Extinction and the Allee effect in an age structured Ricker population model with inter-stage interaction

Abstract

We study the evolution in discrete time of certain age-structured populations, such as adults and juveniles, with a Ricker fitness function. We determine conditions for the convergence of orbits to the origin (extinction) in the presence of the Allee effect and time-dependent vital rates. We show that when stages interact, they may survive in the absence of interior fixed points, a surprising situation that is impossible without inter-stage interactions. We also examine the shift in the interior Allee equilibrium caused by the occurrence of interactions between stages and find that the extinction or Allee threshold does not extend to the new boundaries set by the shift in equilibrium, i.e. no interior equilibria are on the extinction threshold.

A convergence criterion for the solutions of nonlinear difference equations and dynamical systems

“…Such a behavior is not exceptional; it is indeed observed in certain biological population models. In [9], Lemma 8, we find this type of behavior exhibited by interacting adult and juvenile populations; also see Corollary 3 below. This leads to nontrivial issues regarding the nature of the strong Allee effect in biological models; see [2], [3], [5], [8], [9], [11] for background and further information.…”

“…Another issue of potential interest in the context of biological populations involves the connection to the strong Allee effect that was mentioned in the discussion after Corollary 3. For more details on this issue we refer to [9].…”