Intraspecific variation stabilizes classic predator-prey dynamics

In 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][1],[2][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][3],[4][4], who was inspired by the work of his son-in-law, fish biologist Umberto D’Ancona [5][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][6]–[10][7]. 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][8],[12][9]. 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][10],[13][11]. 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. ### Competing Interest Statement The authors have declared no competing interest. [1]: #ref-1 [2]: #ref-2 [3]: #ref-3 [4]: #ref-4 [5]: #ref-5 [6]: #ref-6 [7]: #ref-10 [8]: #ref-11 [9]: #ref-12 [10]: #ref-8 [11]: #ref-13