ELIMINATION OF QUANTITATIVE TRAIT LOCI EQUATIONS IN AN ANIMAL-MODEL INCORPORATING GENETIC-MARKER DATA

An animal model for BLUP of additive effects at marked quantitative tr ait loci and breeding values does not require quantitative trait loci equations for animals that were not marker genotyped and do not provid e relationship ties among genotyped descendants. An animal model in qu antitative trait loci effects and breeding values is equivalent to a p revious model in quantitative trait loci effects and residual breeding values. With no marker data, absorption of quantitative trait loci in to breeding value equations reduces to the standard animal model for p henotypic data. With marker data on some animals, quantitative trait l oci equations for animals without marker data and not providing relati onship ties among genotyped descendants can be eliminated. Resulting m ixed model equations contain the inverse of a variance-covariance matr ix among breeding values and remaining quantitative trait loci effects , which can be computed directly. Quantitative trait loci effects of p rogeny with parental quantitative trait loci effects eliminated are li nked to breeding values of parents. Animals without marker data may be ancestors and nonelite members of the current population. Hence, a su bstantial fraction of a population may not be genotyped. Then, the num ber of equations is reduced considerably.