Intraspecific variation stabilizes classic predator-prey dynamics

Abstract

ABSTRACTIn 1920, Alfred J. Lotka found that, to his “considerable surprise”, the dynamics of a simple predatorprey model he had devised led “to undamped, and hence indefinitely continued, oscillations” 1,2— which he thought epitomized the “rhythm of Nature” dear to the Victorians. In 1926, the same model was proposed independently by mathematician Vito Volterra 3,4, who was inspired by the work of his son-in-law, fish biologist Umberto D’Ancona 5. For over a century, the equations that now bear their names have served as a template for the development of sophisticated models for population dynamics 6–10. Coexistence in this classic predator-prey model is fragile—stochasticity or temporal variability in parameter values result in extinctions. The dynamics can be stabilized by intraspecific competition or other forms of self-regulation, but the prevalence of these processes in large food webs has been questioned 11,12. Here we show that when we consider populations characterized by intraspecific variability, dynamics are stable—despite the absence of any direct self-regulation. Our results can be generalized further, defining a new class of consumer-resource models 8,13. By accounting for intraspecific variation, which is manifest in all biological populations, we obtain dynamics that differ qualitatively and quantitatively from those found for homogeneous populations—challenging a central assumption of many ecological models.