An ecosystem is said to possess ecological stability (or equilibrium) if it does not experience unexpected large changes in its characteristics across time, or if it is capable of returning to its equilibrium state after a perturbation (a capacity known as resilience). Although the terms community stability and ecological stability are sometimes used interchangeably, community stability refers only to the characteristics of communities. It is possible for an ecosystem or a community to be stable in some of their properties and unstable in others; e.g., in response to a drought, a plant community might conserve biomass but lose biodiversity.
The concept of ecological stability emerged in the first half of the 20th century, and with the advancement of theoretical ecology in the 1970s, the usage of the term has expanded to a wide variety of scenarios. This overuse of the term has led to controversy over its definition and implementation. In 1997, Grimm and Wissel made an inventory of 167 definitions used in the literature and found 70 different stability concepts. One of the strategies that these two authors proposed to clarify the subject is to replace ecological stability with more specific terms, such as constancy, resilience and persistence. Following this strategy, an ecosystem which oscillates cyclically around a fixed point, such as the one delineated by the predator-prey equations, would be described as persistent and resilient, but not as constant. Some authors, however, see good reason for the abundance of definitions, because they reflect the extensive variety of real and mathematical systems.
Stable ecological systems abound in nature, and the scientific literature has documented them to a great extent. Scientific studies mainly describe grassland plant communities and microbial communities. Nevertheless, it is important to mention that not every community or ecosystem in nature is stable. Also, noise plays an important role on biological systems and, in some scenarios, it can fully determine their temporal dynamics.
When the species abundances of an ecological system are treated with a set of differential equations, it is possible to test for stability by linearizing the system at the equilibrium point. Robert May developed this stability analysis in the 1970s which uses the Jacobian matrix.