A Comparison of Entropic Diversity and Variance in the Study of Population Structure

AMOVA is a widely used approach that focuses on variance within and among strata to study the hierarchical genetic structure of populations. The recently developed Shannon Informational Diversity Translation Analysis (SIDTA) instead tackles exploration of hierarchical genetic structure using entropic allelic diversity. A mix of artificial and natural population data sets (including allopolyploids) is used to compare the performance of SIDTA (a 'q = 1' diversity measure) vs. AMOVA (a 'q = 2' measure) under different conditions. An additive allelic differentiation index based on entropic allelic diversity measuring the mean difference among populations (Ω_AP) was developed to facilitate the comparison of SIDTA with AMOVA. These analyses show that the genetic population structure seen by AMOVA is notably different in many ways from that provided by SIDTA, and the extent of this difference is greatly affected by the stability of the markers employed. Negative among group values are lacking with SIDTA but occur with AMOVA, especially with allopolyploids. To provide more focus on measuring allelic differentiation among populations, additional measures were also tested including Bray-Curtis Genetic Differentiation (BCGD) and several expected heterozygosity-based indices (e.g., G_ST, G″_ST, Jost's D, and D_EST). Corrections, such as almost unbiased estimators, that were designed to work with heterozygosity-based fixation indices (e.g., F_ST, G_ST) are problematic when applied to differentiation indices (eg., D_EST, G″_ST, G'_STH).