Disequilibrium fine-mapping of a rare allele via coalescent models of gene ancestry

Abstract

Genetic linkage studies based on pedigree data have limited resolution, due to the relatively small number of segregations. Disequilibrium mapping, which uses population associations to infer the location of a disease mutation, provides one possible strategy for narrowing the candidate region. We develop a coalescent model for the ancestry of a random sample of disease alleles, and use it to investigate population association as a tool for fine-mapping a rare disease. Recombination events may be placed on the ancestral coalescent, and define the recombinant classes, the sets of sampled disease alleles descending from the meiosis at which a given recombination occurred. All disease haplotypes within a recombinant class are identical by descent at the marker. This identity by descent underlies linkage disequilibrium, the allelic association that is due to genetic linkage. We first investigate factors influencing marker identity by descent in sampled disease haplotypes, and the power to detect allelic associations. We then combine Monte Carlo generation of recombinant classes with an analytic method for computation of the probability of observed disease haplotypes conditional on latent recombinant classes, to obtain a linkage likelihood for fine-scale mapping. This likelihood can take into account known features of population history, such as changing patterns of population growth. Single-marker disequilibrium mapping in compared with interval disequilibrium mapping, and an extension to multipoint mapping is discussed. The method and its properties are illustrated with simulated data examples, constructed to be typical of fine-scale mapping of rare diseases in the Finnish and Japanese populations. Possible departures from assumptions in applications to real diseases are discussed, along with their effect on estimated recombination fractions.