When searching for trait loci along the genome, properly incorporating prior genomic information
into the analysis will almost certainly increase the chance of success. Recently, we devised a method
that utilizes such prior information in the mapping of trait genes for complex disorders (Vieland,
1998; Wang et al. 1999; Vieland et al. 2000). This method uses the posterior probability of linkage
(PPL) based on the admixture model as a measure of linkage information. In this paper, we study
the consistency of the PPL. It is shown that, as the number of pedigrees increases, the PPL converges
in probability to 1 when there is linkage between the marker and a trait locus, and converges to 0
otherwise. This conclusion is shown to be true for general pedigrees and trait models, even when the
likelihood functions are based on misspecified trait models. As part of the effort to prove this
conclusion, it is shown that when there is no linkage, the maximum likelihood estimator of the
recombination fraction in the admixture model is asymptotically 0.5, even when the admixture
model misrepresents the true model.