Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations

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Abstract

In nonlinear matrix models, strong Allee effects typically arise when the fundamental bifurcation of positive equilibria from the extinction equilibrium at r=1 (or R0=1) is backward. This occurs when positive feedback (component Allee) effects are dominant at low densities and negative feedback effects are dominant at high densities. This scenario allows population survival when r (or equivalently R0) is less than 1, provided population densities are sufficiently high. For r>1 (or equivalently R0>1) the extinction equilibrium is unstable and a strong Allee effect cannot occur. We give criteria sufficient for a strong Allee effect to occur in a general nonlinear matrix model. A juvenile–adult example model illustrates the criteria as well as some other possible phenomena concerning strong Allee effects (such as positive cycles instead of equilibria).

Original languageEnglish (US)
Pages (from-to)57-73
Number of pages17
JournalJournal of biological dynamics
Volume8
Issue number1
DOIs
StatePublished - Jan 25 2014

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Keywords

  • Allee effects
  • backward bifurcation
  • bifurcation
  • equilibrium
  • stability
  • structured population dynamics

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology

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