Estimating Divergence Times and Diversification Rates with the Unresolved Fossilized Birth-Death Process

Tip-dating using Fossilized Birth-Death (FBD) models offers a favorable alternative to conventional node-dating analyses of the evolutionary timescale, bypassing various conceptual and technical difficulties. However, despite their increasing popularity in phylogenetic studies, their use has remained rather limited in taxonomic scope because of the difficulty in collecting morphological data, which is often required for tip-dating analyses, and computational intractability when a large number of fossils are present. Recent studies, however, suggest that FBD models can also be used in a principled way as priors for molecular clock analyses, even in the absence of morphological data, relying only on temporal information and given clade assignments. Heath et al. (2014) introduced an "unresolved" FBD model in which uncertainty in fossil placements is analytically integrated out when morphological data are unavailable, providing a potential solution to this problem. Here, we show that the topological enumeration scheme used by Heath et al. (2014) to marginalize over unresolved fossil attachments overcounts configurations in which multiple fossil taxa can be resolved as a clade, and we provide a correction to this factor, yielding a valid marginalized unresolved likelihood. We apply our implementation to empirical datasets of Cetacea, Emydidae, and Palaeodictyopterida, and show that our method converges and yields reasonable estimates within a reasonable amount of time, even when hundreds of fossils are present.