Properties of Bias and Variance of Two Multiallelic Estimators of FST

This study compares theoretical and simulated properties of two estimators of fixation indices FST for multiallelic data from a single locus. The estimators are due to Weir and Cockerham (θWC) and to Robertson and Hill (θRH), respectively. Both estimators are linear combinations of biallelic estimators which differ in the way frequent and rare alleles are weighted. Consequently, their sampling properties differ as far as bias and variance are concerned. In the infinite island model at migration–drift equilibrium, in the case of one multiallelic locus, we analytically approximate the bias of the two estimators and show that θWC is nearly unbiased, whereas θRH is negatively biased. Hence, we propose a correction of bias of the latter. Moreover, we reexamine the properties of variance of the initial estimators: due to their construction, their variances are minimal, each over different parameter ranges, θRH performing better for low differentiation and θWC for high differentiation. These theoretical properties are confirmed by simulations, which show that our correction of bias of θRH performs well and does not affect its property of minimal variance for low differentiation. Hence, we advocate the use of θWC for high values of differentiation, and the use of θRH, with our correction of bias, for low or moderate differentiation