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Tens of thousands of phylogenetic trees, describing the evolutionary relationships between hundreds of thousands of taxa, are readily obtainable from various databases. From such trees, inferences can be made about the underlying macroevolutionary processes, yet remarkably these processes are still poorly understood. Simple and widely used evolutionary null models are problematic: Empirical trees show very different imbalance between the sizes of the daughter clades of ancestral taxa compared to what models predict. Obtaining a simple evolutionary model that is both biologically plausible and produces the imbalance seen in empirical trees is a challenging problem, to which none of the existing models provide a satisfying answer. Here we propose a simple, biologically plausible macroevolutionary model in which the rate of speciation decreases with species age, whereas extinction rates can vary quite generally. We show that this model provides a remarkable fit to the thousands of trees stored in the online database TreeBase. The biological motivation for the identified age-dependent speciation process may be that recently evolved taxa often colonize new regions or niches and may initially experience little competition. These new taxa are thus more likely to give rise to further new taxa than a taxon that has remained largely unchanged and is, therefore, well adapted to its niche. We show that age-dependent speciation may also be the result of different within-species populations following the same laws of lineage splitting to produce new species. As the fit of our model to the tree database shows, this simple biological motivation provides an explanation for a long standing problem in macroevolution. [ABSTRACT FROM AUTHOR]

Determining whether speciation and extinction rates depend on the state of a particular character has been of long-standing interest to evolutionary biologists. To assess the effect of a character on diversification rates using likelihood methods requires that we be able to calculate the probability that a group of extant species would have evolved as observed, given a particular model of the character's effect. Here we describe how to calculate this probability for a phylogenetic tree and a two-state (binary) character under a simple model of evolution (the "BiSSE" model, binary-state speciation and extinction). The model involves six parameters, specifying two speciation rates (rate when the lineage is in state 0; rate when in state 1), two extinction rates (when in state 0; when in state 1), and two rates of character state change (from 0 to 1, and from 1 to 0). Using these probability calculations, we can do maximum likelihood inference to estimate the model's parameters and perform hypothesis tests (e.g., is the rate of speciation elevated for one character state over the other?). We demonstrate the application of the method using simulated data with known parameter values. [ABSTRACT FROM AUTHOR]