Use of multiple genetic markers in prediction of breeding values

Genotypes at a marker locus give information on transmission of genes from parents to offspring and that information can be used in predicting the individuals' additive genetic value at a linked quantitative trait locus (MQTL). In this paper a recursive method is presented to build the gametic relationship matrix for an autosomal MQTL which requires knowledge on recombination rate between the marker locus and the MQTL linked to it. A method is also presented to obtain the inverse of the gametic relationship matrix. This information can be used in a mixed linear model for simultaneous evaluation of fixed effects, gametic effects at the MQTL and additive genetic effects due to quantitative trait loci unlinked to the marker locus (polygenes). An equivalent model can be written at the animal level using the numerator relationship matrix for the MQTL and a method for obtaining the inverse of this matrix is presented. Information on several unlinked marker loci, each of them linked to a different locus affecting the trait of interest, can be used by including an effect for each MQTL. The number of equations per animal in this case is 2m + 1 where m is the number of MQTL. A method is presented to reduce the number of equations per animal to one by combining information on all MQTL and polygenes into one numerator relationship matrix. It is illustrated how the method can accommodate individuals with partial or no marker information. Numerical examples are given to illustrate the methods presented. Opportunities to use the presented model in constructing genetic maps are discussed.