Algebraic equivalence sampling properties of F-statistics in the genomic era

Abstract

Abstract This note evaluates variance- and heterozygosity-based genomic estimates of F-statistics through algebraic derivation and simulation. Genetic variance was partitioned among populations, among individuals within populations, and within individuals. The method-of-moments estimator of FIS was evaluated in 100 Monte Carlo replicates of 1,000 independent SNPs incorporating population structure, sample-size imbalance, and missing genotypes. In the principal scenario (FIS = 0.25; FST = 0.38), ANOVA, Weir-Cockerham, allele-sharing, and corrected Nei estimates of FIS were 0.2498, 0.2498, 0.2497, and 0.2502, respectively, whereas the pooled statistic was 0.4844. Across the simulations, ANOVA and corrected Nei FIS remained near 0.25 as FST increased from 0 to 0.50, while the pooled measure increased from 0.2481 to 0.5667. The mean within-population FIS was not much affected by missing data (up to 30%) and sample-size imbalances. The formulations therefore agree when they target the same hierarchical parameter and reference set. .