Citation

Vitale C, Kisdi E. Bull. Math. Biol. 2018; ePub(ePub): ePub.

Affiliation

Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland. eva.kisdi@helsinki.fi.

Copyright

(Copyright © 2018, Holtzbrinck Springer Nature Publishing Group)

DOI

10.1007/s11538-018-0472-9

PMID

30120688

Abstract

Under the threat of predation, a species of prey can evolve to its own extinction. Matsuda and Abrams (Theor Popul Biol 45:76-91, 1994a) found the earliest example of evolutionary suicide by demonstrating that the foraging effort of prey can evolve until its population dynamics cross a fold bifurcation, whereupon the prey crashes to extinction. We extend this model in three directions. First, we use critical function analysis to show that extinction cannot happen via increasing foraging effort. Second, we extend the model to non-equilibrium systems and demonstrate evolutionary suicide at a fold bifurcation of limit cycles. Third, we relax a crucial assumption of the original model. To find evolutionary suicide, Matsuda and Abrams assumed a generalist predator, whose population size is fixed independently of the focal prey. We embed the original model into a three-species community of the focal prey, the predator and an alternative prey that can support the predator also alone, and investigate the effect of increasingly strong coupling between the focal prey and the predator's population dynamics. Our three-species model exhibits (1) evolutionary suicide via a subcritical Hopf bifurcation and (2) indirect evolutionary suicide, where the evolution of the focal prey first makes the community open to the invasion of the alternative prey, which in turn makes evolutionary suicide of the focal prey possible. These new phenomena highlight the importance of studying evolution in a broader community context.

Language: en

Keywords

Adaptive dynamics; Evolutionary suicide; Fold bifurcation of limit cycles; Foraging effort; Predator–prey model; Saddle-node bifurcation; Subcritical Hopf bifurcation