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 language | English (US) |
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Pages (from-to) | 57-73 |
Number of pages | 17 |
Journal | Journal of biological dynamics |
Volume | 8 |
Issue number | 1 |
DOIs | |
State | Published - Jan 25 2014 |
Keywords
- Allee effects
- backward bifurcation
- bifurcation
- equilibrium
- stability
- structured population dynamics
ASJC Scopus subject areas
- Ecology, Evolution, Behavior and Systematics
- Ecology