Sampling properties of the heterozygote-excess estimator of the effective number of breeders

Abstract

The effective number of breeders (N _b) for a cohort of progeny can be estimated from an excess of heterozygotes that arises in progeny produced by finite numbers of parents. In principle, N _b is a simple function of the standardized deviation (D) of the proportion of heterozygous progeny from its expectation under random mating. We explored the sampling properties of this D-estimator of N _b through computer simulation. The accuracy of the D-estimator is remarkably robust to variation in numbers of alleles and loci and the presence of rare alleles, though precision can be low if, relative to a given N _b, the sample of progeny or the cumulative number of independent alleles (n _ci) sampled is too small. For N _b up to 30 parents, acceptable accuracy is achieved with sample sizes of 200 or more progeny and 80 or more independent alleles; for N _b of 50–100, a sample of 500–1,000 progeny and 450–900 independent alleles are required for similar accuracy and precision. Though the estimator is most applicable for the situation of random union of gametes (as may occur in some marine invertebrates or fish, for example), it works for other mating systems (monogamous or polygamous pairings, polygyny), when the effective number of breeders is small (N _b ≤ 20). Simulations reveal small overestimation biases with smaller sample sizes, rare alleles, or highly polymorphic loci (≥10 alleles). Despite this bias, multiallelic loci are preferable to many loci with few alleles, which have larger sampling errors.