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A community which would not reach a stable equilibrium may nevertheless persist if there is temporal variation and nonlinear dynamics. A procedure is introduced for taking time averages of the rates of change. Since the average of a nonlinear function is not the function of the average, higher terms such as the variances of resources or covariances among species and environmental factors enter into the coexistence conditions. These measures behave as if they were resources. Therefore the number of consumer species cannot exceed the number of resources plus distinct nonlinearities. The nonlinearities arise from predator saturation, learning, group hunting, multiple nutritional requirements, or seasonally variable feeding rates. It is shown that there is no long term correlation between the abundance of a species and its rates of increase.
Richard Levins (Sat,) studied this question.