A quantitative framework to infer the effect of traits, diversity and environment on dispersal and extinction rates from fossils

Speciation, dispersal and extinction govern the spatial and temporal dynamics of biodiversity. The fossil record offers the opportunity to directly estimate range expansion and contraction via dispersal and extinction, respectively. However, due to the incomplete occurrence record, determining the dynamics of these processes and the biotic and abiotic factors influencing them remains challenging. The dispersal–extinction–sampling (DES) model infers dispersal and extinction rates from present and past geographical ranges of taxa while accounting for the incompleteness of the fossil record via jointly estimated sampling rates. Here, we expand the DES framework to a new suite of models that (a) incorporate heterogeneity in fossil sampling across taxa, (b) reconstruct diversity trajectories through time and across regions, and (c) link rates of range evolution with biotic and abiotic covariates. These models integrate the effects of competitive interaction, traits and environmental change on dispersal and extinction while controlling for phylogenetic effects through higher level taxonomy. We validate our framework through simulations and find that likelihood‐based model testing has the power to discriminate among models with or without biotic and abiotic effects on dispersal and extinction. Among the tested models, we found that trait‐dependent models yielded the most accurate parameter estimates. We then assess the factors influencing geographical range evolution for Eurasian and North American terrestrial carnivores. We identify substantial variation in the fossil sampling rates of carnivore genera and find that global cooling increased their extinction risk while their dispersal rate varied among families and increased with larger body size. The expanded suite of DES models for fossil biogeography is a powerful tool to test hypotheses about the factors influencing geographical range evolution using fossil data.