The effect of linkage disequilibrium and family relationships on the reliability of genomic prediction.

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Abstract

Although the concept of genomic selection relies on linkage disequilibrium (LD) between quantitative trait loci and markers, reliability of genomic predictions is strongly influenced by family relationships. In this study, we investigated the effects of LD and family relationships on reliability of genomic predictions and the potential of deterministic formulas to predict reliability using population parameters in populations with complex family structures. Five groups of selection candidates were simulated by taking different information sources from the reference population into account: (1) allele frequencies, (2) LD pattern, (3) haplotypes, (4) haploid chromosomes, and (5) individuals from the reference population, thereby having real family relationships with reference individuals. Reliabilities were predicted using genomic relationships among 529 reference individuals and their relationships with selection candidates and with a deterministic formula where the number of effective chromosome segments (M(e)) was estimated based on genomic and additive relationship matrices for each scenario. At a heritability of 0.6, reliabilities based on genomic relationships were 0.002 ± 0.0001 (allele frequencies), 0.022 ± 0.001 (LD pattern), 0.018 ± 0.001 (haplotypes), 0.100 ± 0.008 (haploid chromosomes), and 0.318 ± 0.077 (family relationships). At a heritability of 0.1, relative differences among groups were similar. For all scenarios, reliabilities were similar to predictions with a deterministic formula using estimated M(e). So, reliabilities can be predicted accurately using empirically estimated M(e) and level of relationship with reference individuals has a much higher effect on the reliability than linkage disequilibrium per se. Furthermore, accumulated length of shared haplotypes is more important in determining the reliability of genomic prediction than the individual shared haplotype length.

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Accuracy of Predicting the Genetic Risk of Disease Using a Genome-Wide Approach

Hans D Daetwyler, Beatriz Villanueva, John A. Woolliams (2008)

Background The prediction of the genetic disease risk of an individual is a powerful public health tool. While predicting risk has been successful in diseases which follow simple Mendelian inheritance, it has proven challenging in complex diseases for which a large number of loci contribute to the genetic variance. The large numbers of single nucleotide polymorphisms now available provide new opportunities for predicting genetic risk of complex diseases with high accuracy. Methodology/Principal Findings We have derived simple deterministic formulae to predict the accuracy of predicted genetic risk from population or case control studies using a genome-wide approach and assuming a dichotomous disease phenotype with an underlying continuous liability. We show that the prediction equations are special cases of the more general problem of predicting the accuracy of estimates of genetic values of a continuous phenotype. Our predictive equations are responsive to all parameters that affect accuracy and they are independent of allele frequency and effect distributions. Deterministic prediction errors when tested by simulation were generally small. The common link among the expressions for accuracy is that they are best summarized as the product of the ratio of number of phenotypic records per number of risk loci and the observed heritability. Conclusions/Significance This study advances the understanding of the relative power of case control and population studies of disease. The predictions represent an upper bound of accuracy which may be achievable with improved effect estimation methods. The formulae derived will help researchers determine an appropriate sample size to attain a certain accuracy when predicting genetic risk.

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Increased accuracy of artificial selection by using the realized relationship matrix.

B. Hayes, P M Visscher, M. E. Goddard (2009)

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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Linkage disequilibrium and persistence of phase in Holstein-Friesian, Jersey and Angus cattle.

A de Roos, B. Hayes, R J Spelman … (2008)

When a genetic marker and a quantitative trait locus (QTL) are in linkage disequilibrium (LD) in one population, they may not be in LD in another population or their LD phase may be reversed. The objectives of this study were to compare the extent of LD and the persistence of LD phase across multiple cattle populations. LD measures r and r(2) were calculated for syntenic marker pairs using genomewide single-nucleotide polymorphisms (SNP) that were genotyped in Dutch and Australian Holstein-Friesian (HF) bulls, Australian Angus cattle, and New Zealand Friesian and Jersey cows. Average r(2) was approximately 0.35, 0.25, 0.22, 0.14, and 0.06 at marker distances 10, 20, 40, 100, and 1000 kb, respectively, which indicates that genomic selection within cattle breeds with r(2) >or= 0.20 between adjacent markers would require approximately 50,000 SNPs. The correlation of r values between populations for the same marker pairs was close to 1 for pairs of very close markers (<10 kb) and decreased with increasing marker distance and the extent of divergence between the populations. To find markers that are in LD with QTL across diverged breeds, such as HF, Jersey, and Angus, would require approximately 300,000 markers.