Evolutionary Suicide of Prey : Matsuda and Abrams' Model Revisited

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http://hdl.handle.net/10138/308749

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Vitale , C & Kisdi , E 2019 , ' Evolutionary Suicide of Prey : Matsuda and Abrams' Model Revisited ' , Bulletin of Mathematical Biology , vol. 81 , no. 11 , pp. 4778-4802 . https://doi.org/10.1007/s11538-018-0472-9

Title: Evolutionary Suicide of Prey : Matsuda and Abrams' Model Revisited
Author: Vitale, Caterina; Kisdi, Eva
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2019-11
Language: eng
Number of pages: 25
Belongs to series: Bulletin of Mathematical Biology
ISSN: 0092-8240
URI: http://hdl.handle.net/10138/308749
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.
Subject: 111 Mathematics
Adaptive dynamics
Evolutionary suicide
Fold bifurcation of limit cycles
Foraging effort
Predator-prey model
Saddle-node bifurcation
Subcritical Hopf bifurcation
RESIDENT-INVADER DYNAMICS
TRADE-OFF GEOMETRIES
SELF-EXTINCTION
FUNCTIONAL-RESPONSE
ADAPTIVE DYNAMICS
CONSTRUCTION
COEXISTENCE
DERIVATION
PREDATION
ATTRACTOR
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