Reducing the effect of parent averages from animal solutions in mixed model equations

Selection of animals based on their BLUP evaluations from an animal model results in animals that are closely related which leads to increased rates of inbreeding. The tendency for higher inbreeding rates is greater at low heritability values. Several attempts have been made to reduce the impact of parent average breeding values from animals evaluations in order to reduce inbreeding while not sacrificing genetic response. A method that modifies the rules for forming the inverse of the additive genetic relationship matrix for use in best linear unbiased estimation of breeding values via an animal model was developed. This method and several others were compared analytically and empirically, from the perspective of partitioning the animal solutions into contributions from the data, from progeny, and from the parent average. The ratio of genetic progress to average level of inbreeding showed that the modified relationship matrix method was superior to the other methods. Similar results could be obtained by using artificially high heritability in a usual BLUP analysis.