Pascal Croiseau

Improved lasso for genomic selection

Empirical experience with genomic selection in dairy cattle suggests that the distribution of the effects of single nucleotide polymorphisms (SNPs) might be far from normality for some traits. An alternative, avoiding the use of arbitrary prior information, is the Bayesian Lasso (BL). Regular BL uses a common variance parameter for residual and SNP effects (BL1Var). We propose here a BL with different residual and SNP effect variances (BL2Var), equivalent to the original Lasso formulation. The λ parameter in Lasso is related to genetic variation in the population. We also suggest precomputing individual variances of SNP effects by BL2Var, to be later used in a linear mixed model (HetVar-GBLUP). Models were tested in a cross-validation design including 1756 Holstein and 678 Montbéliarde French bulls, with 1216 and 451 bulls used as training data; 51 325 and 49 625 polymorphic SNP were used. Milk production traits were tested. Other methods tested included linear mixed models using variances inferred from pedigree estimates or integrated out from the data. Estimates of genetic variation in the population were close to pedigree estimates in BL2Var but not in BL1Var. BL1Var shrank breeding values too little because of the common variance. BL2Var was the most accurate method for prediction and accommodated well major genes, in particular for fat percentage. BL1Var was the least accurate. HetVar-GBLUP was almost as accurate as BL2Var and allows for simple computations and extensions.

Genomic selection in French dairy cattle

Genomic selection is implemented in French Holstein, Montbeliarde, and Normande breeds (70%, 16% and 12% of French dairy cows). A characteristic of the model for genomic evaluation is the use of haplotypes instead of single-nucleotide polymorphisms (SNPs), so as to maximise linkage disequilibrium between markers and quantitative

High-density marker imputation accuracy in sixteen French cattle breeds

BackgroundGenotyping with the medium-density Bovine SNP50 BeadChip® (50K) is now standard in cattle. The high-density BovineHD BeadChip®, which contains 777 609 single nucleotide polymorphisms (SNPs), was developed in 2010. Increasing marker density increases the level of linkage disequilibrium between quantitative trait loci (QTL) and SNPs and the accuracy of QTL localization and genomic selection. However, re-genotyping all animals with the high-density chip is not economically feasible. An alternative strategy is to genotype part of the animals with the high-density chip and to impute high-density genotypes for animals already genotyped with the 50K chip. Thus, it is necessary to investigate the error rate when imputing from the 50K to the high-density chip.MethodsFive thousand one hundred and fifty three animals from 16 breeds (89 to 788 per breed) were genotyped with the high-density chip. Imputation error rates from the 50K to the high-density chip were computed for each breed with a validation set that included the 20% youngest animals. Marker genotypes were masked for animals in the validation population in order to mimic 50K genotypes. Imputation was carried out using the Beagle 3.3.0 software.ResultsMean allele imputation error rates ranged from 0.31% to 2.41% depending on the breed. In total, 1980 SNPs had high imputation error rates in several breeds, which is probably due to genome assembly errors, and we recommend to discard these in future studies. Differences in imputation accuracy between breeds were related to the high-density-genotyped sample size and to the genetic relationship between reference and validation populations, whereas differences in effective population size and level of linkage disequilibrium showed limited effects. Accordingly, imputation accuracy was higher in breeds with large populations and in dairy breeds than in beef breeds. More than 99% of the alleles were correctly imputed if more than 300 animals were genotyped at high-density. No improvement was observed when multi-breed imputation was performed.ConclusionIn all breeds, imputation accuracy was higher than 97%, which indicates that imputation to the high-density chip was accurate. Imputation accuracy depends mainly on the size of the reference population and the relationship between reference and target populations.

Efficiency of multi-breed genomic selection for dairy cattle breeds with different sizes of reference population

Single-breed genomic selection (GS) based on medium single nucleotide polymorphism (SNP) density (~50,000; 50K) is now routinely implemented in several large cattle breeds. However, building large enough reference populations remains a challenge for many medium or small breeds. The high-density BovineHD BeadChip (HD chip; Illumina Inc., San Diego, CA) containing 777,609 SNP developed in 2010 is characterized by short-distance linkage disequilibrium expected to be maintained across breeds. Therefore, combining reference populations can be envisioned. A population of 1,869 influential ancestors from 3 dairy breeds (Holstein, Montbéliarde, and Normande) was genotyped with the HD chip. Using this sample, 50K genotypes were imputed within breed to high-density genotypes, leading to a large HD reference population. This population was used to develop a multi-breed genomic evaluation. The goal of this paper was to investigate the gain of multi-breed genomic evaluation for a small breed. The advantage of using a large breed (Normande in the present study) to mimic a small breed is the large potential validation population to compare alternative genomic selection approaches more reliably. In the Normande breed, 3 training sets were defined with 1,597, 404, and 198 bulls, and a unique validation set included the 394 youngest bulls. For each training set, estimated breeding values (EBV) were computed using pedigree-based BLUP, single-breed BayesC, or multi-breed BayesC for which the reference population was formed by any of the Normande training data sets and 4,989 Holstein and 1,788 Montbéliarde bulls. Phenotypes were standardized by within-breed genetic standard deviation, the proportion of polygenic variance was set to 30%, and the estimated number of SNP with a nonzero effect was about 7,000. The 2 genomic selection (GS) approaches were performed using either the 50K or HD genotypes. The correlations between EBV and observed daughter yield deviations (DYD) were computed for 6 traits and using the different prediction approaches. Compared with pedigree-based BLUP, the average gain in accuracy with GS in small populations was 0.057 for the single-breed and 0.086 for multi-breed approach. This gain was up to 0.193 and 0.209, respectively, with the large reference population. Improvement of EBV prediction due to the multi-breed evaluation was higher for animals not closely related to the reference population. In the case of a breed with a small reference population size, the increase in correlation due to multi-breed GS was 0.141 for bulls without their sire in reference population compared with 0.016 for bulls with their sire in reference population. These results demonstrate that multi-breed GS can contribute to increase genomic evaluation accuracy in small breeds.

Application of Bayesian least absolute shrinkage and selection operator (LASSO) and BayesCπ methods for genomic selection in French Holstein and Montbéliarde breeds.

Recently, the amount of available single nucleotide polymorphism (SNP) marker data has considerably increased in dairy cattle breeds, both for research purposes and for application in commercial breeding and selection programs. Bayesian methods are currently used in the genomic evaluation of dairy cattle to handle very large sets of explanatory variables with a limited number of observations. In this study, we applied 2 bayesian methods, BayesCπ and bayesian least absolute shrinkage and selection operator (LASSO), to 2 genotyped and phenotyped reference populations consisting of 3,940 Holstein bulls and 1,172 Montbéliarde bulls with approximately 40,000 polymorphic SNP. We compared the accuracy of the bayesian methods for the prediction of 3 traits (milk yield, fat content, and conception rate) with pedigree-based BLUP, genomic BLUP, partial least squares (PLS) regression, and sparse PLS regression, a variable selection PLS variant. The results showed that the correlations between observed and predicted phenotypes were similar in BayesCπ (including or not pedigree information) and bayesian LASSO for most of the traits and whatever the breed. In the Holstein breed, bayesian methods led to higher correlations than other approaches for fat content and were similar to genomic BLUP for milk yield and to genomic BLUP and PLS regression for the conception rate. In the Montbéliarde breed, no method dominated the others, except BayesCπ for fat content. The better performances of the bayesian methods for fat content in Holstein and Montbéliarde breeds are probably due to the effect of the DGAT1 gene. The SNP identified by the BayesCπ, bayesian LASSO, and sparse PLS regression methods, based on their effect on the different traits of interest, were located at almost the same position on the genome. As the bayesian methods resulted in regressions of direct genomic values on daughter trait deviations closer to 1 than for the other methods tested in this study, bayesian methods are suggested for genomic evaluations of French dairy cattle.

A comparison of partial least squares (PLS) and sparse PLS regressions in genomic selection in French dairy cattle.

Genomic selection involves computing a prediction equation from the estimated effects of a large number of DNA markers based on a limited number of genotyped animals with phenotypes. The number of observations is much smaller than the number of independent variables, and the challenge is to find methods that perform well in this context. Partial least squares regression (PLS) and sparse PLS were used with a reference population of 3,940 genotyped and phenotyped French Holstein bulls and 39,738 polymorphic single nucleotide polymorphism markers. Partial least squares regression reduces the number of variables by projecting independent variables onto latent structures. Sparse PLS combines variable selection and modeling in a one-step procedure. Correlations between observed phenotypes and phenotypes predicted by PLS and sparse PLS were similar, but sparse PLS highlighted some genome regions more clearly. Both PLS and sparse PLS were more accurate than pedigree-based BLUP and generally provided lower correlations between observed and predicted phenotypes than did genomic BLUP. Furthermore, PLS and sparse PLS required similar computing time to genomic BLUP for the study of 6 traits.

Genomic selection in domestic animals: Principles, applications and perspectives.

The principles of genomic selection are described, with the main factors affecting its efficiency and the assumptions underlying the different models proposed. The reasons of its fast adoption in dairy cattle are explained and the conditions of its application to other species are discussed. Perspectives of development include: selection for new traits and new breeding objectives; adoption of more robust approaches based on information on causal variants; predictions of genotype×environment interactions.

Meta-analysis of genome-wide association studies for cattle stature identifies common genes that regulate body size in mammals

Stature is affected by many polymorphisms of small effect in humans1. In contrast, variation in dogs, even within breeds, has been suggested to be largely due to variants in a small number of genes2,3. Here we use data from cattle to compare the genetic architecture of stature to those in humans and dogs. We conducted a meta-analysis for stature using 58,265 cattle from 17 populations with 25.4 million imputed whole-genome sequence variants. Results showed that the genetic architecture of stature in cattle is similar to that in humans, as the lead variants in 163 significantly associated genomic regions (P < 5 × 10−8) explained at most 13.8% of the phenotypic variance. Most of these variants were noncoding, including variants that were also expression quantitative trait loci (eQTLs) and in ChIP–seq peaks. There was significant overlap in loci for stature with humans and dogs, suggesting that a set of common genes regulates body size in mammals.Meta-analysis of data from 58,265 cattle shows that the genetic architecture underlying stature is similar to that in humans, where many genomic regions individually explain only a small amount of phenotypic variance.

Alternative haplotype construction methods for genomic evaluation

Genomic evaluation methods today use single nucleotide polymorphism (SNP) as genomic markers to trace quantitative trait loci (QTL). Today most genomic prediction procedures use biallelic SNP markers. However, SNP can be combined into short, multiallelic haplotypes that can improve genomic prediction due to higher linkage disequilibrium between the haplotypes and the linked QTL. The aim of this study was to develop a method to identify the haplotypes, which can be expected to be superior in genomic evaluation, as compared with either SNP or other haplotypes of the same size. We first identified the SNP (termed as QTL-SNP) from the bovine 50K SNP chip that had the largest effect on the analyzed trait. It was assumed that these SNP were not the causative mutations and they merely indicated the approximate location of the QTL. Haplotypes of 3, 4, or 5 SNP were selected from short genomic windows surrounding these markers to capture the effect of the QTL. Two methods described in this paper aim at selecting the most optimal haplotype for genomic evaluation. They assumed that if an allele has a high frequency, its allele effect can be accurately predicted. These methods were tested in a classical validation study using a dairy cattle population of 2,235 bulls with genotypes from the bovine 50K SNP chip and daughter yield deviations (DYD) on 5 dairy cattle production traits. Combining the SNP into haplotypes was beneficial with all tested haplotypes, leading to an average increase of 2% in terms of correlations between DYD and genomic breeding value estimates compared with the analysis when the same SNP were used individually. Compared with haplotypes built by merging the QTL-SNP with its flanking SNP, the haplotypes selected with the proposed criteria carried less under- and over-represented alleles: the proportion of alleles with frequencies <1 or >40% decreased, on average, by 17.4 and 43.4%, respectively. The correlations between DYD and genomic breeding value estimates increased by 0.7 to 0.9 percentage points when the haplotypes were selected using any of the proposed methods compared with using the haplotypes built from the QTL-SNP and its flanking markers. We showed that the efficiency of genomic prediction could be improved at no extra costs, only by selecting the proper markers or combinations of markers for genomic prediction. One of the presented approaches was implemented in the new genomic evaluation procedure applied in dairy cattle in France in April 2015.

Which individuals to choose to update the reference population? Minimizing the loss of genetic diversity in animal genomic selection programs

Genomic selection (GS) is commonly used in livestock and increasingly in plant breeding. Relying on phenotypes and genotypes of a reference population, GS allows performance prediction for young individuals having only genotypes. This is expected to achieve fast high genetic gain but with a potential loss of genetic diversity. Existing methods to conserve genetic diversity depend mostly on the choice of the breeding individuals. In this study, we propose a modification of the reference population composition to mitigate diversity loss. Since the high cost of phenotyping is the limiting factor for GS, our findings are of major economic interest. This study aims to answer the following questions: how would decisions on the reference population affect the breeding population, and how to best select individuals to update the reference population and balance maximizing genetic gain and minimizing loss of genetic diversity? We investigated three updating strategies for the reference population: random, truncation, and optimal contribution (OC) strategies. OC maximizes genetic merit for a fixed loss of genetic diversity. A French Montbéliarde dairy cattle population with 50K SNP chip genotypes and simulations over 10 generations were used to compare these different strategies using milk production as the trait of interest. Candidates were selected to update the reference population. Prediction bias and both genetic merit and diversity were measured. Changes in the reference population composition slightly affected the breeding population. Optimal contribution strategy appeared to be an acceptable compromise to maintain both genetic gain and diversity in the reference and the breeding populations.