A juvenile–adult population model: climate change, cannibalism, reproductive synchrony, and strong Allee effects

Abstract

We study a discrete time, structured population dynamic model that is motivated by recent field observations concerning certain life history strategies of colonial-nesting gulls, specifically the glaucouswinged gull (Larus glaucescens). The model focuses on mechanisms hypothesized to play key roles in a population's response to degraded environment resources, namely, increased cannibalism and adjustments in reproductive timing. We explore the dynamic consequences of these mechanics using a juvenile-adult structure model. Mathematically, the model is unusual in that it involves a high co-dimension bifurcation at R 0 = 1 which, in turn, leads to a dynamic dichotomy between equilibrium states and synchronized oscillatory states. We give diagnostic criteria that determine which dynamic is stable. We also explore strong Allee effects caused by positive feedback mechanisms in the model and the possible consequence that a cannibalistic population can survive when a non-cannibalistic population cannot. ARTICLE HISTORY

Non-linear population discrete models with two time scales: re-scaling of part of the slow process

“…We propose the model of a population inhabiting a two-patch environment. Following the model presented in [9], locally the population is considered structured into three classes corresponding to juveniles and two adult stages. Adults that reproduce at the end of an interval of time do not reproduce at the end of the following one.…”

“…We also assume, following the example in Sect. 2 of [9], that the survival rates are constant and fecundities and transitions from reproductive inactivity are locally dependent on the number of active adults. Specifically, we set…”

“…This general framework is used to illustrate the effects of fast dispersals on local demography that emerge at the global metapopulation level. To this end, we extend the nonspatial model presented in [9] to a habitat with two patches between which fast dispersals are considered. The model is structured into three classes: juveniles and two adult stages.…”

“…The aim of this consideration is studying the reproductive synchrony of adults. The model in [9] is a discrete-time nonlinear matrix model whose inherent projection matrix is imprimitive [10]. This entails that the stability of the extinction equilibrium when R 0 increases through 1 bifurcates either to the stability of a non-extinction equilibrium or of a synchronous 2-cycle.…”

“…Both metapopulation models, with or without re-scaled survival, and with local dynamics based on the model [9], can be studied through their associated reduced systems. Indeed, these have the same functional form as the system in [9] so that the results therein can be applied.…”