Comparative phylogeographic summary statistics for testing simultaneous vicariance

Testing for simultaneous vicariance across comparative phylogeographic data sets is a notoriously difficult problem hindered by mutational variance, the coalescent variance, and variability across pairs of sister taxa in parameters that affect genetic divergence. We simulate vicariance to characterize the behaviour of several commonly used summary statistics across a range of divergence times, and to characterize this behaviour in comparative phylogeographic datasets having multiple taxon-pairs. We found Tajima's D to be relatively uncorrelated with other summary statistics across divergence times, and using simple hypothesis testing of simultaneous vicariance given variable population sizes, we counter-intuitively found that the variance across taxon pairs in Nei and Li's net nucleotide divergence (π_net), a common measure of population divergence, is often inferior to using the variance in Tajima's D across taxon pairs as a test statistic to distinguish ancient simultaneous vicariance from variable vicariance histories. The opposite and more intuitive pattern is found for testing more recent simultaneous vicariance, and overall we found that depending on the timing of vicariance, one of these two test statistics can achieve high statistical power for rejecting simultaneous vicariance, given a reasonable number of intron loci (> 5 loci, 400 bp) and a range of conditions. These results suggest that components of these two composite summary statistics should be used in future simulation-based methods which can simultaneously use a pool of summary statistics to test comparative the phylogeographic hypotheses we consider here.