Funded Grants

Alternative stable states and stochasticity in ecological dynamics

Ecological communities are complicated: their composition and the abundances of their component species can fluctuate wildly. Their dynamics are often so complex that they cannot be understood without the aid of theoretical models that link underlying ecological mechanisms to the dynamical patterns those mechanisms are expected to produce1,2. Traditionally, ecological theory has built upon the principles of deterministic nonlinear dynamical systems3, producing models that capture one of the prime causes of complicated ecological dynamics: nonlinear interactions within and among species. Stochasticity is also well known to influence ecological dynamics4,5. When we nevertheless invoke deterministic theory, we implicitly assume that stochasticity will primarily act to blur the deterministic signal such that the theory will still be approximately true in more realistic stochastic settings. By this design, we miss any qualitative effects of stochasticity so, although ecological theory grounded in determinism is often quite useful1, where it does fail us, the failure is big. A major goal of my research program is to understand qualitative effects of stochasticity in ecological systems6-9, where stochastic models can sometimes behave quite differently from their deterministic analogues10.

My current research is on qualitative effects of stochasticity within an ecological context of great concern: the potential for ecosystems to shift suddenly and unexpectedly from their historical state to a new and very different state, with no imminent shift back11,12. Ecologists have largely sought to understand this phenomenon through the analysis and application of deterministic models that have “alternative stable states”: multiple stable equilibria under a single set of conditions13-15. While this theoretical framework has lead to great advances in our understanding of some sudden regime shifts in ecology16, its sole emphasis on deterministic stability makes it fairly narrow in scope. In stochastic systems, stable equilibria don’t tell the whole story. For instance, some unstable solutions can trap stochastic dynamics for long periods of time17, essentially masquerading as additional stable states within the stochastic system. Some systems with one stable state (and one or several unstable ones) may therefore behave indistinguishably, in the presence of stochasticity, from those with multiple stable states.

The idea that stochasticity can blur the distinction between stable and unstable dynamics has the potential to transform our thinking on alternative states. Because only a relatively narrow subset of ecological models displays deterministic multi-stability, ecosystems with alternative stable states have garnered special concern. However, virtually all models have multiple (stable plus unstable) equilibria. My research asks when these systems can have an equivalent potential for sudden state shifts, and whether our focus on deterministically multi-stable systems in the study of regime shifts is dangerously narrow.



Cited references
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  17. Hastings, A. Transients: the key to long-term ecological understanding? Trends Ecol Evol 19, 39–45 (2004).