PALEOBIOLOGICAL DIVERSIFICATION METRICS AND BIRTH-DEATH MODELS AS CONTROLS FOR THE EFFECTS OF RATE HETEROGENEITIES ON TIP-DATING

Tip-dating methods infer branch durations assuming general rates of morphological character change. Although numerous studies show correlations between branch duration and morphological change, one concern is that a variety of relatively rare events (e.g., as correlated character change, shifts in modularity, or heterochronic change) can induce numerous morphological changes over short intervals of time. A possible antidote to this problem is putting prior probabilities on branch durations. These prior probabilities are specified using birth-death or coalescent models, and long durations considered likely given numerous changes might be improbable if speciation and/or sampling is high. However, these approaches have not yet taken advantage of paleobiological approaches for deriving estimates of origination (birth) and extinction (death) rates. Unfortunately, paleobiological estimates of rates are inexact, particularly at the levels at which most paleobiological phylogenies are estimated (e.g., species within families). One solution is to borrow from the phylogeneticists’ tradition of using rate distributions rather than particular rates. For example, when analyzing species within a given family, one can estimate the distribution of origination and extinction rates of species among families within a larger clade, and then use those to inform the parameters of the birth-death tree prior. We apply this approach here to Ordovician gastropod clades. Based on species-level occurrence data divided into substages, we use gamma distributions to model per-substage “kill curves” and “birth curves” for species within families. These offer good predictions of diversification rate variation with only two parameters. Combining these with lognormal distributions for sampling rates can constrain plausible divergence times without assuming specific rates. This in turn allows tip‑dating to be more tolerant of “hiccups” in general rates and also permits more powerful tests of phylogenetically or temporally localized shifts in overall rates of change.