Genetic evaluation and parameter estimation using marker and trait information

This thesis presents theory and computing methods for genetic evaluation and parameter estimation using marker and trait information for purebreed and multibreed populations. We consider a single marker locus (ML) and a quantitative trait locus linked to the marker, referred to as the marked QTL (MQTL).; Best linear unbiased prediction (BLUP) can be applied for genetic evaluation using marker and trait information. This application requires modeling genetic means, variances, and covariances, and computing the inverse of the conditional covariance matrix (G_v) between relatives for the MQTL effects, given marker, breed and trait information.; In the presence of gametic equilibrium between the marker locus and marked QTL, this thesis presents theory and algorithms to construct (G _v) and to compute its inverse efficiently given marker and trait information. These algorithms are sufficiently general to accommodate situations where: (1) paternal or maternal origin of marker alleles cannot be determined, and (2) the marker genotypes of some individuals in the pedigree are unknown.; Incomplete gametic disequilibrium between the marker locus and marked QTL is also considered. For this situation, theory and algorithms are presented to model means and to construct the conditional covariance matrix ( G_v) between relatives for the MQTL effects, given marker and trait information, in a multibreed population. An efficient algorithm to invert (G_v) is presented. Theory presented accounts for heterogeneity of variances among pure breeds and for segregation variances between pure breeds.; Genetic evaluation by BLUP using marker and trait information requires knowledge of genetic parameters, such as the recombination rate ( r) between a marker locus and a marked QTL. Maximum likelihood methods are widely used to estimate genetic parameters. This thesis 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 optimum strategy to cut loops 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 approximation is efficient for large pedigrees with complex loops in terms of computing speed and memory requirements.