Increased accuracy of selection by using the realised relationship matrix

Biosciences Research Division, Department of Primary Industries Victoria, 1 Park Drive, Bundoora 3083, Australia.
Genetics Research (Impact Factor: 1.47). 03/2009; 91(1):47-60. DOI: 10.1017/S0016672308009981
Source: PubMed


Dense marker genotypes allow the construction of the realized relationship matrix between individuals, with elements the realized proportion of the genome that is identical by descent (IBD) between pairs of individuals. In this paper, we demonstrate that by replacing the average relationship matrix derived from pedigree with the realized relationship matrix in best linear unbiased prediction (BLUP) of breeding values, the accuracy of the breeding values can be substantially increased, especially for individuals with no phenotype of their own. We further demonstrate that this method of predicting breeding values is exactly equivalent to the genomic selection methodology where the effects of quantitative trait loci (QTLs) contributing to variation in the trait are assumed to be normally distributed. The accuracy of breeding values predicted using the realized relationship matrix in the BLUP equations can be deterministically predicted for known family relationships, for example half sibs. The deterministic method uses the effective number of independently segregating loci controlling the phenotype that depends on the type of family relationship and the length of the genome. The accuracy of predicted breeding values depends on this number of effective loci, the family relationship and the number of phenotypic records. The deterministic prediction demonstrates that the accuracy of breeding values can approach unity if enough relatives are genotyped and phenotyped. For example, when 1000 full sibs per family were genotyped and phenotyped, and the heritability of the trait was 0.5, the reliability of predicted genomic breeding values (GEBVs) for individuals in the same full sib family without phenotypes was 0.82. These results were verified by simulation. A deterministic prediction was also derived for random mating populations, where the effective population size is the key parameter determining the effective number of independently segregating loci. If the effective population size is large, a very large number of individuals must be genotyped and phenotyped in order to accurately predict breeding values for unphenotyped individuals from the same population. If the heritability of the trait is 0.3, and N(e)=100, approximately 12474 individuals with genotypes and phenotypes are required in order to predict GEBVs of un-phenotyped individuals in the same population with an accuracy of 0.7 [corrected].

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    • "Methods such as Bayes A and Bayes B assume that the variance of marker effects has an a priori inverse x 2 distribution (Meuwissen et al. 2001) that produces shrinkage as well as variable selection. Nevertheless, when the true marker effects have a multivariate normal distribution and the size of the training population and the number of markers is large, all methods produce GEBVs that are highly correlated with the true breeding values of the candidates for selection (Hayes et al. 2009; Verbyla et al. 2010). Copyright © 2015 Ceron-Rojas et al. doi: 10.1534/g3.115.019869 "
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    • "Its success depends on accurate genomic predictions. A key factor affecting accuracy of genomic prediction is the amount of information from reference population (Daetwyler et al., 2008; Goddard, 2009; Goddard and Hayes, 2009). In dairy cattle, reference populations are usually composed of progeny-tested bulls, since they have reliable phenotypic information from a large group of daughters. "
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    ABSTRACT: Small reference populations limit the accuracy of genomic prediction in numerically small breeds, such like Danish Jersey. The objective of this study was to investigate two approaches to improve genomic prediction by increasing size of reference population in Danish Jersey. The first approach was to include North American Jersey bulls in Danish Jersey reference population. The second was to genotype cows and use them as reference animals. The validation of genomic prediction was carried out on bulls and cows, respectively. In validation on bulls, about 300 Danish bulls (depending on traits) born in 2005 and later were used as validation data, and the reference populations were: (1) about 1050 Danish bulls, (2) about 1050 Danish bulls and about 1150 US bulls. In validation on cows, about 3000 Danish cows from 87 young half-sib families were used as validation data, and the reference populations were: (1) about 1250 Danish bulls, (2) about 1250 Danish bulls and about 1150 US bulls, (3) about 1250 Danish bulls and about 4800 cows, (4) about 1250 Danish bulls, 1150 US bulls and 4800 Danish cows. Genomic best linear unbiased prediction model was used to predict breeding values. De-regressed proofs were used as response variables. In the validation on bulls for eight traits, the joint DK-US bull reference population led to higher reliability of genomic prediction than the DK bull reference population for six traits, but not for fertility and longevity. Averaged over the eight traits, the gain was 3 percentage points. In the validation on cows for six traits (fertility and longevity were not available), the gain from inclusion of US bull in reference population was 6.6 percentage points in average over the six traits, and the gain from inclusion of cows was 8.2 percentage points. However, the gains from cows and US bulls were not accumulative. The total gain of including both US bulls and Danish cows was 10.5 percentage points. The results indicate that sharing reference data and including cows in reference population are efficient approaches to increase reliability of genomic prediction. Therefore, genomic selection is promising for numerically small population.
    animal 09/2015; -1:1-9. DOI:10.1017/S1751731115001792 · 1.84 Impact Factor
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    • "These 55 differences may be due to several causes, like different data sets or noise due to uncertainty in the 56 estimation. Estimated variance components may also refer to different genetic bases, for instance, 57 genomic relationship matrices refers to the genotyped population whereas pedigree relationships 58 refer to the founders of the pedigree (VanRaden, 2008; Hayes et al., 2009; Powell et al., 2010). In this 59 work I will analyze the last point, i.e., if the researcher has several available methods for the same 60 data set, can he/she meaningfully compare estimates of heritabilites? "
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    ABSTRACT: Use of relationships between individuals to estimate genetic variances and heritabilities via mixed models is standard practice in human, plant and livestock genetics. Different models or information for relationships may give different estimates of genetic variances. However, comparing these estimates across different relationship models is not straightforward as the implied base populations differ between relationship models. In this work, I present a method to compare estimates of variance components across different relationship models. I suggest referring genetic variances obtained using different relationship models to the same reference population, usually a set of individuals in the population. Expected genetic variance of this population is the estimated variance component from the mixed model times a statistic, Dk, which is the average self-relationship minus the average (self- and across-) relationship. For most typical models of relationships, Dk is close to 1. However, this is not true for very deep pedigrees, for identity-by-state relationships, or for non-parametric kernels, which tend to overestimate the genetic variance and the heritability. Using mice data, I show that heritabilities from identity-by-state and kernel-based relationships are overestimated. Weighting these estimates by Dk scales them to a base comparable to genomic or pedigree relationships, avoiding wrong comparisons, for instance, “missing heritabilities”.
    Theoretical Population Biology 08/2015; accepted. DOI:10.1016/j.tpb.2015.08.005 · 1.70 Impact Factor
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