Finite-size effects, demographic noise, and ecosystem dynamics

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.