How reliably can we infer diversity‐dependent diversification from phylogenies?

Summary Slowdowns in lineage accumulation in phylogenies suggest that speciation rates decline as diversity increases. Likelihood methods have been developed to detect such diversity dependence. However, a thorough test of whether such approaches correctly infer diversity dependence is lacking. Here, we simulate phylogenetic branching under linear negative diversity‐dependent and diversity‐independent models and estimate from the simulated phylogenies the maximum‐likelihood parameters for three different conditionings – on survival of the birth–death process given the crown age, on tree size ( N ) and on tree size given the crown age. We report the accuracy of recovering the simulation parameters and the reliability of the model selection based on the χ 2 likelihood ratio test. Parameter estimate accuracy: Conditioning on survival given the crown age yields a severe bias of the carrying capacity K towards N and an upward bias of the speciation rate, particularly in clades where diversity‐dependent feedbacks are still weak ( N « K ). Conditioning on N yields an overestimate of K and an underestimate of speciation rate, particularly when saturation has been reached. Dual conditioning yields relatively unbiased parameter estimates on average, but the deviation from the true value for any single estimate may be large. Model selection reliability: The frequency of incorrectly rejecting a diversity‐independent model when the simulation was diversity‐independent (type I error) differs substantially from the significance level α used in the likelihood ratio test, rendering the likelihood ratio test inappropriate. The frequency of correctly rejecting the diversity‐independent model when the simulation was diversity‐dependent (power) is larger when the clade is closer to equilibrium and for conditioning on crown age. We conclude that conditioning on crown age has the best statistical properties overall, but caution that parameter estimates may be biased. To assess parameter uncertainty in future studies of diversity dependence on real data, we recommend parametric bootstrapping, examination of the likelihood surface and comparison of estimates across the types of conditioning. To assess model selection reliability, we discourage the use of the χ 2 likelihood ratio test or AIC (which are equivalent in this case), but recommend a likelihood ratio test based on parametric bootstrap. We illustrate this method for the diversification of Dendroica warblers.