The empirical Bayes estimators of fine-scale population structure in high gene flow species

An empirical Bayes (EB) pairwise F_ST estimator was previously introduced and evaluated for its performance by numerical simulation. In this study, we conducted coalescent simulations and generated genetic population structure mechanistically, and compared the performance of the EBF_ST with Nei's G_ST , Nei and Chesser's bias-corrected G_ST (G_{ST_NC} ), Weir and Cockerham's θ (θ_WC ) and θ with finite sample correction (θ_{WC_F} ). We also introduced EB estimators for Hedrick' G'_ST and Jost' D. We applied these estimators to publicly available SNP genotypes of Atlantic herring. We also examined the power to detect the environmental factors causing the population structure. Our coalescent simulations revealed that the finite sample correction of θ_WC is necessary to assess population structure using pairwise F_ST values. For microsatellite markers, EBF_ST performed the best among the present estimators regarding both bias and precision under high gene flow scenarios (FST≤0.032). For 300 SNPs, EBF_ST had the highest precision in all cases, but the bias was negative and greater than those for G_{ST_NC} and θ_{WC_F} in all cases. G_{ST_NC} and θ_{WC_F} performed very similarly at all levels of F_ST . As the number of loci increased up to 10 000, the precision of G_{ST_NC} and θ_{WC_F} became slightly better than for EBF_ST for cases with FST≥0.004, even though the size of the bias remained constant. The EB estimators described the fine-scale population structure of the herring and revealed that ~56% of the genetic differentiation was caused by sea surface temperature and salinity. The R package finepop for implementing all estimators used here is available on CRAN.