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Equilibrium

The equilibrium concept is quite important in the study of ecology, as well as many other sciences, and thorough explanation is somewhat beyond the scope of this lab. The information provided here should be just enough to get you through this study.

Equilibrium may be defined as a "balance of opposing forces." In ecological studies these forces are often birth and death, or as is the case in this study it is the balance of the proportion of two types (cooperators and defectors). A point equilibrium is the point at which the two opposing forces are perfectly balanced, so that if no outside forces disturb this balance it will remain there indefinitely. In this case that point would be the exact proportions of competitors and cooperators. These equilibria can often be calculated analytically.

Point equilibria can be further classified as either stable or unstable. A stable point equilibrium will tend to return to that value if it is disturbed slightly by outside forces, while an unstable point equilibrium will stray further from the equilibrium if disturbed slightly.

The models involved in this study are all stochastic (random) so that there are outside forces constantly disturbing the equilibria. This will result in the observation of only stable equilibria. Unstable equilibria will move right past the point of equilibrium, and thus will not be seen. An example of a stable equilibrium is shown in the following figure:

In this example the equilibrium is with 1/3 cooperators and 2/3 defectors. Although there is some fluctuation, the percent of cooperators and defectors stay close to these values.