Dynamics and stability in coevolutionary ecological systems. I. Community stability and coevolutionarily stable states.

An extension of J. Roughgarden's [1979, Theor. Pop. Biol. 9, 388; 1979, "An Introduction to Evolutionary Ecology and Population Genetic Theory," Macmillan, New York] formalism for investigating the effects of coevolution on community structure is presented. The extension assumes the result that a coevolved community is asymptotically stable when coevolution takes place at a genetically noninvasible boundary. This is proved for the general case of n interacting species. From this a community persistence function, phi (P), is defined that allows measuring the domain of attraction for the community as well as the resilience time, that is, the time taken for a perturbation to decay to 1-1/e (63%) of its initial value.