Grantee: ** Case Western Reserve University**, Cleveland, OH, USA

Researcher: Karen C. Abbott, Ph.D.

Grant Title: Alternative stable states and stochasticity in ecological dynamics

https://doi.org/10.37717/220020364

Program Area: Studying Complex Systems

Grant Type: Scholar Award

Amount: $450,000

Year Awarded: 2013

Duration: 6 years

**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 produce^{1,2}. Traditionally, ecological theory has built upon the principles of deterministic nonlinear dynamical systems^{3}, 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
dynamics^{4,5}. 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
useful^{1}, 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 systems^{6-9}, where stochastic models
can sometimes behave quite differently from their deterministic analogues^{10}.

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
back^{11,12}. 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 conditions^{13-15}. While this theoretical framework has lead to great
advances in our understanding of some sudden regime shifts in ecology^{16}, 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 time^{17}, 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.

- May, R. M. The role of theory in ecology.
*Am Zool***21**, 903–910 (1981). - Turchin, P. V.
*Complex Population Dynamics*. (Princeton University Press, 2003). - May, R. M.
*Stability and Complexity in Model Ecosystems*. (Princeton University Press, 1974). - Ellner, S. & Turchin, P. V. Chaos in a noisy world: new methods and evidence from timeseries
analysis.
*Am Nat***145**, 343–375 (1995). - Lande, R., Engen, S. & Saether, B. E.
*Stochastic Population Dynamics in Ecology and Conservation*. (Oxford University Press, 2003). - Abbott, K. C., Ripa, J. & Ives, A. R. Environmental variation in ecological communities and
inferences from single-species data.
*Ecology***90**, 1268–1278 (2009). - Ives, A. R., Abbott, K. C. & Ziebarth, N. L. Analysis of ecological time series with
ARMA(p,q) models.
*Ecology***91**, 858–871 (2010). - Ziebarth, N. L., Abbott, K. C. & Ives, A. R. Weak population regulation in ecological time
series.
*Ecol Lett***13**, 21–31 (2010). - Abbott, K. C. A dispersal-induced paradox: synchrony and stability in stochastic
metapopulations.
*Ecol Lett***14**, 1158–1169 (2011). - Coulson, T., Rohani, P. & Pascual, M. Skeletons, noise and population growth: the end of
an old debate?
*Trends Ecol Evol***19**, 359–364 (2004). - Scheffer, M., Carpenter, S., Foley, J. A., Folke, C. & Walker, B. Catastrophic shifts in
ecosystems.
*Nature***413**, 591–596 (2001). - Barnosky, A. D. et al. Approaching a state shift in Earth’s biosphere.
*Nature***486**, 52–58 (2012). - Lewontin, R. C. The meaning of stability.
*Brookhaven Sympoisa in Biology*13–23 (1969). - May, R. M. Thresholds and breakpoints in ecosystems with a multiplicity of stable states.
*Nature***269**, 471–477 (1977). - Scheffer, M. & Carpenter, S. R. Catastrophic regime shifts in ecosystems: linking theory to
observation.
*Trends Ecol Evol***18**, 648–656 (2003). - Scheffer, M. et al. Early-warning signals for critical transitions.
*Nature***461**, 53–59 (2009). - Hastings, A. Transients: the key to long-term ecological understanding?
*Trends Ecol Evol***19**, 39–45 (2004).