Estimators for pairwise relatedness and individual inbreeding coefficients

Abstract

Method-of-moments estimators (MMEs) for the two-gene coefficients of relationship and inbreeding, and for the four-gene Cotterman coefficients, are described. These estimators, which use co-dominant genetic markers, are most appropriate for estimating pairwise relatedness or individual inbreeding coefficients, as opposed to their mean values in a group. This is because, compared to the maximum likelihood estimate (MLE), they show reduced small-sample bias and lack distributional assumptions. The 'efficient' MME is an optimally weighted average of estimates given by each allele at each locus. Generally, weights must be computed numerically, but if true coefficients are assumed zero, simplified estimators are obtained whose relative efficiencies are quite high. Population gene frequency is assumed to be assayed in a larger,'reference population' sample, and the biases introduced by small reference samples and/or genetic drift of the reference population are discussed. Individual-level estimates of relatedness or inbreeding, while displaying high variance, are useful in several applications as a covariate in population studies.