Estimators for pairwise relatedness and individual inbreeding coefficients

TLDR

The estimators have lower small‑sample bias than MLE, make no distributional assumptions, and rely on population gene frequencies from a reference sample, with potential bias from small reference samples or genetic drift. The paper describes method‑of‑moments estimators for two‑gene relationship and inbreeding coefficients and four‑gene Cotterman coefficients. The estimators use co‑dominant markers, with an efficient MME that averages allele‑level estimates; weights are computed numerically unless coefficients are assumed zero, yielding simplified high‑efficiency estimators, and they rely on gene frequencies from a reference population. Compared with MLE, the estimators have lower small‑sample bias, no distributional assumptions, and simplified versions achieve high relative efficiency; although individual estimates have high variance, they are useful as covariates in population studies.

Abstract

Summary Method-of-moments estimators (MMEs) for the two-gene coefficients of relationship and inbreeding, and for thxe 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, simplifiedestimators are obtained whose relative efficiencies are quite high. Population gene frequency is assumed to be assayed ina 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.