Genetic evaluation with autosomal and X-chromosomal inheritance
Theoretical and Applied Genetics, 80 (1):
75--80 (Jul 1, 1990)DOI: 10.1007/BF00224018
Abstract
At present, genetic evaluation in livestock using best linear unbiased prediction (BLUP) assumes autosomal inheritance. There is evidence, however, of X-chromosomal inheritance for some traits of economic importance. BLUP can accommodate models that include X-chromosomal in addition to autosomal inheritance. To obtain BLUP with autosomal and X-chromosomal additive inheritance for a population in which allelic frequency is equal in the sexes, and that is in gametic equilibrium, we write yi = x´xi$\beta$ + ai + si + ei, where yi is the phenotypic value for individual i, x´xi, is a vector of constants relating yi to fixed effects, $\beta$ is a vector of fixed effects, ai is the additive genetic effect for autosomal loci, Si is the additive genetic effect for X-chromosomal loci, and ei is random error. The covariance matrix of ai's is A$\sigma$A2, where A is the matrix of twice the co-ancestries between relatives for autosomal loci, and $\sigma$A2is the variance of additive genetic effects for autosomal loci. The covariance matrix of si's is S$\sigma$F2, where S is a matrix of functions of co-ancestries between relatives for X-chromosomal loci and $\sigma$F2is the variance of additive genetic effects for X-chromosomal loci for noninbred females. Given the covariance matrices of random effects ai, si, and ei, BLUPs of autosomal and of X-chromosomal additive effects can be obtained using mixed model equations. Recursive rules to construct S and an efficient algorithm to compute its inverse are given.