title: Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations.
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).
authors: a Department of Mathematics , University of Arizona , 617 N Santa Rita, Tucson , AZ 85721 , USA.
authors: J M
authors: JM
authors: Cushing
mesh_terms: D005246:Feedback; D006801:Humans; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011157:Population Dynamics
keywords: Allee effects; backward bifurcation; bifurcation; equilibrium; stability; structured population dynamics