Empirical Bayes inference of pairwise FsT and its distribution in the genome

Populations often have very complex hierarchical structure. Therefore, it is crucial in genetic monitoring and conservation biology to have a reliable estimate of the pattern of population subdivision. F-ST's for pairs of sampled localities or subpopulations are crucial statistics for the exploratory analysis of population structures, such as cluster analysis and multidimensional scaling. However, the estimation of F-ST is not precise enough to reliably estimate the population structure and the extent of heterogeneity. This article proposes an empirical Bayes procedure to estimate locus-specific pairwise F-ST's. The posterior mean of the pair-wise F-ST can be interpreted as a shrinkage estimator, which reduces the variance of conventional estimators largely at the expense of a small bias. The global F-ST of a population generally varies among loci in the genome. Our maximum-likelihood estimates of global F-ST's can be used as sufficient statistics to estimate the distribution of F-ST in the genome. We demonstrate the efficacy and robustness of our model by simulation and by an analysis of the microsatellite allele frequencies of the Pacific herring. The heterogeneity of the global FST in the genome is discussed on the basis of the estimated distribution of the global F-ST for the herring and examples of human single nucleotide polymorphisms (SNPs).