Covariance between relatives in multibreed populations: additive model.
TL;DR: The inverse of the genotypic covariance matrix given here can be used both to obtain genetic evaluations by best linear unbiased prediction and to estimate genetic parameters by maximum likelihood in multibreed populations.
Abstract: Covariance between relatives in a multibreed population was derived for an additive model with multiple unlinked loci. An efficient algorithm to compute the inverse of the additive genetic covariance matrix is given. For an additive model, the variance for a crossbred individual is a function of the additive variances for the pure breeds, the covariance between parents, and segregation variances. Provided that the variance of a crossbred individual is computed as presented here, the covariance between crossbred relatives can be computed using formulae for purebred populations. For additive traits the inverse of the genotypic covariance matrix given here can be used both to obtain genetic evaluations by best linear unbiased prediction and to estimate genetic parameters by maximum likelihood in multibreed populations. For nonadditive traits, the procedure currently used to analyze multibreed data can be improved using the theory presented here to compute additive covariances together with a suitable approximation for nonadditive covariances.
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TL;DR: Using GS based on high-density marker data, purebreds can be accurately selected for crossbred performance without the need for pedigree or breed information, and haplotype segments with strong linkage disequilibrium are shorter in crossbred and admixed populations than in purebreedings.
Abstract: In livestock, genomic selection (GS) has primarily been investigated by simulation of purebred populations. Traits of interest are, however, often measured in crossbred or mixed populations with uncertain breed composition. If such data are used as the training data for GS without accounting for breed composition, estimates of marker effects may be biased due to population stratification and admixture. To investigate this, a genome of 100 cM was simulated with varying marker densities (5 to 40 segregating markers per cM). After 1,000 generations of random mating in a population of effective size 500, 4 lines with effective size 100 were isolated and mated for another 50 generations to create 4 pure breeds. These breeds were used to generate combined, F 1 , F 2 , 3- and 4-way crosses, and admixed training data sets of 1,000 individuals with phenotypes for an additive trait controlled by 100 segregating QTL and heritability of 0.30. The validation data set was a sample of 1,000 genotyped individuals from one pure breed. Method Bayes-B was used to simultaneously estimate the effects of all markers for breeding value estimation. With 5 (40) markers per cM, the correlation of true with estimated breeding value of selection candidates (accuracy) was greatest, 0.79 (0.85), when data from the same pure breed were used for training. When the training data set consisted of crossbreds, the accuracy ranged from 0.66 (0.79) to 0.74 (0.83) for the 2 marker densities, respectively. The admixed training data set resulted in nearly the same accuracies as when training was in the breed to which selection candidates belonged. However, accuracy was greatly reduced when genes from the target pure breed were not included in the admixed or crossbred population. This implies that, with high-density markers, admixed and crossbred populations can be used to develop GS prediction equations for all pure breeds that contributed to the population, without a substantial loss of accuracy compared with training on purebred data, even if breed origin has not been explicitly taken into account. In addition, using GS based on high-density marker data, purebreds can be accurately selected for crossbred performance without the need for pedigree or breed information. Results also showed that haplotype segments with strong linkage disequilibrium are shorter in crossbred and admixed populations than in purebreds, providing opportunities for QTL fine mapping.
206 citations
TL;DR: GS can be conducted in crossbred population and models that fit breed-specific effects of SNP alleles may not be necessary, especially with high marker density, demonstrating that crossbred data can be used to evaluate purebreds for commercial crossbred performance.
Abstract: Background: One of the main limitations of many livestock breeding programs is that selection is in pure breeds housed in high-health environments but the aim is to improve crossbred performance under field conditions. Genomic selection (GS) using high-density genotyping could be used to address this. However in crossbred populations, 1) effects of SNPs may be breed specific, and 2) linkage disequilibrium may not be restricted to markers that are tightly linked to the QTL. In this study we apply GS to select for commercial crossbred performance and compare a model with breed-specific effects of SNP alleles (BSAM) to a model where SNP effects are assumed the same across breeds (ASGM). The impact of breed relatedness (generations since separation), size of the population used for training, and marker density were evaluated. Trait phenotype was controlled by 30 QTL and had a heritability of 0.30 for crossbred individuals. A Bayesian method (Bayes-B) was used to estimate the SNP effects in the crossbred training population and the accuracy of resulting GS breeding values for commercial crossbred performance was validated in the purebred population. Results: Results demonstrate that crossbred data can be used to evaluate purebreds for commercial crossbred performance. Accuracies based on crossbred data were generally not much lower than accuracies based on pure breed data and almost identical when the breeds crossed were closely related breeds. The accuracy of both models (ASGM and BSAM) increased with marker density and size of the training data. Accuracies of both models also tended to decrease with increasing distance between breeds. However the effect of marker density, training data size and distance between breeds differed between the two models. BSAM only performed better than AGSM when the number of markers was small (500), the number of records used for training was large (4000), and when breeds were distantly related or unrelated. Conclusion: In conclusion, GS can be conducted in crossbred population and models that fit breed-specific effects of SNP alleles may not be necessary, especially with high marker density. This opens great opportunities for genetic improvement of purebreds for performance of their crossbred descendents in the field, without the need to track pedigrees through the system.
182 citations
Additional excerpts
...As an alternative to CCPS, Dekkers [1] proposed to select purebreds for commercial crossbred performance using genomic selection....
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...In addition, using CCPS increases the rate of inbreeding [8] and makes it difficult to accommodate non-additive gene action [6]....
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...Genomic selection for crossbred performance has three main advantages over CCPS: 1) it does not require pedigree information on crossbreds, 2) after estimates of SNP effects are obtained using genotype and phenotype data, prediction can continue for several generations without additional phenotypes [9], 3) it reduces the rate of inbreeding [12], and 4) it makes accommodating nonadditive gene action easier [1]....
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...In order to avoid these problems, it has been proposed to select purebred relatives based on crossbred performance using combined crossbred and purebred selection or CCPS [2-6]....
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TL;DR: Effective use of MAS requires estimates of the effect on CC performance, and MAS based on such estimates enables more effective selection for CC performance without the need for extensive pedigree recording and while reducing rates of inbreeding.
Abstract: Several studies have shown that selection of purebreds for increased performance of their crossbred descendants under field conditions is hampered by low genetic correlations between purebred and commercial crossbred (CC) performance. Although this can be addressed by including phenotypic data from CC relatives for selection of purebreds through combined crossbred and purebred selection (CCPS), this also increases rates of inbreeding and requires comprehensive systems for collection of phenotypic data and pedigrees at the CC level. This study shows that both these limitations can be overcome with marker-assisted selection (MAS) by using estimates of the effects of markers on CC performance. To evaluate the potential benefits of CC-MAS, a model to incorporate marker information in selection strategies was developed based on selection index theory, which allows prediction of responses and rates of inbreeding by using standard deterministic selection theory. Assuming a genetic correlation between purebred and CC performance of 0.7 for a breeding program representing a terminal sire line in pigs, CC-MAS was shown to substantially increase rates of response and reduce rates of inbreeding compared with purebred selection and CCPS, with 60 CC half sibs available for each purebred selection candidate. When the accuracy of marker-based EBV was 0.6, CC-MAS resulted in 34 and 10% greater responses in CC performance than purebred selection and CCPS. Corresponding rates of inbreeding were 1.4% per generation for CC-MAS, compared with 2.1% for purebred selection and 3.0% for CCPS. For marker-based EBV with an accuracy of 0.9, CC-MAS resulted in 75 and 43% greater responses than purebred selection and CCPS, and further reduced rates of inbreeding to 1.0% per generation. Selection on marker-based EBV derived from purebred phenotypes resulted in substantially less response in CC performance than in CC-MAS. In conclusion, effective use of MAS requires estimates of the effect on CC performance, and MAS based on such estimates enables more effective selection for CC performance without the need for extensive pedigree recording and while reducing rates of inbreeding.
138 citations
TL;DR: A method is described for the prediction of breeding values incorporating genomic information that combines genomic predictions with traditional ancestral information lost between the process of deregression of the national breeding values and subsequent re-estimation using the genomic relationship matrix.
Abstract: A method is described for the prediction of breeding values incorporating genomic information. The first stage involves the prediction of genomic breeding values for genotyped individuals. A novel component of this is the estimation of the genomic relationship matrix in the context of a multi-breed population. Because not all ancestors of genotyped animals are genotyped, a selection index procedure is used to blend genomic predictions with traditional ancestral information that is lost between the process of deregression of the national breeding values and subsequent re-estimation using the genomic relationship matrix. Finally, the genomically enhanced predictions are filtered through to nongenotyped descendants using a regression procedure.
138 citations
TL;DR: A conceptual framework is suggested that considers each ancestral population as a finite-sized pool of gametes and generates across-individual relationships and contrasts with the classical view which each population is considered as an infinite, unrelated pool.
Abstract: Recent use of genomic (marker-based) relationships shows that relationships exist within and across base population (breeds or lines). However, current treatment of pedigree relationships is unable to consider relationships within or across base populations, although such relationships must exist due to finite size of the ancestral population and connections between populations. This complicates the conciliation of both approaches and, in particular, combining pedigree with genomic relationships. We present a coherent theoretical framework to consider base population in pedigree relationships. We suggest a conceptual framework that considers each ancestral population as a finite-sized pool of gametes. This generates across-individual relationships and contrasts with the classical view which each population is considered as an infinite, unrelated pool. Several ancestral populations may be connected and therefore related. Each ancestral population can be represented as a "metafounder," a pseudo-individual included as founder of the pedigree and similar to an "unknown parent group." Metafounders have self- and across relationships according to a set of parameters, which measure ancestral relationships, i.e., homozygozities within populations and relationships across populations. These parameters can be estimated from existing pedigree and marker genotypes using maximum likelihood or a method based on summary statistics, for arbitrarily complex pedigrees. Equivalences of genetic variance and variance components between the classical and this new parameterization are shown. Segregation variance on crosses of populations is modeled. Efficient algorithms for computation of relationship matrices, their inverses, and inbreeding coefficients are presented. Use of metafounders leads to compatibility of genomic and pedigree relationship matrices and to simple computing algorithms. Examples and code are given.
127 citations
Cites background or methods from "Covariance between relatives in mul..."
...The additional variance in the F2 cross compared to the variance in the F1 cross is termed segregation variance (Lande 1981; Lo et al. 1993)....
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...This is typically Metafounders in Pedigrees 461 ignored in a classical framework, although methods exist (Lo et al. 1993; Garcia-Cortes and Toro 2006)....
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References
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1,006 citations
TL;DR: In this article, the inverse of a numerator relationship matrix is needed for best linear unbiased prediction of breeding values, and a simple method for computing the elements of this inverse without computing the relationship matrix itself is presented.
Abstract: The inverse of a numerator relationship matrix is needed for best linear unbiased prediction of breeding values. The purpose of this paper to is present a rapid and simple method for computation of the elements of this inverse without computing the relationship matrix itself. The method is particularly useful in noninbred populations but is much faster than the conventional method in the presence of inbreeding.
793 citations
TL;DR: The minimum number of genes involved in producing a large difference between populations in a quantitative trait is typically estimated to be about 5 or 10, with occasional values up to 20, which strongly supports the neo-Darwinian theory that large evolutionary changes usually occur by the accumulation of multiple genetic factors with relatively small effects.
Abstract: A procedure is outlined for estimating the minimum number of freely segregating genetic factors, nE, contributing to the difference in a quantitative character between two populations that have diverged by artificial or natural selection. If certain simple criteria are satisfied approximately on an appropriate scale of measurement, nE can be estimated by comparing the phenotypic means and variances in the two parental populations and in their F1 and F2 hybrids (and backcrosses). This generalizes the method of Wright to genetically heterogeneous (or wild) parental populations, as well as inbred lines. Standard errors of the estimates are derived for large samples. The minimum number of genes involved in producing a large difference between populations in a quantitative trait is typically estimated to be about 5 or 10, with occasional values up to 20. This strongly supports the neo-Darwinian theory that large evolutionary changes usually occur by the accumulation of multiple genetic factors with relatively small effects.
603 citations
TL;DR: This approach allows simultaneous evaluation of fixed effects, effects of MQTL alleles, and effects of alleles at the remaining QTLs, using known relationships and phenotypic and marker information.
Abstract: Best linear unbiased prediction (BLUP) is applied to a mixed linear model with additive effects for alleles at a market quantitative trait locus (MQTL) and additive effects for alleles at the remaining quantitative trait loci (QTL). A recursive algorithm is developed to obtain the covariance matrix of the effects of MQTL alleles. A simple method is presented to obtain its inverse. This approach allows simultaneous evaluation of fixed effects, effects of MQTL alleles, and effects of alleles at the remaining QTLs, using known relationships and phenotypic and marker information. The approach is sufficiently general to accommodate individuals with partial or no marker information. Extension of the approach to BLUP with multiple markers is discussed.
505 citations
01 Jan 1968
445 citations