Calculating Elements of Gametic Relationship Matrix in the Model Containing Effects of Marked QTL-Cluster

Abstract

In recent years, a variety of mixed linear models have been proposed for QTL interval mapping and marker-assisted prediction of QTL-and polygene-effects in outbred populations of livestock species. For a model containing the effects of a cluster of linked QTLs or a chromosomal segment marked, a computing procedure is proposed herein for constructing the gametic relationship matrix whose elements are the expected values of the identity-by-descent (IBD) proportions between gametes for individuals. It is shown that the IBD set for two gametes given can be systematically partitioned into some sub-sets that have lower dimensional components according to the related gametogenesis processes. Noticing such property of the IBD set and using the joint gametogenesis process at the marker locus, a recursive method is developed to systematically calculate the required IBD sets and the elements of the gametic relationship matrix. It is expected that the proposed method is efficient compared to the path counting-like method, especially for complex pedigrees of many animals. Further investigation is needed to develop a computing strategy for directly making up the inverse of the gametic relationship matrix.