GENETIC EVALUATION METHODS FOR POPULATIONS WITH DOMINANCE AND INBREEDING

The effect of inbreeding on mean and genetic covariance matrix for a q uantitative trait in a population with additive and dominance effects is shown. This genetic covariance matrix is a function of five relatio nship matrices and five genetic parameters describing the population. Elements of the relationship matrices are functions of Gillois' (1964) identity coefficients for the four genes at a locus in two individual s. The equivalence of the path coefficient method (Jacquard 1966) and the tabular method (Smith and Maki-Tanila 1990) to compute the covaria nce matrix of additive and dominance effects in a population with inbr eeding is shown. The tabular method is modified to compute, relationsh ip matrices rather than the covariance matrix, which is trait dependen t. Finally, approximate and exact Best Linear Unbiased Predictions (BL UP) of additive and dominance effects are compared using simulated dat a with inbreeding but no directional selection. The trait simulated wa s affected by 64 unlinked biallelic loci with equal effect and complet e dominance. Simulated average inbreeding levels ranged from zero in g eneration one to 0.35 in generation five. The approximate method only accounted for the effect of inbreeding on mean and additive genetic co variance matrix, whereas the exact accounted for all of the changes in mean and genetic covariance matrix due to inbreeding. Approximate BLU P, which is computable for large populations where exact BLUP is not f easible, yielded unbiased predictions of additive and dominance effect s in each generation with only slightly reduced accuracies relative to exact BLUP.