Asymptotic normality of breeding values under segmental inheritance

CANTET, R. J. C.; MUNILLA, SEBASTIÁN

Madison, Wisconsin

Congreso; 5th International Conference on Quantitative Genetics; 2016

International Conference on Quantitative Genetics

Normality in the infinitesimal additive model is based on the assumption of a large number of loci segregating independently across the genome. Thus, depending on parental inbreeding Mendelian residuals explain somewhat less than half the additive variance. To increase the accuracy of predictions of breeding value, genomic markers bring extra‐information that reduce Mendelian residual variance and allow detecting realized  relationships rather than those expected by the pedigree. When looking at the inheritance process in diploids in which segments of genomes are passed rather single loci, genomicmarkers are informative sources of recombinations with respect to the expected proportions of ancestral genomes received by an individual from ancestral generations. We model the inheritance of segments using R. A. Fisher?s theory of junctions and P. Stam?s number of segments (Ns) in the population. The variance of a segment involves two parameters: the additive variance and the covariance between additive effects from loci in linkage disequilibrium. Whereas covariances of segments involves the same two parameters, specification of the joint distribution of segments within and across individuals requires the two‐locus theory of C. C. Cockerham and B. S. Weir involving digametic, trigametic, and tetragametic probabilities. All of these probabilities are functions of the product of gene frequencies under linkage equilibrium, plus terms that are functions of linkage disequilibrium measures among two, three or four alleles. These latter terms are also functions of (1/Ns). Hence, as Ns gets large the terms involving linkage disequilibrium measures go to zero and so does the covariance between additive effects under linkage disequilibrium. This argument is used to prove the asymptotic normality of the breeding values under segmental inheritance of the additive two locus model and, in separate research, the covariance of breeding values using pedigree plus genomic markers.