Properties of Weir and Cockerham’s estimators and associated bootstrap confidence intervals

Weir and Cockerham introduced single locus and multiloci F s t estimators for the parameter θ . These estimators are commonly used, but little beyond their bias and variance is known. In this work, we develop formulas that allow us to describe how the underlying value of θ and the genetic diversity of sampled loci affect the distributions of these estimators. We show that in certain settings, these estimators are close to normal, while in others they are far from normal. We use these results to analyze confidence interval construction for θ , showing that the percentile- t bootstrap works well while the BCa bootstrap works poorly. Our results are derived using a novel coalescent based method.