Linkage disequilibrium between loci with unknown phase.

Linkage disequilibrium is often measured by two statistics, D and r, which can be interpreted as the covariance and the correlation between loci and across gametes. When data consist of diploid genotypes, however, gametes cannot be identified. A variety of iterative statistical methods are used in such cases, all of which assume random mating. Previous work has shown that D and r can be expressed as covariances and correlations across diploid genotypes, provided that mating is random. We show here that this result also holds approximately when mating is nonrandom. This provides a means of estimating these parameters without iteration and without assuming random mating. This estimator is nearly as accurate as the widely used EM estimator and is many times faster.