"Regime shifts, extinctions and long transients in discrete-time models of population dynamics"Morozov, AndrewPredicting ecosystems' regime shifts has long been a focus of biological conservation and ecological management. Traditionally, mathematical models of regime shifts focused on long-term, asymptotic behaviour of ecosystems. However, recently, there has been a growing appreciation of the role of transients both in empirical ecology and theoretical studies, in particular in the context of regime shifts and species extinctions. In this study, we theoretically explore long transients and extinctions due to regime shifts occurring in several paradigmatic models of population dynamics, such as single species, two-species and three-species systems. We consider the population dynamics in a local ‘patch’, the patch being connected to the rest of the population via density-dependent dispersal. We explore both deterministic and stochastic versions of the models. We find a large number of different patterns of long transient dynamics with quick regime shifts between ‘safe’ (persistent) dynamics and unsafe ones resulting in extinctions. Remarkably, delayed extinction can occur after thousands of generations of apparently safe population dynamics. We classify transient regimes and reveal their underlying mechanisms. Environmental noise can either shorten transients or can create a new type of a long transient. Our study suggests that not only are long transients ubiquitous in population models, but there is also a great variety of them. The omnipresence of long transients emphasizes the need to account for them in nature conservation programs as well as future theoretical research. |
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