Likelihood analysis of disequilibrium mapping, and related problems

In this paper a theory is developed that provides the sampling distribution of alleles at a diallelic marker locus closely linked to a low-frequency allele that arose as a single mutant. The sampling distribution provides a basis for maximum-likelihood estimation of either the recombination rate, the mutation rate, or the age of the allele, provided that the two other parameters are known. This theory is applied to (1) the data of Hastbacka et al., to estimate the recombination rate between a locus associated with diastrophic dysplasia and a linked RFLP marker; (2) the data of Risch et al., to estimate the age of a presumptive allele causing idiopathic distortion dystonia in Ashkenazi jews; and (3) the data of Tishkoff et al., to estimate the date at which, at the CD4 locus, non-African lineages diverged from African lineages. We conclude that the extent of linkage disequilibrium can lead to relatively accurate estimates of recombination and mutation rates and that those estimates are not very sensitive to parameters, such as the population age, whose values are not known with certainty. In contrast, we also conclude that, in many cases, linkage disequilibrium may not lead to useful estimates of allele age, because of the relatively large degree of uncertainly in those estimates.