Abstract
We present a discrete-time model of a spatially structured population and explore the effects of coupling when the local dynamics contain a strong Allee effect and overcompensation. While an isolated population can exhibit only bistability and essential extinction, a spatially structured population can exhibit numerous coexisting attractors. We identify mechanisms and parameter ranges that can protect the spatially structured population from essential extinction, whereas it is inevitable in the local system. In the case of weak coupling, a state where one subpopulation density lies above and the other one below the Allee threshold can prevent essential extinction. Strong coupling, on the other hand, enables both populations to persist above the Allee threshold when dynamics are (approximately) out of phase. In both cases, attractors have fractal basin boundaries. Outside of these parameter ranges, dispersal was not found to prevent essential extinction. We also demonstrate how spatial structure can lead to long transients of persistence before the population goes extinct.
Highlights
One of the simplest systems with the potential to exhibit a regime shift is a population with a strong Allee effect (Johnson and Hastings 2018)
We present a discrete-time model of a spatially structured population and explore the effects of coupling when the local dynamics contain a strong Allee effect and overcompensation
We examine the interplay between essential extinction due to local chaotic dynamics with Allee effect and the between-patch effects due to coupling
Summary
One of the simplest systems with the potential to exhibit a regime shift is a population with a strong Allee effect (Johnson and Hastings 2018). Allee effects were considered mostly in models for spatially structured populations in continuous time (Gruntfest et al 1997; Amarasekare 1998; Gyllenberg et al 1999; Kang and Lanchier 2011; Wang 2016; Johnson and Hastings 2018). Different states can be caused by the Allee effect (Dennis 1989; Gruntfest et al 1997; Amarasekare 1998; Courchamp et al 1999; Gyllenberg et al 1999; Schreiber 2003) These exist in isolated patches unless there is essential extinction. – Extremely large population densities lead to extremely small population densities in the generation These conditions hold for other models of that type, e.g. the logistic map with Allee effect or a harvesting term.
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