Evolution of Fast and Slow Life Histories in Resource-Constrained Populations with Mass-Mortality Events

Abstract

We study the evolution of the speed of life history in populations competing for a single growth-limiting resource subject to demographic stochasticity and mass mortality events. We focus on a quasi-neutral regime in which competing types have equal resource-use efficiency but differ in life-history speed. In the large-carrying-capacity scaling limit, we reduce the model to a one-dimensional jump-diffusion supported on the manifold of ecological equilibria. The drift and diffusion components capture the joint effects of demographic stochasticity and density regulation, while the jump component is driven by the catastrophic mortality events. Using this limiting process, we derive a first-order approximation for the fixation probability of an invading type that differs slightly in life history speed from the resident population. Calculations show that small demographic events tend to favor slower life histories, whereas catastrophic mortality events create transient periods of resource abundance that benefit faster types. The interaction of these two evolutionary forces allows for the existence of a nontrivial evolutionarily attractive life-history speed, which is an increasing function of the frequency and intensity of the catastrophic mortality events. These results provide a rigorous mathematical framework for some classical r/K-selection arguments, and furthermore demonstrate how mass mortality events can maintain selection for faster life histories even in resource-constrained populations.