Elimination of Quantitative Trait Loci Equations in an Animal Model Incorporating Genetic Marker Data

Abstract

An animal model for BLUP of additive effects at marked quantitative trait loci and breeding values does not require quantitative trait loci equations for animals that were not marker genotyped and do not provide relationship ties among genotyped descendants. An animal model in quantitative trait loci effects and breeding values is equivalent to a previous model in quantitative trait loci effects and residual breeding values. With no marker data, absorption of quantitative trait loci into breeding value equations reduces to the standard animal model for phenotypic data. With marker data on some animals, quantitative trait loci equations for animals without marker data and not providing relationship ties among genotyped descendants can be eliminated. Resulting mixed model equations contain the inverse of a variance-covariance matrix among breeding values and remaining quantitative trait loci effects, which can be computed directly. Quantitative trait loci effects of progeny with parental quantitative trait loci effects eliminated are linked to breeding values of parents. Animals without marker data may be ancestors and nonelite members of the current population. Hence, a substantial fraction of a population may not be genotyped. Then, the number of equations is reduced considerably. © 1993, American Dairy Science Association. All rights reserved.