, Jost's D, and F_ST are similarly constrained by allele frequencies: A mathematical, simulation, and empirical study

Statistics $$ and Jost's D have been proposed for replacing F_ST as measures of genetic differentiation. A principal argument in favour of these statistics is the independence of their maximal values with respect to the subpopulation heterozygosity H_S , a property not shared by F_ST . Nevertheless, it has been unclear if these alternative differentiation measures are constrained by other aspects of the allele frequencies. Here, for biallelic markers, we study the mathematical properties of the maximal values of $$ and D, comparing them to those of F_ST . We show that $$ and D exhibit the same peculiar frequency-dependence phenomena as F_ST , including a maximal value as a function of the frequency of the most frequent allele that lies well below one. Although the functions describing $$ , D, and F_ST in terms of the frequency of the most frequent allele are different, the allele frequencies that maximize them are identical. Moreover, we show using coalescent simulations that when taking into account the specific maximal values of the three statistics, their behaviours become similar across a large range of migration rates. We use our results to explain two empirical patterns: the similar values of the three statistics among North American wolves, and the low D values compared to $$ and F_ST in Atlantic salmon. The results suggest that the three statistics are often predictably similar, so that they can make quite similar contributions to data analysis. When they are not similar, the difference can be understood in relation to features of genetic diversity.