Survival behavior in the cyclic Lotka-Volterra model with a randomly switching reaction rate

Robert West, Mauro Mobilia, and Alastair M. Rucklidge
Phys. Rev. E 97, 022406 – Published 16 February 2018

Abstract

We study the influence of a randomly switching reproduction-predation rate on the survival behavior of the nonspatial cyclic Lotka-Volterra model, also known as the zero-sum rock-paper-scissors game, used to metaphorically describe the cyclic competition between three species. In large and finite populations, demographic fluctuations (internal noise) drive two species to extinction in a finite time, while the species with the smallest reproduction-predation rate is the most likely to be the surviving one (law of the weakest). Here we model environmental (external) noise by assuming that the reproduction-predation rate of the strongest species (the fastest to reproduce and predate) in a given static environment randomly switches between two values corresponding to more and less favorable external conditions. We study the joint effect of environmental and demographic noise on the species survival probabilities and on the mean extinction time. In particular, we investigate whether the survival probabilities follow the law of the weakest and analyze their dependence on the external noise intensity and switching rate. Remarkably, when, on average, there is a finite number of switches prior to extinction, the survival probability of the predator of the species whose reaction rate switches typically varies nonmonotonically with the external noise intensity (with optimal survival about a critical noise strength). We also outline the relationship with the case where all reaction rates switch on markedly different time scales.

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  • Received 23 November 2017

DOI:https://doi.org/10.1103/PhysRevE.97.022406

©2018 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living SystemsInterdisciplinary PhysicsStatistical Physics & ThermodynamicsNonlinear Dynamics

Authors & Affiliations

Robert West*, Mauro Mobilia, and Alastair M. Rucklidge

  • Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

  • *mmrw@leeds.ac.uk
  • M.Mobilia@leeds.ac.uk
  • A.M.Rucklidge@leeds.ac.uk

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Issue

Vol. 97, Iss. 2 — February 2018

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