Integrating fossils samples with heterogeneous diversification rates: a combined Multi-Type Fossilized Birth-Death model

Birth-death models are widely used to describe the diversification process which leads to the observed species and phylogenies. When integrated into Bayesian phylogenetic inference, birth-death models allow the joint inference of the phylogeny and the diversification parameters from molecular information. Two major classes of extensions of the birth-death process are considered in this article. The first extends the phylogenetic tree to include fossil samples alongside extant species, allowing the inference to integrate information about the past diversity. The second extension models diversification rates which can vary between lineages, and is thus able to infer patterns of variation in speciation or extinction rates. In this work, we combine these two types of extension into a multi-type fossilized birth-death (MTFBD) process, which can perform the joint inference of a phylogeny including extinct and extant samples, and lineage-specific diversification and fossilization rates in a Bayesian framework. The MTFBD model is implemented as part of the phylogenetic inference framework BEAST2. Using simulated and empirical datasets, we demonstrate the performance and accuracy of the new model compared to a model with rate heterogeneity but using only extant samples, and compared to a model without rate variation including fossils. We demonstrate that including fossils improves the accuracy of the phylogeny and diversification rates, especially extinction rates, provided that the inference includes morphological information to accurately place the fossil samples. When this information is not available however, MTFBD estimates are strongly driven by the priors and are thus no better or even worse than estimates obtained only with extant samples. With informative fossil characters, the MTFBD model provides accurate phylogenies, and precisely characterizes how speciation, extinction and fossilization rates vary as diversification proceeds.