A fossilized birth-death model for fossil records lacking sampled ancestors

Fossilized birth-death (FBD) models provide a powerful framework for estimating diversification from phylogenies that include fossil taxa. However, the original formulation makes a key assumption that sampled ancestors (k-type fossils) should be commonly observed. Beaulieu & OMeara (2023) showed that this assumption is often violated in empirical datasets, where fossils are represented mostly or entirely as extinct terminal taxa (m-type fossils), which can lead to biased parameter estimates. Here, we derive the fossilized birth-death of terminal fossils (FBDT) model, an extension of the FBD that accommodates incomplete fossil samples in which only terminal fossil occurrences are observed. We implement the model within the state-dependent speciation and extinction (SSE) framework and evaluate its performance using simulations spanning homogeneous and heterogeneous diversification scenarios. Across a wide range of fossil sampling rates, the FBDT model recovered diversification parameters that closely matched those obtained from complete fossil samples while avoiding the systematic biases that arise when sampled ancestors are unobserved. These results demonstrate that modifying the likelihood to reflect how fossil datasets are assembled provides a simple and effective extension of the FBD framework for many empirical applications.