Continuous traits and speciation rates: Alternatives to state-dependent diversification models

1. Many quantitative traits, for example body size, have been hypothesized to influence the diversification dynamics of lineages over macroevolutionary time-scales. The Quantitative State Speciation-Extinction (QuaSSE) model and related methods provide an elegant framework for jointly modelling the relationship between change in continuous traits and diversification. However, model misspecification and phylogenetic pseudoreplication can result in elevated false discovery rates in this and other state-dependent speciation-extinction models. 2. Here, we evaluate alternative trait-dependent diversification methods that do not formally model the relationship between traits and diversification, but instead test for correlations between summary statistics of phylogenetic branching patterns and trait variation at the tips of a phylogenetic tree (hereafter tip-rate correlations or TRCs). We compare alternative branching pattern statistics and significance tests, and we evaluate their performance relative to QuaSSE under a range of evolutionary scenarios. 3. We found that a simple statistic derived from branch lengths (inverse equal splits) can detect trait-associated rate variation, and that a simulation-based method performs better than phylogenetic generalized least squares for testing the significance of trait-rate correlations. This test (ES-sim) had better power to detect trait-dependent diversification than other TRCs. By testing the approach across a diverse set of simulation scenarios, we found that ES-sim is similar to QuaSSE in statistical power. However, the approach rarely led to false inferences of trait-dependent diversification, even under conditions that are problematic for formal state-dependent models. We illustrate the application of ES-sim to real data by reassessing the relationship between dispersal ability and diversification in Furnariid birds. 4. We conclude that simple, semi-parametric tests like ES-sim represent a promising approach for trait-dependent diversification analyses in groups with heterogeneous diversification histories and provide a useful alternative or complement to formal state-dependent speciation-extinction models.