Bootstrap variance of diversity and differentiation estimators in a subdivided population

We have recently proposed new estimators of the parameters of genetic diversity and differentiation and of their variances for a haploid locus in a population subdivided into a large number of subpopulations, with a two-stage sampling of populations and individuals. Here they are compared with bootstrap estimators. Several resampling methods are evaluated: sampling of populations only, individuals within populations only, or both. Theoretical results and a numerical example show that the most appropriate bootstrap variance estimators are obtained by resampling the populations alone and not both populations and individuals. However, some bias is apparent in the bootstrap methods, and the direct estimators proposed previously should therefore be preferred.