Theoretical and Applied Genetics

, Volume 80, Issue 1, pp 75–80 | Cite as

Genetic evaluation with autosomal and X-chromosomal inheritance

  • R. L. Fernando
  • M. Grossman


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′iβ + ai + si + ei, where yi is the phenotypic value for individual i, x′i, is a vector of constants relating yi to fixed effects, β 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 2 , where A is the matrix of twice the co-ancestries between relatives for autosomal loci, and σ A 2 is the variance of additive genetic effects for autosomal loci. The covariance matrix of si's is F 2 , where S is a matrix of functions of co-ancestries between relatives for X-chromosomal loci and σ F 2 is 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.

Key words

X-linkage Covariance Genetic evaluation BLUP 


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • R. L. Fernando
    • 1
  • M. Grossman
    • 1
  1. 1.Department of Animal SciencesUniversity of IllinoisUrbanaUSA

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