Simple a posteriori insertion of fossil tips in molecular phylogenies can improve inferences of continuous trait evolution

Integrating neontological and paleontological information improves inferences about the tempo and mode of phenotypic evolution over long timescales. However, outside a few exemplar clades, morphological matrices establishing formal phylogenetic placements of fossils within molecular phylogenies are often lacking, limiting the inclusion of fossil data in macroevolutionary inferences. Informal fossil placements are commonly established through morphological assessment (e.g., as is often the case for node-age calibrations) but determining branch length durations is less straightforward. Using simulations, we compared four contrasting methods of a posteriori fossil insertion and assess their impacts on estimating the tempo and mode of continuous trait evolution. We find that arbitrarily assigning branch lengths to fossil taxa or analytically estimating them using continuous trait data had negligible biases on phenotypic inferences relative to true branch lengths. However, use of minimum fossil branch lengths biased model selection toward an Ornstein-Uhlenbeck process and inflated rate estimates. We find that the inclusion of fossil taxa using our preferred approaches improves support for an early burst when it is the generating model. Applying these methods to a comparative dataset of carangarian fishes (flatfishes, jacks, barracudas, and billfishes) reveals high rates of phenotypic evolution early in the clade's history, a signal forecasted by the fossil record but not shown in extant-only analyses. We conclude that a posteriori insertion of fossils, even with designated rather than inferred branch lengths, can strengthen phenotypic inferences relative to analyses including only living taxa.