Genomic selection has become a very important tool in animal genetics and is rapidly emerging in plant genetics. It holds the promise to be particularly beneficial to select for traits that are ...difficult or expensive to measure, such as traits that are measured in one environment and selected for in another environment. The objective of this paper was to develop three models that would permit multi-trait genomic selection by combining scarcely recorded traits with genetically correlated indicator traits, and to compare their performance to single-trait models, using simulated datasets.
Three (SNP) Single Nucleotide Polymorphism based models were used. Model G and BCπ0 assumed that contributed (co)variances of all SNP are equal. Model BSSVS sampled SNP effects from a distribution with large (or small) effects to model SNP that are (or not) associated with a quantitative trait locus. For reasons of comparison, model A including pedigree but not SNP information was fitted as well.
In terms of accuracies for animals without phenotypes, the models generally ranked as follows: BSSVS > BCπ0 > G > > A. Using multi-trait SNP-based models, the accuracy for juvenile animals without any phenotypes increased up to 0.10. For animals with phenotypes on an indicator trait only, accuracy increased up to 0.03 and 0.14, for genetic correlations with the evaluated trait of 0.25 and 0.75, respectively.
When the indicator trait had a genetic correlation lower than 0.5 with the trait of interest in our simulated data, the accuracy was higher if genotypes rather than phenotypes were obtained for the indicator trait. However, when genetic correlations were higher than 0.5, using an indicator trait led to higher accuracies for selection candidates. For different combinations of traits, the level of genetic correlation below which genotyping selection candidates is more effective than obtaining phenotypes for an indicator trait, needs to be derived considering at least the heritabilities and the numbers of animals recorded for the traits involved.
Levels of inbreeding in cattle populations have increased in the past due to the use of a limited number of bulls for artificial insemination. High levels of inbreeding lead to reduced genetic ...diversity and inbreeding depression. Various estimators based on different sources, e.g., pedigree or genomic data, have been used to estimate inbreeding coefficients in cattle populations. However, the comparative advantage of using full sequence data to assess inbreeding is unknown. We used pedigree and genomic data at different densities from 50k to full sequence variants to compare how different methods performed for the estimation of inbreeding levels in three different cattle breeds.
Five different estimates for inbreeding were calculated and compared in this study: pedigree based inbreeding coefficient (F(PED)); run of homozygosity (ROH)-based inbreeding coefficients (F(ROH)); genomic relationship matrix (GRM)-based inbreeding coefficients (F(GRM)); inbreeding coefficients based on excess of homozygosity (F(HOM)) and correlation of uniting gametes (F(UNI)). Estimates using ROH provided the direct estimated levels of autozygosity in the current populations and are free effects of allele frequencies and incomplete pedigrees which may increase in inaccuracy in estimation of inbreeding. The highest correlations were observed between F(ROH) estimated from the full sequence variants and the F(ROH) estimated from 50k SNP (single nucleotide polymorphism) genotypes. The estimator based on the correlation between uniting gametes (F(UNI)) using full genome sequences was also strongly correlated with F(ROH) detected from sequence data.
Estimates based on ROH directly reflected levels of homozygosity and were not influenced by allele frequencies, unlike the three other estimates evaluated (F(GRM), F(HOM) and FU(NI)), which depended on estimated allele frequencies. F(PED) suffered from limited pedigree depth. Marker density affects ROH estimation. Detecting ROH based on 50k chip data was observed to give estimates similar to ROH from sequence data. In the absence of full sequence data ROH based on 50k can be used to access homozygosity levels in individuals. However, genotypes denser than 50k are required to accurately detect short ROH that are most likely identical by descent (IBD).
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Genomic-enabled prediction is becoming increasingly important in animal and plant breeding and is also receiving attention in human genetics. Deriving accurate predictions of complex traits requires ...implementing whole-genome regression (WGR) models where phenotypes are regressed on thousands of markers concurrently. Methods exist that allow implementing these large-p with small-n regressions, and genome-enabled selection (GS) is being implemented in several plant and animal breeding programs. The list of available methods is long, and the relationships between them have not been fully addressed. In this article we provide an overview of available methods for implementing parametric WGR models, discuss selected topics that emerge in applications, and present a general discussion of lessons learned from simulation and empirical data analysis in the last decade.
The genomic prediction of phenotypes and breeding values in animals and plants has developed rapidly into its own research field. Results of genomic prediction studies are often difficult to compare ...because data simulation varies, real or simulated data are not fully described, and not all relevant results are reported. In addition, some new methods have been compared only in limited genetic architectures, leading to potentially misleading conclusions. In this article we review simulation procedures, discuss validation and reporting of results, and apply benchmark procedures for a variety of genomic prediction methods in simulated and real example data. Plant and animal breeding programs are being transformed by the use of genomic data, which are becoming widely available and cost-effective to predict genetic merit. A large number of genomic prediction studies have been published using both simulated and real data. The relative novelty of this area of research has made the development of scientific conventions difficult with regard to description of the real data, simulation of genomes, validation and reporting of results, and forward in time methods. In this review article we discuss the generation of simulated genotype and phenotype data, using approaches such as the coalescent and forward in time simulation. We outline ways to validate simulated data and genomic prediction results, including cross-validation. The accuracy and bias of genomic prediction are highlighted as performance indicators that should be reported. We suggest that a measure of relatedness between the reference and validation individuals be reported, as its impact on the accuracy of genomic prediction is substantial. A large number of methods were compared in example simulated and real (pine and wheat) data sets, all of which are publicly available. In our limited simulations, most methods performed similarly in traits with a large number of quantitative trait loci (QTL), whereas in traits with fewer QTL variable selection did have some advantages. In the real data sets examined here all methods had very similar accuracies. We conclude that no single method can serve as a benchmark for genomic prediction. We recommend comparing accuracy and bias of new methods to results from genomic best linear prediction and a variable selection approach (e.g., BayesB), because, together, these methods are appropriate for a range of genetic architectures. An accompanying article in this issue provides a comprehensive review of genomic prediction methods and discusses a selection of topics related to application of genomic prediction in plants and animals.
High levels of pairwise linkage disequilibrium (LD) in single nucleotide polymorphism (SNP) array or whole-genome sequence data may affect both performance and efficiency of genomic prediction ...models. Thus, this warrants pruning of genotyping data for high LD. We developed an algorithm, named SNPrune, which enables the rapid detection of any pair of SNPs in complete or high LD throughout the genome.
LD, measured as the squared correlation between phased alleles (r
), can only reach a value of 1 when both loci have the same count of the minor allele. Sorting loci based on the minor allele count, followed by comparison of their alleles, enables rapid detection of loci in complete LD. Detection of loci in high LD can be optimized by computing the range of the minor allele count at another locus for each possible value of the minor allele count that can yield LD values higher than a predefined threshold. This efficiently reduces the number of pairs of loci for which LD needs to be computed, instead of considering all pairwise combinations of loci. The implemented algorithm SNPrune considered bi-allelic loci either using phased alleles or allele counts as input. SNPrune was validated against PLINK on two datasets, using an r
threshold of 0.99. The first dataset contained 52k SNP genotypes on 3534 pigs and the second dataset contained simulated whole-genome sequence data with 10.8 million SNPs and 2500 animals.
SNPrune removed a similar number of SNPs as PLINK from the pig data but SNPrune was almost 12 times faster than PLINK. From the simulated sequence data with 10.8 million SNPs, SNPrune removed 6.4 and 1.4 million SNPs due to complete and high LD. Results were very similar regardless of whether phased alleles or allele counts were used. Using allele counts and multi-threading with 10 threads, SNPrune completed the analysis in 21 min. Using a sliding window of up to 500,000 SNPs, PLINK removed ~ 43,000 less SNPs (0.6%) in the sequence data and SNPrune was 24 to 170 times faster, using one or ten threads, respectively.
The SNPrune algorithm developed here is able to remove SNPs in high LD throughout the genome very efficiently in large datasets.
Whole-genome sequence data is expected to capture genetic variation more completely than common genotyping panels. Our objective was to compare the proportion of variance explained and the accuracy ...of genomic prediction by using imputed sequence data or preselected SNPs from a genome-wide association study (GWAS) with imputed whole-genome sequence data.
Phenotypes were available for 5503 Holstein-Friesian bulls. Genotypes were imputed up to whole-genome sequence (13,789,029 segregating DNA variants) by using run 4 of the 1000 bull genomes project. The program GCTA was used to perform GWAS for protein yield (PY), somatic cell score (SCS) and interval from first to last insemination (IFL). From the GWAS, subsets of variants were selected and genomic relationship matrices (GRM) were used to estimate the variance explained in 2087 validation animals and to evaluate the genomic prediction ability. Finally, two GRM were fitted together in several models to evaluate the effect of selected variants that were in competition with all the other variants.
The GRM based on full sequence data explained only marginally more genetic variation than that based on common SNP panels: for PY, SCS and IFL, genomic heritability improved from 0.81 to 0.83, 0.83 to 0.87 and 0.69 to 0.72, respectively. Sequence data also helped to identify more variants linked to quantitative trait loci and resulted in clearer GWAS peaks across the genome. The proportion of total variance explained by the selected variants combined in a GRM was considerably smaller than that explained by all variants (less than 0.31 for all traits). When selected variants were used, accuracy of genomic predictions decreased and bias increased.
Although 35 to 42 variants were detected that together explained 13 to 19% of the total variance (18 to 23% of the genetic variance) when fitted alone, there was no advantage in using dense sequence information for genomic prediction in the Holstein data used in our study. Detection and selection of variants within a single breed are difficult due to long-range linkage disequilibrium. Stringent selection of variants resulted in more biased genomic predictions, although this might be due to the training population being the same dataset from which the selected variants were identified.
Differences in linkage disequilibrium and in allele substitution effects of QTL (quantitative trait loci) may hinder genomic prediction across populations. Our objective was to develop a ...deterministic formula to estimate the accuracy of across-population genomic prediction, for which reference individuals and selection candidates are from different populations, and to investigate the impact of differences in allele substitution effects across populations and of the number of QTL underlying a trait on the accuracy.
A deterministic formula to estimate the accuracy of across-population genomic prediction was derived based on selection index theory. Moreover, accuracies were deterministically predicted using a formula based on population parameters and empirically calculated using simulated phenotypes and a GBLUP (genomic best linear unbiased prediction) model. Phenotypes of 1033 Holstein-Friesian, 105 Groninger White Headed and 147 Meuse-Rhine-Yssel cows were simulated by sampling 3000, 300, 30 or 3 QTL from the available high-density SNP (single nucleotide polymorphism) information of three chromosomes, assuming a correlation of 1.0, 0.8, 0.6, 0.4, or 0.2 between allele substitution effects across breeds. The simulated heritability was set to 0.95 to resemble the heritability of deregressed proofs of bulls.
Accuracies estimated with the deterministic formula based on selection index theory were similar to empirical accuracies for all scenarios, while accuracies predicted with the formula based on population parameters overestimated empirical accuracies by ~25 to 30%. When the between-breed genetic correlation differed from 1, i.e. allele substitution effects differed across breeds, empirical and deterministic accuracies decreased in proportion to the genetic correlation. Using a multi-trait model, it was possible to accurately estimate the genetic correlation between the breeds based on phenotypes and high-density genotypes. The number of QTL underlying the simulated trait did not affect the accuracy.
The deterministic formula based on selection index theory estimated the accuracy of across-population genomic predictions well. The deterministic formula using population parameters overestimated the across-population genomic accuracy, but may still be useful because of its simplicity. Both formulas could accommodate for genetic correlations between populations lower than 1. The number of QTL underlying a trait did not affect the accuracy of across-population genomic prediction using a GBLUP method.
The preconditioned conjugate gradient (PCG) method is an iterative solver of linear equations systems commonly used in animal breeding. However, the PCG method has been shown to encounter convergence ...issues when applied to single-step single nucleotide polymorphism BLUP (ssSNPBLUP) models. Recently, we proposed a deflated PCG (DPCG) method for solving ssSNPBLUP efficiently. The DPCG method introduces a second-level preconditioner that annihilates the effect of the largest unfavourable eigenvalues of the ssSNPBLUP preconditioned coefficient matrix on the convergence of the iterative solver. While it solves the convergence issues of ssSNPBLUP, the DPCG method requires substantial additional computations, in comparison to the PCG method. Accordingly, the aim of this study was to develop a second-level preconditioner that decreases the largest eigenvalues of the ssSNPBLUP preconditioned coefficient matrix at a lower cost than the DPCG method, in addition to comparing its performance to the (D)PCG methods applied to two different ssSNPBLUP models.
Based on the properties of the ssSNPBLUP preconditioned coefficient matrix, we proposed a second-level diagonal preconditioner that decreases the largest eigenvalues of the ssSNPBLUP preconditioned coefficient matrix under some conditions. This proposed second-level preconditioner is easy to implement in current software and does not result in additional computing costs as it can be combined with the commonly used (block-)diagonal preconditioner. Tested on two different datasets and with two different ssSNPBLUP models, the second-level diagonal preconditioner led to a decrease of the largest eigenvalues and the condition number of the preconditioned coefficient matrices. It resulted in an improvement of the convergence pattern of the iterative solver. For the largest dataset, the convergence of the PCG method with the proposed second-level diagonal preconditioner was slower than the DPCG method, but it performed better than the DPCG method in terms of total computing time.
The proposed second-level diagonal preconditioner can improve the convergence of the (D)PCG methods applied to two ssSNPBLUP models. Based on our results, the PCG method combined with the proposed second-level diagonal preconditioner seems to be more efficient than the DPCG method in solving ssSNPBLUP. However, the optimal combination of ssSNPBLUP and solver will most likely be situation-dependent.
Genomic selection has revolutionized genetic improvement in animals and plants, but little is known about its long-term effects. Here, we investigated the long-term effects of genomic selection on ...response to selection, genetic variance, and the genetic architecture of traits using stochastic simulations. We defined the genetic architecture as the set of causal loci underlying each trait, their allele frequencies, and their statistical additive effects. We simulated a livestock population under 50 generations of phenotypic, pedigree, or genomic selection for a single trait, controlled by either only additive, additive and dominance, or additive, dominance, and epistatic effects. The simulated epistasis was based on yeast data.
Short-term response was always greatest with genomic selection, while response after 50 generations was greater with phenotypic selection than with genomic selection when epistasis was present, and was always greater than with pedigree selection. This was mainly because loss of genetic variance and of segregating loci was much greater with genomic and pedigree selection than with phenotypic selection. Compared to pedigree selection, selection response was always greater with genomic selection. Pedigree and genomic selection lost a similar amount of genetic variance after 50 generations of selection, but genomic selection maintained more segregating loci, which on average had lower minor allele frequencies than with pedigree selection. Based on this result, genomic selection is expected to better maintain genetic gain after 50 generations than pedigree selection. The amount of change in the genetic architecture of traits was considerable across generations and was similar for genomic and pedigree selection, but slightly less for phenotypic selection. Presence of epistasis resulted in smaller changes in allele frequencies and less fixation of causal loci, but resulted in substantial changes in statistical additive effects across generations.
Our results show that genomic selection outperforms pedigree selection in terms of long-term genetic gain, but results in a similar reduction of genetic variance. The genetic architecture of traits changed considerably across generations, especially under selection and when non-additive effects were present. In conclusion, non-additive effects had a substantial impact on the accuracy of selection and long-term response to selection, especially when selection was accurate.
The single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) method, such as single-step genomic BLUP (ssGBLUP), simultaneously analyses phenotypic, pedigree, and ...genomic information of genotyped and non-genotyped animals. In contrast to ssGBLUP, SNP effects are fitted explicitly as random effects in the ssSNPBLUP model. Similarly, principal components associated with the genomic information can be fitted explicitly as random effects in a single-step principal component BLUP (ssPCBLUP) model to remove noise in genomic information. Single-step genomic BLUP is solved efficiently by using the preconditioned conjugate gradient (PCG) method. Unfortunately, convergence issues have been reported when solving ssSNPBLUP by using PCG. Poor convergence may be linked with poor spectral condition numbers of the preconditioned coefficient matrices of ssSNPBLUP. These condition numbers, and thus convergence, could be improved through the deflated PCG (DPCG) method, which is a two-level PCG method for ill-conditioned linear systems. Therefore, the first aim of this study was to compare the properties of the preconditioned coefficient matrices of ssGBLUP and ssSNPBLUP, and to document convergence patterns that are obtained with the PCG method. The second aim was to implement and test the efficiency of a DPCG method for solving ssSNPBLUP and ssPCBLUP.
For two dairy cattle datasets, the smallest eigenvalues obtained for ssSNPBLUP (ssPCBLUP) and ssGBLUP, both solved with the PCG method, were similar. However, the largest eigenvalues obtained for ssSNPBLUP and ssPCBLUP were larger than those for ssGBLUP, which resulted in larger condition numbers and in slow convergence for both systems solved by the PCG method. Different implementations of the DPCG method led to smaller condition numbers, and faster convergence for ssSNPBLUP and for ssPCBLUP, by deflating the largest unfavourable eigenvalues.
Poor convergence of ssSNPBLUP and ssPCBLUP when solved by the PCG method are related to larger eigenvalues and larger condition numbers in comparison to ssGBLUP. These convergence issues were solved with a DPCG method that annihilates the effect of the largest unfavourable eigenvalues of the preconditioned coefficient matrix of ssSNPBLUP and of ssPCBLUP on the convergence of the PCG method. It resulted in a convergence pattern, at least, similar to that of ssGBLUP.
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