Information sources in linkage disequilibrium-linkage mapping using half-sib designs

A mixed models approach to QTL mapping can optimally combine linkage disequilibrium (LD) information both across and within families. In this model the distribution of the additive QTL effects can be defined as (0, GVQTL) where G is the genetic relationship matrix, and VQTL the additive QTL variance. G has dimensions n x n, where n is the number of haplotypes, with elements representing the probability that haplotypes carry a QTL allele that is identical by descent (IBD). To utilize LD information across families, IBD probabilities between founder QTL alleles can be estimated based on similarities between the sampled haplotypes (Meuwissen and Goddard, 2001). To utilize LD information within families (also referred to as linkage information) the IBD probabilities between QTL alleles of relatives is estimated conditional on the transmission of markers (Meuwissen et al., 2002). The combination of these approaches is referred to as linkage disequilibrium – linkage (LDL) mapping. Designs suitable for LDL mapping include complex pedigrees, as well as half-sib families (Meuwissen et al., 2002; Lee and Van der Werf, 2004). In the case of paternal half-sib families, the source of LD information is the sire haplotypes as well as the maternal haplotypes of the progeny, and the source of linkage information the paternal haplotypes of the progeny.