A genealogical approach to quantifying lineage divergence

We introduce a statistic, the genealogical sorting index (gsi), for quantifying the degree of exclusive ancestry of labeled groups on a rooted genealogy and demonstrate its application. The statistic is simple, intuitive, and easily calculated. It has a normalized range to facilitate comparisons among different groups, trees, or studies and it provides information on individual groups rather than a composite measure for all groups. It naturally handles polytomies and accommodates measures of uncertainty in phylogenetic relationships. We use coalescent simulations to explore the behavior of the gsi across a range of divergence times, with the mean value increasing to 1, the maximum value when exclusivity within a group reached monophyly. Simulations also demonstrate that the power to reject the null hypothesis of mixed genealogical ancestry increased markedly as sample size increased, and that the gsi provides a statistically more powerful measure of divergence than F-ST. Applications to data from published studies demonstrated that the gsi provides a useful way to detect significant exclusivity even when groups are not monophyletic. Although we describe this statistic in the context of divergence, it is more broadly applicable to quantify and assess the significance of clustering of observations in labeled groups on any tree.