Ecological stability can refer to types of stability in a continuum ranging from resilience (returning quickly to a previous state) to constancy to persistence. The precise definition depends on the ecosystem in question, the variable or variables of interest, and the overall context. In the context of conservation ecology, stable populations are often defined as ones that do not go extinct. Researchers applying mathematical models from system dynamics usually use Lyapunov stability.
Types of ecological stability 
Local stability indicates that a system is stable over small short-lived disturbances, while global stability indicates a system highly resistant to change in species composition and/or food web dynamics.
Constancy and persistence 
Observational studies of ecosystems use salinas constancy to describe living systems that can remain unchanged.
Resistance and inertia (persistence) 
Resistance and inertia deal with a system's inherent response to some perturbation.
A perturbation is any externally imposed change in conditions, usually happening in a short time period. Resistance is a measure of how little the variable of interest changes in response to external pressures. Inertia (or persistence) implies that the living system is able to resist external fluctuations. In the context of changing ecosystems in post-glacial North America, E.C. Pielou remarked at the outset of her overview,
"It obviously takes considerable time for mature vegetation to become established on newly exposed ice scoured rocks or glacial till...it also takes considerable time for whole ecosystems to change, with their numerous interdependent plant species, the habitats these create, and the animals that live in the habitats. Therefore, climatically caused fluctuations in ecological communities are a damped, smoothed-out version of the climatic fluctuations that cause them."
Resilience, elasticity and amplitude 
Resilience is the tendency of a system to return to a previous state after a perturbation. Elasticity and amplitude are measures of resilience. Elasticity is the speed with which a system returns. Amplitude is a measure of how far a system can be moved from the previous state and still return. Ecology borrows the idea of neighborhood stability and a domain of attraction from dynamical systems theory.
- Justus, James (2006). "Ecological and Lyanupov Stability" (PDF). Paper presented at the Biennial Meeting of The Philosophy of Science Association, Vancouver, Canada.
- Justus, J (2008). "Ecological and Lyanupov Stability". Philosophy of Science 75 (4): 421–436. doi:10.1086/595836.(Published version of above paper)
- Pielou, After the Ice Age: The Return of Life to Glaciated North America (Chicago: University of Chicago Press) 1991:13
- Hall, Charles A.S. (Publication date unclear). ""Ecology" (Accessed at World Book online reference centre)". Retrieved 2009-06-16.[dead link] Note: This appears to be a business site, accessible via subscription only. Unable to verify Hall's publication. However, Hall has published a large number of works pertaining to ecology, and the link to his website is below.
- Homepage, for publications of Charles A S Hall with. "Hall's publications on ecology". Retrieved 2009-10-08. See Complete Publications List in Publications section.
See also 
- Dynamic equilibrium
- Keystone species
- Principle of faunal succession
- Resilience (ecology)
- Systems analysis