No abstract

This paper presents a new approximation to the likelihood for a pedigree with loops, based on cutting all loops and extending the pedigree at the cuts. An opimum loop-cutting strategy and an iterative extension technique are presented. The likelihood for a pedigree with loops is then approximated by the conditional likelihood for the entire cut-extended pedigree given the extended part. The approximate likelihoods are compared with the exact likelihoods obtained using the program MENDEL for several small pedigrees with loops. The approximation is efficient for large pedigrees with complex loops in terms of computing speed and memory requirements.

No abstract

Miller, K.D., Bleck, G.T., Wang, T., Feltes, R.J., Schook, L.B., McKeith

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.