Extinction of oscillating populations

Naftali R. Smith, Baruch Meerson

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

Established populations often exhibit oscillations in their sizes that, in the deterministic theory, correspond to a limit cycle in the space of population sizes. If a population is isolated, the intrinsic stochasticity of elemental processes can ultimately bring it to extinction. Here we study extinction of oscillating populations in a stochastic version of the Rosenzweig-MacArthur predator-prey model. To this end we develop a WKB (Wentzel, Kramers and Brillouin) approximation to the master equation, employing the characteristic population size as the large parameter. Similar WKB theories have been developed previously in the context of population extinction from an attracting multipopulation fixed point. We evaluate the extinction rates and find the most probable paths to extinction from the limit cycle by applying Floquet theory to the dynamics of an effective four-dimensional WKB Hamiltonian. We show that the entropic barriers to extinction change in a nonanalytic way as the system passes through the Hopf bifurcation. We also study the subleading pre-exponential factors of the WKB approximation.

Original languageEnglish
Article number032109
JournalPhysical Review E
Volume93
Issue number3
DOIs
StatePublished - 7 Mar 2016
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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