Testing for temporal variation in diversification rates when sampling is incomplete and nonrandom

Abstract.—A common pattern found in phylogeny-based empirical studies of diversification is a decrease in the rate of lineage accumulation toward the present. This early-burst pattern of cladogenesis is often interpreted as a signal of adap-tive radiation or density-dependent processes of diversification. However, incomplete taxonomic sampling is also known to artifactually produce patterns of rapid initial diversification. The Monte Carlo constant rates (MCCR) test, based upon Pybus and Harvey’s gamma (γ)-statistic, is commonly used to accommodate incomplete sampling, but this test assumes that missing taxa have been randomly pruned from the phylogeny. Here we use simulations to show that pref-erentially sampling disparate lineages within a clade can produce severely inflated type-I error rates of the MCCR test, especially when taxon sampling drops below 75%. We first propose two corrections for the standard MCCR test, the pro-portionally deeper splits that assumes missing taxa are more likely to be recently diverged, and the deepest splits only MCCR that assumes that all missing taxa are the youngest lineages in the clade, and assess their statistical properties. W