Assessment of linkage disequilibrium by the decay of haplotype sharing, with application to fine-scale genetic mapping

Linkage disequilibrium (LD) is of great interest for gene mapping and the s tudy of population history. We propose a multilocus model for LD, based on the decay of haplotype sharing (DHS). The DHS model is most appropriate whe n the LD in which one is interested is due to the introduction of a variant on an ancestral haplotype, with recombinations in succeeding generations r esulting in preservation of only a small region of the ancestral haplotype around the variant. This is generally the scenario of interest for gene map ping by LD. The DHS parameter is a measure of LD that can be interpreted as the expected genetic distance to which the ancestral haplotype is preserve d, or, equivalently, 1/(time in generations to the ancestral haplotype). Th e method allows for multiple origins of alleles and for mutations, and it t akes into account missing observations:and ambiguities in haplotype determi nation, via a hidden Markov model. Whereas most commonly used measures of L D apply to pairs of loci, the DHS measure is designed for application to th e densely mapped haplotype data that are increasingly available. The DHS me thod explicitly models the dependence among multiple tightly linked loci on a chromosome. When the assumptions about population structure are sufficie ntly tractable, the estimate of LD is obtained by maximum likelihood. For m ore-complicated models of population history, we find means and covariances based on the model and solve a quasi-score estimating equation. Simulation s show that this approach works extremely well both for estimation of LD an d for fine mapping. We apply the DHS method to published data sets for cyst ic fibrosis and progressive myoclonus epilepsy.