Demographic noise can promote abrupt transitions in ecological systems

Abstract

Strong positive feedback is considered a necessary condition to observe abrupt shifts of 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 or continuous. In this paper, we show that demographic noise may, in fact, promote abrupt transitions in systems that would otherwise show continuous transitions. We present our methods and results in a tutorial-like format. We begin with a simple spatially-explicit individual-based model with local births and deaths influenced by positive feedback processes. We then derive a stochastic differential equation that describes how local probabilistic rules scale to stochastic population dynamics. The infinite-size well-mixed limit of this SDE for our model is consistent with mean-field models of abrupt regime-shifts. Finally, we analytically show that as a consequence of demographic noise, finite-size systems can undergo abrupt shifts even with weak positive interactions. Numerical simulations of our spatially-explicit model confirm this prediction. Thus, we predict that small-sized populations and ecosystems may undergo abrupt collapse even when larger systems - with the same microscopic interactions - show a smooth response to environmental stress.