Estimation of Conditional Multilocus Gene Identity Among Relatives

this paper we present a sampling-based approach for linkage detection which is well suited to sparse data at multiple loci on individuals in an extended complex pedigree. 2. Gene identity and linkage likelihoods. There are many ways to partition linkage likelihoods, the probability Pr/ (Y) of phenotypic data Y under a genetic linkage model /. Let Y consist of trait data Y T and marker data YM . The model (genetic map positions and marker alleles frequencies) is assumed known for the data, YM , at marker loci. In this paper, we shall focus on the problem of linkage detection, in which no trait specific genetic model for the trait data YT is assumed. However, the development is similar in the case where hypothesized trait loci are explicitly modeled and linkage estimation is the goal of the analysis [Thompson (1994b)]. Let BM denote the pattern of gene IBD at marker loci among observed individuals. The likelihood for the genetic model on the basis of data Y = (Y T ; YM ) is Pr/ (Y) = Pr/ (YT ; YM ) / Pr/ (YT j YM ) (2.1)