Marker assisted selection using best linear unbiased prediction

Best linear unbiased prediction (BLUP) is applied to a mixed linear model with additive effects for alleles at a market quantitative trait locus (MQTL) and additive effects for alleles at the remaining quantitative trait loci (QTL). A recursive algorithm is developed to obtain the covariance matrix of the effects of MQTL alleles. A simple method is presented to obtain its inverse. This approach allows simultaneous evaluation of fixed effects, effects of MQTL alleles, and effects of alleles at the remaining QTLs, using known relationships and phenotypic and marker information. The approach is sufficiently general to accommodate individuals with partial or no marker information. Extension of the approach to BLUP with multiple markers is discussed.