and a burn-in period of 10,000 steps. STRUCTURE results were parsed with STRUCTURE HARVESTER [cross-validation method implemented in the package and from one to three discriminant components were retained according to the amount of population structure variation they explained. Finally, outlier loci potentially under selection (OL), i.e. those showing higher or lower differentiation values (i.e. FST) across populations than the neutral background, were detected using the Bayesian approach implemented in BAYESCAN 2.1 [Observed and expected heterozygosity  samples . Table S2. Number of SNPs and population metrics for common edible cockle (Cerastoderma edule) samples . Table S3. Number of SNPs and population metrics for brown trout  samples . Table S4. Number of SNPs and population metrics for silver catfish (Rhamdia quelen) samples . Table S5. Number of SNPs and population metrics for small-spotted catshark (Scyliorhinus canicula) samples . Table S6. Geographical coordinates of sampling localities for the five species used in this study. Table S7. Building-loci pipelines options selected for process_radtags (A), STACKS 2 (B), and Meyer’s 2b-RAD v2.1 (C). Supplementary figures: Figure S1. Differences in genotyping between common SNPs (COM panel) from both building-loci pipelines in each species. Figure S2. Differences in genotyping between common SNPs from reference genome and de novo approach comparisons (i.e. RG-STA and RG-ALT) in Manila clam and brown trout. Figure S3. Type of genotype differences between common SNPs (COM panel) from both building-loci pipelines in each species. Figure S4. Type of genotype differences between common SNPs from reference genome and de novo approach comparisons (i.e. RG-STA and RG-ALT) in Manila clam and brown trout.Additional file 2 CLUMPAK and DAPC output comparisons for all species: Figure S5. Comparison between CLUMPAK and DAPC outputs for Manila clam (Ruditapes philippinarum) samples (N = 110). Figure S6. Comparison between CLUMPAK and DAPC outputs for common edible cockle (Cerastoderma edule) samples (N = 120). Figure S7. Comparison between CLUMPAK and DAPC outputs for brown trout  samples (N = 52). Figure S8. . Comparison between CLUMPAK and DAPC outputs for silver catfish (Rhamdia quelen) samples (N = 21). Figure S9. Comparison between CLUMPAK and DAPC outputs for small-spotted catshark (Scyliorhinus canicula) samples (N = 28).Additional file 3. Description of the information included within GitHub website (https://github.com/abhortas/USC-RAD-seq-scripts) where custom Perl scripts and file examples to obtain shared SNPs and compare genotypes from the two building-loci pipelines used in the present study are available.


Developing binary classification rules based on SNP observations has been a major challenge for many modern bioinformatics applications, e.g., predicting risk of future disease events in complex conditions such as cancer. Small-sample, high-dimensional nature of SNP data, weak effect of each SNP on the outcome, and highly non-linear SNP interactions are several key factors complicating the analysis. Additionally, SNPs take a finite number of values which may be best understood as ordinal or categorical variables, but are treated as continuous ones by many algorithms.linear approximation for block second order HDMR expansion of categorical observations (LABS-HDMR-CO), to approximate the HDMR coefficients. We show how HDMR can be used to detect pairwise SNP interactions, and propose the fixed pattern test (FPT) to identify statistically significant pairwise interactions.We use the theory of high dimensional model representation (HDMR) to build appropriate low dimensional glass-box models, allowing us to account for the effects of feature interactions. We compute the second order HDMR expansion of the log-likelihood ratio to account for the effects of single SNPs and their pairwise interactions. We propose a regression based approach, called We apply LABS-HDMR-CO and FPT to synthetically generated HAPGEN2 data as well as to two GWAS cancer datasets. In these examples LABS-HDMR-CO enjoys superior accuracy compared with several algorithms used for SNP classification, while also taking pairwise interactions into account. FPT declares very few significant interactions in the small sample GWAS datasets when bounding false discovery rate (FDR) by 5%, due to the large number of tests performed. On the other hand, LABS-HDMR-CO utilizes a large number of SNP pairs to improve its prediction accuracy. In the larger HAPGEN2 dataset FTP declares a larger portion of SNP pairs used by LABS-HDMR-CO as significant.LABS-HDMR-CO and FPT are interesting methods to design prediction rules and detect pairwise feature interactions for SNP data. Reliably detecting pairwise SNP interactions and taking advantage of potential interactions to improve prediction accuracy are two different objectives addressed by these methods. While the large number of potential SNP interactions may result in low power of detection, potentially interacting SNP pairs, of which many might be false alarms, can still be used to improve prediction accuracy. Many modern bioinformatics applications utilize data analysis methods originally developed and studied in the fields of statistics, signal processing, and machine learning. In particular, in many cases, the application can be formulated as a classification or regression problem. Data encountered in bioinformatics is typically “small-sample high-dimensional”, a challenge not encountered in many classical statistics problems and machine learning applications. For instance, to predict the risk of a person being diagnosed with a specific complex disease in the future, or to predict the effect of a treatment, e.g., for targeted therapy, one may collect several hundred thousand single nucleotide polymorphisms (SNPs) in a sample of several hundred or a few thousand patients with known labels. Although current “omics” data provide a deluge of information per sample point, research being restricted to small sample sizes impedes reliable analysis. While being a small-sample high-dimensional problem is typical of many bioinformatics applications, it seems to be more pronounced when analyzing SNPs as (a) current technologies measure hundreds of thousands of SNPs, and (b) sample size can easily be much smaller than the number of disease associated SNPs. Furthermore, many molecular features, and in particular SNPs, can be weak markers, meaning each individual feature alone cannot reliably predict the disease outcome, and a large collection of features need to be considered together to obtain reliable predictions. Additionally, biological features are typically heavily dependent, for instance due to linkage disequilibrium (LD), and have complex interactions, which may exacerbate the difficulties in developing accurate prediction rules. Finally, note that interpretability is an important aspect in biological research. Not only do we look for biological markers and prediction rules with high accuracy, but also require a glass-box model that can explain “how” and “why” the prediction rule has come to a specific decision. For example, that a specific mutation increases cancer risk by some amount, or presence of a combination of mutations is an indicator of high risk.To that end, many pipelines implement a first phase of feature selection to reduce dimensionality, improve replicability, and increase prediction accuracy. It has been shown in many studies that such approach in indeed valuable and useful in practical applications –4. AdditDue to the large number of biological markers, their complex interactions, the need for interpretability, and the relative lack of large datasets as compared with other machine learning applications, it is typically desired to use low dimensional generative models. The idea is that although the “optimal” rule can be highly complex, it can be well approximated by a low dimensional model, and a proper low dimensional family, for instance generalized linear models (GLMs) with logit or probit links, is large enough to contain a point close to the best low dimensional representation. Thereby, such approximation will avoid over-fitting, improving prediction reliability and accuracy.SNPs are among the most challenging biological features to analyze. Indeed a single mutation in the deoxyribonucleic acid (DNA) might not greatly impact the risk of a complex disease. Therefore, it is reasonable to assume mutations are weak markers that should be jointly studied to arrive at a reliable decision rule. For instance, GLMs with logit link that take dosage data, i.e., the number of minor alleles at each SNP, are a very popular, if not the most popular, method for binary classification given SNP data. Refer to –8 for suk nearest neighbors (kNN), and naive Bayes are other methods used for binary classification of SNP data , i.e., Z=f(X), HDMR decomposes f(X) based on partial observations. Let F={1,⋯,D}. The HDMR expansion of Z is the collection of functions fu(Xu) for all u⊆F such thatHDMR is a powerful tool to represent a function of a random vector based on marginal observations. HDMR provides us with a hierarchy of functions that describe how the interactions of variables affect the output. In particular, assuming output under the condition thatxu is the restriction of x to elements in u, xu− is the restriction of x to elements not in u, and μ is the probability measure of random vector X described by probability density function (p.d.f.) w  for each binarized SNP used with LABS-HDMR-CO and α= for each non-binarized SNP used with other classification rules. Note the choice of α to be the all one vector simplifies to a uniform prior. As LABS-HDMR-CO uses feature pairs, a uniform prior on binarized SNP patterns suggests α=.Here we use a model developed to generate SNP data to evaluate the performance of LABS-HDMR-CO, and compare it with several popular methods used for binary classification. We consider three datasets, a dataset based on the HAPGEN2 project, a lung cancer dataset, and a breast cancer dataset. OBF takes Here we generate data from the HAPGEN2 project , reportiL1) penalty λ and another that uses top 500 features with elastic net putting equal weights on L1 and L2 penalties with penalty coefficient λ. We also use a variant that accounts for pairwise SNP interactions by considering terms of the form XiXj using top 50 features and L1 penalty λ. We only use the top 50 features  In the data generation model the risk of an SNP mutation is modeled as additional linear risk; corresponding to the logit link. Therefore, models based on the logit link get an unfair advantage that they exactly match the data generation model; while in reality almost always the assumed model deviates from reality. (2) We observed the computational cost to train a probit link is much less, about a third, of the logit link. Hence, to reduce computational cost of the GLM variants we compare with, we selected the probit link. (3) In practice the probit link behaves similar to the logit link, which is not surprising as the sigmoid and the cumulative distribution function (CDF) of the standard normal distribution are rather similar. Hence this choice better illustrates how slights deviations in the assumed link might affect performance of a GLM when dealing with SNP data.χ2-test as well, and obtained lower AUCs for the GLMs and naive Bayes. This results strengthens the observations made in [χ2-test.Finally, note that all GLM variants and naive Bayes use OBF assuming three categories, i.e., three dosage values, for ranking features. We tested the popular  made in  that OBFL1 penalty ), second order probit model with L1 penalty ), linear probit using elastic net ) and naive Bayes are 91.03%, 84.52%, 86.44%,84.28%, and 86.83%, respectively. The larger AUC of LABS-HDMR-CO suggests it enjoys superior overall performance, i.e., LABS-HDMR-CO should typically enjoy a higher probability of detection for a fixed false alarm rate value. Figure λ=0.01:0.01:0.2, and for each variant report the AUC of the λ with superior performance, i.e., highest AUC. Also, the parameters of LABS-HDMR-CO are chosen through cross validation. As the results suggest LABS-HDMR-CO enjoys superior performance compared with other algorithms. In particular, for false positive rates larger than 2% LABS-HDMR-CO enjoys higher probability of detection compared with all other algorithms. For small false alarm rates though, naive Bayes had the highest true positive rate, but was closely followed by LABS-HDMR-CO. While the ROC curve of probit seems to monotonically increase with respect to false positive rate, true positive rate of probit and probit seem to only infinitesimally increase for false positive rates between 0.04 and 0.05. Given that ROC curves must be concave, we initially believed this might be an artifact of not enough iterations (here being 100); however, simulations only implementing these two GLMs with more iterations resulted in rather similar graphs. However, in many iterations (using MATLAB’s default settings) the warning of reaching maximum number of iterations was reported for these two methods. Therefore, this may be an artifact of the limited number of iterations or numerical instabilities of the training stage.The AUCs for LABS-HDMR-CO, the linear probit model using α, the relative weights between L1 and L2 penalties; however, we expect the two dimensional search for such model might result in computation costs comparable to LABS-HDMR-CO.Finally, we observed the runtime of LABS-HDMR-CO using 1000 SNPs is comparable to the probit variant using 500 SNPs and elastic net. This suggests LABS-HDMR-CO is extremely fast for a method that accounts for pairwise SNP interactions. Note given 1000 SNPs there are about 500,000 SNP pairs to evaluate. However, LABS-HDMR-CO has more parameters to tune via cross validation, its total runtime is more than a GLM with one tunable parameter. Note in this work we did not test an elastic net probit that also optimizes over rf and % of all tests, are significant when bounding FDR by 5%. Given than many selected SNPs are on the same chromosome this is not surprising. Furthermore, we observed that all single SNPs that were not significant after bounding FDR are present in at least one SNP pair, emphasizing the importance of considering pairwise SNP interactions See for details.Finally, we use all of data, to find the top SNPs and SNP pairs with largest risks, i.e., rocedure  785 SNPsD=900, T1=0.25, T2=1.2, and T3=0.8. Linear and quadratic probit with LASSO penalty set λ to 0.2 and 0.02, respectively, and the linear probit with elastic net sets λ=0.13.Data obtained in  is deposD=900 SNPs for prediction, the Fisher’s exact test using the Benjamini-Hochberg [Tables Hochberg  procedurHochberg , 33. LooHochberg , but itsHochberg . In thisT=1.2, resulting in using 169324 SNP pairs in its analysis. These results suggest although we cannot reliably tell which SNP pairs are true discoveries and which are false discoveries, the information present of the weak SNP pairs outweighs the noise, by aggregating these pairs we can extract the information of encoded in the pairs more than the noise that may be inserted to the decision rule, insert the added information in the prediction rule, and the net effect is more reliable performance. Note that by encoding the SNP pairs in the analysis we may be able to say that for a new test point the net effect of SNP pair interactions is increased risk, i.e., likelihood of being a cancerous point; however, we may not be able to pinpoint which SNP pairs brought us to this conclusion, rather, we can only comment on their agglomerated net effect.Now, using FPT to detect significant pairwise SNP interactions, bounding FDR by 5% using the Benjamini-Hochberg procedure, none of the pairs are significant; however, cross validation suggests Finally, we plot the amount of difference in correlation coefficients of SNP pairs in Fig. D=1250, T1=0.25, T2=1, and T3=0.5. Linear and quadratic probit with LASSO penalty set λ to 0.01 and 0.03, respectively, and the linear probit with elastic net sets λ=0.02. Figure Data obtained in  is deposD=1250 for classification, only looking at this set, 269 binarized SNPs are significant using the Fisher’s exact test bounding FDR by 5% using the Benjamini-Hochberg procedure. Going back to the literature we observe several of the genes top SNPs and SNP pairs map to are shown or suggested to be affected in breast cancer. For example, rs13129525 which ranks 9 is located on the FAM171A1 gene which is suggested to be affected in breast cancer [Tables t cancer . Furthert cancer  and CCDCt cancer  genes, wD=1250 SNPs, bounding FDR by 5% using the Benjamini-Hochberg procedure only 4 pairs are significant, although cross validation suggests T2=1, resulting in using 567190 SNP pairs for classification. This suggests in order to boost our prediction accuracies we need to use many SNP pairs that are not significant, but the information contained in the true discoveries outweighs the noise of the many false discoveries present in the prediction rule. Finally, Fig. Using FPT to detect significant pairwise interactions among the top Analyzing SNP data and developing classification rules given SNP observations is difficult when studying complex diseases. The small-sample high-dimensional nature of the problem, individual SNPs being potentially weak markers, SNPs being categorical variables in nature, and their complex interactions are several important factors that make classifier design a challenging task. Due to each individual SNP contributing only minimally to the class labels, it seems necessary to account for SNP interactions to obtain reliable predictions. The proposed algorithm, LABS-HDMR-CO aims to balance computation cost, complexity, and prediction performance by using a representation that accounts for pairwise interactions. Although higher order HDMR expansions can be considered, given current technology, computation power, and sample sizes, accounting only for pairwise interactions seems to be the most one can hope for.Interestingly, we observed in our simulated examples described here that the linear models seem to perform better than expected. Although the current simulations are not sufficient to verify the performance and robustness of linear models for SNP classification, we expect this rather good performance to be due to closeness of GLMs to the first degree HDMR expansions. Note that probit and logit links have rather similar graphs, and the linear model of the logit link aims to compute the log likelihood ratio. In other words, the GLM with logit link assumes the log likelihood ratio is linear, and assumes the risk of a SNP with two minor alleles is twice the risk of a SNP with one minor allele. Note the linear term basically resembles the first order HDMR expansion under this additional “dose-effect linearity” assumption. This assumption, similar to the assumptions we made here in the development of LABS-HDMR-CO, reduces complexity and the number of parameters to estimate. Note that the training of a logit model is usually done by maximum likelihood (ML) estimation of the parameters. Finally, note that since probit and logit links are very similar in shape, the superior performance of LABS-HDMR-CO over GLMs may be due to the following three reasons: (1) LABS-HDMR-CO uses second order HDMR expansion while most GLMs used in practice mimic first order HDMR expansion, (2) the preprocessing of LABS-HDMR-CO decomposing SNP dosage data to two indicators seems to better grasp the nonlinear nature of SNPs, while not affecting the flexibility of the algorithm to account for SNPs that are neither recessive nor dominant, and (3) the additional assumptions made in LABS-HDMR-CO seem to enforce less rigidness in the model than the assumptions of GLMs on linear additive risks.When analyzing cancer datasets reporting SNP dosage values, in the lung cancer dataset we observed that LABS-HDMR-CO may enjoy much superior performance compared with other popular algorithms, and in the breast cancer dataset we observed may perform only slightly inferior to them. Furthermore, when lack of reliable biological knowledge results in the need of considering extremely large number of potential SNP pairs, although we may not be able to reliably detect which SNP pairs are affected in the disease under study, we may be able to aggregate the information of many potential SNP pairs to improve prediction accuracy. In other words, when working with SNP data, it seems sets with large FDRs might still carry enough signal to improve prediction accuracies. Finally, note that the HAPGEN2 data is based on real work sequences, and we can expect it to adequately mimic real world scenarios. We observed much higher accuracies for all classification rules for the HAPGEN2 dataset compared with other cancer datasets. As SNPs seem to be equally weak in all datasets, for instance risks of individual SNPs are not very different, we may hypothesize that the relatively small sample size of cancer datasets may contribute to inferior performance, as the trained classifiers have errors much larger than the Bayes error, and that the larger samples are necessary for more reliable predictions.The analysis of genetic variants and their joint effect on complex diseases is a challenging task. In particular, SNPs are a difficult data type to handle due to their high-dimensionality, weak effects of each individual SNP on the phenotype under study, the need to account their joint complex interactions, and their categorical nature. These challenges make it difficult to develop classification rules with reliable predictions, and are exacerbated by the small sample sizes in many applications.D, T1, T2, and T3) in cross validation, the training of the model may become quite computationally expensive. However, note that different thresholds can be evaluated independent of each other, making LABS-HDMR-CO an ideal candidate for parallel computing. Further development of techniques to speed up the training process is an interesting direction for future work that should be explored in more detail.Here we revisited the binary classification problem given categorical SNP observations when reported in dosage, and proposed LABS-HDMR-CO as an algorithm that produces classification rules with good prediction performance that can take several hundred SNPs as input, and account for their pairwise interactions. Additionally, LABS-HDMR-CO is a very fast algorithm in nature, with runtime comparable to a GLM with LASSO penalty. However, due to the 4 parameters to tune  sense . TherefoThe ability of HDMR to acknowledge categorical nature of SNP data with complex non-linear interactions opens up a new avenue of research to develop low dimensional models suitable for categorical data. Last but not least, the close connection of HDMR with the Sobol indices gives one the ability to identify significant SNP pairs with high interactions, using the same methodology as used for classification problems. Interestingly, we observed that although we may not be able to detect which SNP pairs are affected in the disease under study, the net effect of aggregating many high-profile SNP pairs can boost the prediction accuracy. In other words, in spite of not being able to declare where the “signal” is, i.e., which specific pairwise patterns are affected, it is possible to implicitly extract and take advantage of such information to improve prediction accuracy.The power, of LABS-HDMR-CO to account for and combine many SNP pairs in its decision rule opens up many avenues of research demanding further investigation. For instance, the type of a classification problem for categorical observations considered here may be extended to non-binary cases (multiple phenotypes) as well, and we will pursue such an extension of our approach in future work. We note, however, that binary classification is the cornerstone of classification theory and many solutions to multiclass problems can be formulated as a sequence of solutions to binary class problems.s: indicator function of statement s being true y: the class label taking values 0 or 1 D: the number of features that pass the first phase filtration of the LABS-HDMR-CO classification algorithm F: the set of feature indices u: an arbitrary subset of Ffu: the HDMR component for set u⊆FX: the observation random vector comprised of categorical variables Xu: restriction of X to features in u⊆FXf: used instead of Xf}{ for f∈FL(X): the log likelihood ratio of point X belonging to class 1 ny: sample size in class yf taking value c in class yfi and fj taking values ci and cj, respectively, in class yu takes value cCf: the set of categorical values feature f∈F can take rf: the risk associated to binarized feature ffi and fjR(X): the risk associated to observation XyS(u): the Sobol index of feature set uSc(u): the main effect Sobol index of feature set uT: the threshold used to assign a class to a test point T1: the threhsold used to remove weak features T2: the threhsold used to remove weak feature pairs T3: the threhsold used to remove weak feature blocks b∗: the estimated approximate HDMR coefficients obtained from the training sampleu satisfy constraint qZ=f(X): is the dependent varibale whose HDMR expansion is being computed Ed(Z|X): the dth order HDMR expansion of Z given observation Xfi and fj taking values ci and cj, respectivelyfi and fjfi and fj taking values ci and cj,repectievly, and the probability mass function value assuming fi and fj are independent in class yfi and fjfi, (c) fi takes value c1, and (d) the other feature in the pair, fj, takes value c2fi, (c) fi takes value c1, and (d) the other feature in the pair, fj, takes value c2rA: the risk associated to block A being the ratio of observed pairwise feature patterns of A averaged over all samples1Additional file 1 Supplementary: top SNPs of LABS-HDMR-CO. The top SNPs used by LABS-HDMR-CO for the HAPGEN2, breast cancer, and lung cancer datasets are provided in the Supplementary.


Number of teats is very important for lactating sows. We conducted genome-wide association studies (GWAS) and estimated the genetic parameters for traits related to teat number. Results showed that there were nine and 22 SNPs exceeding genome-wide significance and suggestive significance levels, respectively. Eighteen genes annotated near them were concentrated on chromosomes 7 and 10. Among them, three new candidate genes were located on the genomic regions around the significant SNPs. Our findings provide new insight into investigating the complex genetic mechanism of traits related to teat number in pigs.VRTN and SYNDIG1L) were located in genomic region around this SNP. Three significant SNPs were shown to be associated with TTN, RTN and MAX traits. Seven significant SNPs were simultaneously detected in two traits of TTN and RTN. Other two SNPs were only identified in TTN. These 13 SNPs were clustered in the genomic region between 96.10—98.09 Mb on chromosome 7. Moreover, nine significant SNPs were shown to be significantly associated with SLR. In total, four and 22 SNPs surpassed genome-wide significance and suggestive significance levels, respectively. Among candidate genes annotated, eight genes have documented association with the teat number relevant traits. Out of them, DPF3 genes on Sus scrofa chromosome (SSC) 7 and the NRP1 gene on SSC 10 were new candidate genes identified in this study. Our findings demonstrate the genetic mechanism of teat number relevant traits and provide a reference to further improve reproductive performances in practical pig breeding programs.The number of teats is related to the nursing ability of sows. In the present study, we conducted genome-wide association studies (GWAS) for traits related to teat number in Duroc pig population. Two mixed models, one for counted and another for binary phenotypic traits, were employed to analyze seven traits: the right (RTN), left (LTN), and total (TTN) teat numbers; maximum teat number on a side (MAX); left minus right side teat number (LR); the absolute value of LR (ALR); and the presence of symmetry between left and right teat numbers (SLR). We identified 11, 1, 4, 13, and 9 significant SNPs associated with traits RTN, LTN, MAX, TTN, and SLR, respectively. One significant SNP (MARC0038565) was found to be simultaneous associated with RTN, LTN, MAX and TTN. Two annotated genes ( The teat number (NT) is an important determinant of the maternal ability of sows , which cThe teat number, unlike other reproductive traits, is an inborn trait that is less affected by environmental factors . Heritabhttps://www.animalgenome.org/cgi-bin/QTLdb/SS/ontrait?trait_ID=722, accessed on 4 March 2021). One of the most important QTLs for the number of teats VRTN gene is considered to be the most promising candidate gene for this QTL [Biologically, the development of embryonic mammary glands requires the coordination of many signaling pathways to direct cell shape changes, cell movements, and cell-cell interactions that are necessary for proper morphogenesis of mammary glands . To datethis QTL . The cauIn the current study, we analyzed the complex genetic mechanism of differences in the number and location of NT, and further provide a theoretical reference for breeding pigs. The aim of the present study was to identify SNPs and candidate genes associated with NT traits in a Duroc pig population genotyped with a dense SNP array.All animals were treated following the guidelines established by the Council of China for Animal Welfare. The experimental protocols were approved by the Science Research Department of the Institute of Animal Sciences, Chinese Academy of Agricultural Sciences (CAAS) (IASCAAS-AE-07) .Data on NT were obtained from a total of 982 American Duroc pigs born from 2014 to 2016 on a commercial company in Henan province. The teat counts were recorded in the right and left sides of piglets at birth. Phenotypes evaluated were the right (RTN), left (LTN), and total (TTN) teat numbers. Moreover, other four traits constructed were also analyzed, including left minus right side teat number (LR), the absolute value of LR (ALR), the presence of symmetry between left and right teat numbers (SLR), and maximum teat number on a side (MAX). Detailed summary statistics of all traits are shown in Sus scrofa 11.1.All pigs were genotyped using the PorcineSNP60 BeadChip (Illumina). The genotyping platform of Infinium II Multi-Sample Assay was used. SNP chips were scanned using iScan and analyzed using Illumina GenomeStudio . To assess the technical reliability of the genotyping panel, two or more randomly selected DNA samples were genotyped, and over 99.9% identity was obtained. To update the SNP positions, we reordered the SNPs according to the newest version of the pig genome, Quality control was performed using PLINK v1.90 . The fily is the vector of the phenotypic value of the trait under study; b is a vector of fixed effects, i.e., sex; a is a vector of additive genetic effect vector following N, the following model was applied:y is the vector of the phenotypic value of the trait under study; µ is overall population mean; β is the vector of fixed effects: sex; α is the regression coefficient of substituting allele of the candidate SNP to be tested; u is the vector of polygenic effect; X is the incidence matrix regarding to observations to fixed effects; S is the incidence matrix relating observations to SNP effects with elements coded as 0, 1, 2 for homozygote of the reference allele, heterozygote, and homozygote of the alternative allele; u is the vector of random polygenic effects; and e is the vector of random residual error. The random effects u were assumed to be normally distributed with zero means and the following covariance structure G is the genomic relationship matrix (GRM) and For the binary trait (SLR), the following model was employed:p-value) = 5.79 , respectively.Associations between counted or binary traits under study and the SNPs were analyzed one SNP at a time using GCTA software  and GenAhttp://ftp.ensembl.org/pub/release-103/fasta/sus_scrofa/dna/Sus_scrofa.Sscrofa11.1.dna.toplevel.fa.gz, accessed on 4 March 2021) and National Center for Biotechnology Information (NCBI) Genome  were retrieved to characterize candidate genes in targeted regions. The search to for positional candidate genes was extended 50 kb up- and downstream from the significant SNPs.The porcine genome assembly 11.1  7 (VRTN and SYNDIG1L) resided in a span distance of 50 kb around the SNP . Seven significant SNPs  were simultaneously detected in TTN and RTN. Eight candidate genes  were located in the genomic regions containing these seven SNPs. Other two SNPs (M1GA0010637 and ALGA0043904) were identified only in TTN and were located in DPF3 gene region. Nine significant SNPs were shown to be significantly associated with SLR. Eight of them were located on SSC 10 and one on SSC 17. Two genes were annotated as NRP1 and ITBG1. Among candidate genes annotated, eight genes have documented association with the teat number relevant traits. They were VRTN, SYNDIG1L, YLPM1, PROX2, DPF3, NUMB, AREL1, and FCF1.Totally, four and 22 SNPs surpassed genome-wide significance and suggestive significance levels, respectively . Moreove (SSC) 7 ; signifi the SNP . Three sThe teat number-relevant traits play an important role in rearing piglets and are easy to measure in both males and females. Although the teat number-relevant traits in pigs are characterized as a discontinuous counting variable. However, the observed distribution of the NT in our data was approximately followed the Gaussian distribution. It was showed that Gaussian distribution would be better fitted to this trait compared to the Poisson distribution ,23.−7. The same result was reported by Gary A. et al. [In the current study, the estimated pedigree-based heritabilities of LTN, RTN, TTN, and MAX were larger than those of genomic-based heritabilities. This result is consistent with that of Gary A. Rohrer et al. . Total t. et al. ., which In the present study, 13, 11, 1, and 4 SNPs were found to be associated with TTN, RTN, LTN, and MAX, respectively. These SNPs were located in one genomic region between 96.10 and 98.09 Mb on SSC 7. This genomic region is almost overlapped with a QTL hotspot on SSC 7 between 96.1 and 98.2 Mb (Sscrofa 11.1) that was also identified to be associated with TTN in the Canadian Duroc pig population by Zhuang et al. , signifiVRTN and SYNDIG1L resided in upstream about 28 kb and downstream 5 kb of the top SNP (MARC0038565), respectively. This was further confirmed that VRTN can be proposed as the most promising candidate gene; however, we still did not identify the genetic variants in this genic region related to number of teat relevant traits. It had been documented that VRTN had a major effect on the development of thoracic vertebrae (ribs) in pigs as well [It should be noted that one SNP  was found to be simultaneous associated with RTN, LTN, MAX, and TTN in the present study. This SNP was also identified in Canadian Duroc pigs [ as well ,31,32,33VRTN and SYNDIG1L had shown to be associated with the teat number relevant traits. The most significant SNP identified in RTN was located on the PROX2 genic region. Coupling with PROX2, SYNDIG1L, and YLMP1 have been reported as the key candidate genes for teat number traits [FCF1 and AREL1 genes associated with teat number [NUMB and FCF1 associated with RTN and TTN. NUMB plays an important role in regulation on mammary development [DPF3 plays an indispensable function in the progression of breast cancer [NRP1 genic region. NRP1 acts as a Neutrophil elastase (NE) receptor mediating uptake and PR1 cross-presentation in breast cancer cells [In this study, 18 genes were annotated genomic regions around the significant SNPs. Out of them, eight genes including r traits . A studyt number . There welopment . Lin et t cancer . Furtherer cells . The curDuroc sires are commonly utilized as a terminal sire in three-way crossbreeding programs. The breeding program of the Duroc pig has emphasized growth and efficiency traits rather than reproduction, therefore teat numbers and related traits have not been selected for in Duroc pig population in which there are theoretically ample of genetic variants on teat numbers. Zhuang et al. reported that significant SNPs identified in two different lines of Duroc pigs were totally different . MoscateDPF3 on SSC 7 for TTN and another is NRP1 gene on SSC 10 for SLR. Our findings may provide the information resource to further understanding of the genetic mechanism of teat number relevant traits, and a reference to optimize breeding program for improvement of reproductive performances in pigs.We carried out genome-wide association studies on teat number-relevant traits in a Duroc population. In total, there were nine and 22 SNPs exceeding genome-wide significance and suggestive significance levels, respectively. The identified SNPs are concentrated on SSC 7 and 10. Eighteen genes were annotated near them. Out of them, two new candidate genes were found: one is