Finite-size effects, demographic noise, and ecosystem dynamics
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Date
2021-10
Publication Type
Journal Article
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yes
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Abstract
Strong positive feedback is considered a necessary condition to observe abrupt shifts in ecosystems. A few previous studies have shown that demographic noise-arising from the probabilistic and discrete nature of birth and death processes in finite systems-makes the transitions gradual. In this paper, we investigate the impact of demographic noise on finite ecological systems. We use a simple cellular automaton model with births and deaths influenced by positive feedback processes. We present our methods in a tutorial like format. Using the approach of van Kampen's system-size expansion, we derive a stochastic differential equation that describes how local probabilistic rules scale to stochastic population dynamics in finite systems. We illustrate that as a consequence of enhanced demographic noise, finite-sized ecological systems can show an 'effective abrupt transition' even with weak positive interactions. Numerical simulations of our spatially explicit model confirm this analytical expectation. Thus, we predict that small-sized populations and ecosystems, in response to environmental drivers, are prone to abrupt collapse while larger systems-with the same microscopic interactions-show a smooth response.
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Publication status
published
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Journal / series
Volume
230 (16)
Pages / Article No.
3389 - 3401
Publisher
Springer