We can think of the idea of stability as playing multiple roles in ecological theory. One role that we will emphasize is that it is a way to begin to analyze models. If our goal is to understand the distribution and abundance of species, what properties of simple models correspond to the patterns we observe in nature? Stability is one way to approach this question. Here we are forced to think seriously about the relationship between models and natural systems.

A second question concerns the effects of change on ecological systems. Here, the idea is to understand how much external change (either temporary or permanent) can be imposed on an ecological system and have the system still maintain its integrity. Almost every word with more than 4 letters in the previous sentence requires a careful definition. Here, the concept of resilience originally introduced by Holling, is playing a role. However, the best way to think about these problems is still not clear.

A classic issue in ecology that includes the concept of stability is the stability-diversity relationship that goes back at least to Elton, but is still the subject of current research. Here again, careful definitions are required.

The idea of stability first needs to be approached on a conceptual basis. These concepts are both biological (how would we measure stability?) and model related (what should a concept of stability entail?).

- constancy in numbers
- persistence
- resilience
- issues of multiple stable states
- relating mathematical concepts to biological ones

When applying stability concepts and using them in the context of model formulation and analysis, one needs to be very precise. Here we begin to be more precise, which points out some of the advantages, limitations, and difficulties with the stability concept.

- perturbation
- deteministic systems
- neigborhood stability
- global stability
- stochastic systems
- stability and nonequilibrium solutions

When using stability in models and theories, we need to worry about how we would actually carry out computations.

- computing stability of equilibria
- computing stability of nonequilibrium solutions
- persistence/permanence
- stability computations in stochastic models

* means required reading

Adger, W. N., T. Hughes, C. Folke, S. R. Carpenter, and J. Rockström. 2005. Social-ecological resilience to coastal disasters. Science 309:1036-1039.

Chesson, P.L. 1982. The stabilizing role effect of a random environment. J. Math. Biol. 15:1-36.

*Connell, J.H., Sousa, W.P. 1983. On the evidence needed to judge ecological stability or persistence. Amer. Nat. 121:789-824.

Gunderson, L. H. 2000. Resilience in theory and practice. Annual Review of Ecology and Systematics 31:425-439.

Gunderson, L., and C. Folke. 2005. Resilience—now more than ever. Ecology and Society 10(2): 22. [online] URL: www.ecologyandsociety.org/vol10/iss2/art22/

Hastings, A. 2004. Transients: the key to long-term ecological understanding? Trends in Ecology and Evolution 19:39-45

Hastings, A. et al. 1993. Chaos in ecology: Is mother nature a strange attractor? Annu. Rev. Ecol. Syst. 24:1-33.

Holling, C.S. 1973. Resilience and stability of ecological systems. Ann. Rev. Ecol. Syst. 4:1-23.

Law, R., Morton, R.D. 1996. Permanence and the assembly of ecological communities. Ecology 77:762-775.

*Lewontin, R.C. 1969. The meaning of stability. in Diversity and Stability in Ecological Systems, Brookhaven Symp. Biol. 22:13-24.

May, R.M. 1973. Stability and Complexity in Model Ecosystems. Princeton University Press.

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On 4 Jan 2006, 13:46.