MODELING SAMPLING-RATE DISTRIBUTIONS OVER TIME, SPACE AND TAXA WITH OCCURRENCE DATA AND ITS EFFECT ON MACROEVOLUTIONARY INFERENCE

Observed patterns in the fossil record reflect not just macroevolutionary dynamics, but sampling rates. Sampling rates themselves vary not simply over time or among major taxonomic groups, but within time intervals over geography and environment, and among species within clades. Large databases of presences of taxa in fossil-bearing collections allow us to quantify variation in per-collection sampling rates among species within a clade not just for different time/stratigraphic intervals, but also for different geographic or ecologic units within time/stratigraphic intervals. Given occurrence data for Meso-Cenozoic mammals drawn from the Paleobiology Database and the New and Old Worlds fossil mammal database, we find that lognormal models do excellent jobs of summarizing sampling-rate variation among taxa to assess general models of per-locality sampling rate distributions given occurrences among appropriate fossiliferous localities. However, these distributions vary substantially over both time and among continents.

As an example of the utility of these rates, we assess the most likely divergence times for basal (Eocene-Oligocene) carnivoramorphan mammals from North America and Eurasia using both stratigraphic and morphological data. Divergence times on phylogeny represent a particularly useful example. The divergence times of different phylogenies with the same cladistic topology can generate different inferences about rates of change or speciation models; using sampling-rate distributions allows us to weight different rates. Moreover, because we can infer the likelihood of ancestral distributions, we can use different sampling rate distributions for different geographic areas without assuming that the geographic distribution of an unsampled ancestor is “known.” We illustrate how taking full(er) advantage of the distribution of fossil occurrences implies divergence times typically intermediate between those implied by morphology alone (and ignoring occurrence data) and those implied by single-rate sampling models.