Genetic evaluation by best linear unbiased prediction using marker and trait information in a multibreed population

Genetic evaluation by best linear unbiased prediction (BLUP) requires modeling genetic means, variances, and covariances. This paper presents theory to model means, variances, and covariances in a multibreed population, given marker and breed information, in the presence of gametic disequilibrium between the marker locus (ML) and linked quantitative trait locus (MQTL). Theory and algorithms are presented to construct the matrix of conditional covariances between relatives (Gv) for the MQTL effects in a multibreed population and to obtain the inverse of Gv efficiently. Theory presented here accounts for heterogeneity of variances among pure breeds and for segregation variances between pure breeds. A numerical example was used to illustrate how the theory and algorithms can be used for genetic evaluation by BLUP using marker and trait information in a multibreed population.