A theoretical framework linking the birth-death and protracted birth-death models, with implications for the phylogenetic analysis of diversification

Abstract

Standard birth-death processes used in macroevolutionary studies assume instantaneous speciation, an unrealistic premise that limits the interpretation of speciation and extinction rates. The protracted birth-death (PBD) model instead assumes that speciation involves two steps: initiation and completion. In order to understand their respective influence on macroevolutionary speciation rates, we compute a standard time-varying birth-death scenario that is "equivalent" to the PBD model in terms of speciation and extinction probabilities. First, we find a sharp decline in the equivalent birth rate near the present, indicating that rates estimated at the tips of phylogenies may not accurately reflect the underlying speciation process. Second, the completion rate controls the timing of the decay rather than the asymptotic equivalent rates. The equivalent birth rate in the past scales with the speciation initiation rate, with a scaling factor depending mostly on the population extinction rate. Our results suggest that the rates of population formation and extinction may often play a larger role than the speed of accumulation of reproductive isolation in modulating speciation rates. Our study establishes a theoretical framework for understanding how microevolutionary processes combine to explain the diversification of species on macroevolutionary time scales.