The impact of gene-tree/species-tree discordance on diversification-rate estimation

Molecular phylogenies are often used to test hypotheses about the tempo and mode of speciation and extinction. One commonly used statistic is Pybus and Harvey's γ, which measures the density of ordered internode distances on an ultrametric tree to infer earlier (negative γ) or later (positive γ) bursts of diversification. However, coalescent theory predicts that γ might be biased toward negative values (inferring early bursts of diversification) when using gene trees rather than species trees. Gene divergences predate species divergences, increasingly so at higher effective population sizes (N(e)), and proportionally more so toward the tips of the tree. Thus, gene trees will have a higher density of older nodes in many cases (particularly at higher N(e)), due to the disproportionate lengthening of terminal branches. This will yield an artifactual signature of early bursts of diversification when estimating γ from gene trees. We simulate gene trees within species trees under both Yule (pure-birth) and birth-death processes, and demonstrate support for these predictions. However, for most realistic estimates of θ in natural populations, gene trees provide relatively good estimates of γ, despite the disproportionate overestimation of younger node ages. This is corroborated with an empirical dataset of North American fence lizards (Sceloporus).