In this chapter I discussed models that go beyond constant rate birth-death models. We can fit models where speciation rate varies across clades or through time (or both). In some cases, very different models predict the same pattern in phylogenetic trees, warranting some caution until direct fossil data can be incorporated. I also described a model of protracted speciation, where speciation takes some time to complete. This latter model is potentially better connected to microevolutionary models of speciation, and could point towards fruitful directions for the field. We know that simple birth-death models do not capture the richness of speciation and extinction across the tree of life, so these models that range beyond birth and death are critical to the growth of comparative methods.
1: Even though this approach requires topology, Morlon et al. (2011) show that their likelihood is equivalent to other approaches, such as Nee and Maddison, that rely only on branching times and ignore topology completely. This is because trees with the same set of branching times but different topologies have identical likelihoods under this model.
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