Estimating clade-specific diversification rates and palaeodiversity dynamics from reconstructed phylogenies

One of the central goals of macroevolution is to understand palaeodiversity dynamics through time and space, and its potential drivers. Estimating palaeodiversity dynamics has been historically addressed with the fossil record because it directly reflects the past variations of biodiversity. Unfortunately, some groups or regions lack a good fossil record, and dated phylogenies can be useful to estimate deep-time diversification dynamics. Recent methodological developments have unlocked the possibility to investigate palaeodiversity dynamics with dated phylogenies by using birth-death models with non-homogeneous rates through time and across clades. One of them, which models rate heterogeneity as a local clock, seems particularly promising to detect clades whose diversity has declined through time. However, empirical applications of the method have been hampered by its lack of automation. Here we propose an automation with additional features accounting for recent developments and we implement it in the R package RPANDA. We also test the approach with simulations focusing on its ability to detect shifts of diversification and to infer palaeodiversity dynamics. Finally, we illustrate the automation by investigating the palaeodiversity dynamics of Cetacea, Vangidae, Parnassiinae, and Cycadales. Simulations showed that we accurately detected shifts of diversification although false positive errors are higher for complex models. The median global error of palaeodiversity dynamics estimated with the automated model is low showing that the method is able to capture diversity declines. We detected shifts of diversification for three of the four empirical examples considered (Cetacea, Parnassiinae and Cycadales). These heterogeneities of diversification rates unveil a waxing-and-waning pattern due to a phase of negative net diversification rate embedded in the trees after isolating recent radiations. Our work allows to easily apply non-homogeneous models of diversification in which rates can vary through time and across clades to reconstruct palaeodiversity dynamics. By doing so, we detected palaeodiversity declines among three of the four groups tested, highlighting that such periods of negative net diversification might be common. We discuss the extent to which this approach might provide reliable estimates of extinction rates and we provide guidelines for users.