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Covariance Between Genotypic Effects and its Use for Genomic Inference in Half-Sib Families.

ABSTRACT: In livestock, current statistical approaches utilize extensive molecular data, e.g., single nucleotide polymorphisms (SNPs), to improve the genetic evaluation of individuals. The number of model parameters increases with the number of SNPs, so the multicollinearity between covariates can affect the results obtained using whole genome regression methods. In this study, dependencies between SNPs due to linkage and linkage disequilibrium among the chromosome segments were explicitly considered in methods used to estimate the effects of SNPs. The population structure affects the extent of such dependencies, so the covariance among SNP genotypes was derived for half-sib families, which are typical in livestock populations. Conditional on the SNP haplotypes of the common parent (sire), the theoretical covariance was determined using the haplotype frequencies of the population from which the individual parent (dam) was derived. The resulting covariance matrix was included in a statistical model for a trait of interest, and this covariance matrix was then used to specify prior assumptions for SNP effects in a Bayesian framework. The approach was applied to one family in simulated scenarios (few and many quantitative trait loci) and using semireal data obtained from dairy cattle to identify genome segments that affect performance traits, as well as to investigate the impact on predictive ability. Compared with a method that does not explicitly consider any of the relationship among predictor variables, the accuracy of genetic value prediction was improved by 10-22%. The results show that the inclusion of dependence is particularly important for genomic inference based on small sample sizes.

SUBMITTER: Wittenburg D

PROVIDER: S-EPMC5015933 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Key messageGenomic prediction of GCA effects based on model training with full-sib rather than half-sib families yields higher short- and long-term selection gain in reciprocal recurrent genomic selection for hybrid breeding, if SCA effects are important. Reciprocal recurrent genomic selection (RRGS) is a powerful tool for ensuring sustainable selection progress in hybrid breeding. For training the statistical model, one can use half-sib (HS) or full-sib (FS) families produced by inter-population crosses of candidates from the two parent populations. Our objective was to compare HS-RRGS and FS-RRGS for the cumulative selection gain ([Formula: see text]), the genetic, GCA and SCA variances ([Formula: see text],[Formula: see text], [Formula: see text]) of the hybrid population, and prediction accuracy ([Formula: see text]) for GCA effects across cycles. Using SNP data from maize and wheat, we simulated RRGS programs over 10 cycles, each consisting of four sub-cycles with genomic selection of [Formula: see text] out of 950 candidates in each parent population. Scenarios differed for heritability [Formula: see text] and the proportion [Formula: see text] of traits, training set (TS) size ([Formula: see text]), and maize vs. wheat. Curves of [Formula: see text] over selection cycles showed no crossing of both methods. If [Formula: see text] was high, [Formula: see text] was generally higher for FS-RRGS than HS-RRGS due to higher [Formula: see text]. In contrast, HS-RRGS was superior or on par with FS-RRGS, if [Formula: see text] or [Formula: see text] and [Formula: see text] were low. [Formula: see text] showed a steeper increase and higher selection limit for scenarios with low [Formula: see text], high [Formula: see text] and large [Formula: see text]. [Formula: see text] and even more so [Formula: see text] decreased rapidly over cycles for both methods due to the high selection intensity and the role of the Bulmer effect for reducing [Formula: see text]. Since the TS for FS-RRGS can additionally be used for hybrid prediction, we recommend this method for achieving simultaneously the two major goals in hybrid breeding: population improvement and cultivar development.

Project description:BackgroundThe covariance matrix of breeding values is at the heart of prediction methods. Prediction of breeding values can be formulated using either an "observed" or a theoretical covariance matrix, and a major argument for choosing one or the other is the reduction of the computational burden for inverting such a matrix. In this regard, covariance matrices that are derived from Markov causal models possess properties that deliver sparse inverses.ResultsBy using causal Markov models, we express the breeding value of an individual as a linear regression on ancestral breeding values, plus a residual term, which we call residual breeding value (RBV). The latter is a noise term that accounts for the uncertainty in prediction due to lack of fit of the linear regression. A notable property of these models is the parental Markov condition, through which the multivariate distribution of breeding values is uniquely determined by the distribution of the mutually independent RBV. Animal breeders have long been relying on a causal Markov model, while using the additive relationship matrix as the covariance matrix structure of breeding values, which is calculated assuming gametic equilibrium. However, additional covariances among breeding values arise due to identity disequilibrium, which is defined as the difference between the covariance matrix under the multi-loci probability of identity-by-descent ([Formula: see text]) and its expectation under gametic phase equilibrium, i.e., A. The disequilibrium term [Formula: see text]-A is considered in the model for predicting breeding values called the "ancestral regression" (AR), a causal Markov model. Here, we introduce the "ancestral regression to parents" (PAR) causal Markov model, which reduces the computational burden of the AR approach. By taking advantage of the conditional independence property of the PAR Markov model, we derive covariances between the breeding values of grandparents and grand-offspring and between parents and offspring. In addition, we obtain analytical expressions for the covariance between collateral relatives under the PAR model, as well as for the inbreeding coefficient.ConclusionsWe introduced the causal PAR Markov model that captures identity disequilibrium in the covariances among breeding values and produces a sparse inverse covariance matrix to build and solve a set of mixed model equations.

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Covariance Between Genotypic Effects and its Use for Genomic Inference in Half-Sib Families.

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