When can competition for resources lead to ecological equivalence?

Question: Under what conditions do species using distinct niches evolve and converge to become ecologically equivalent? Does evolution in a community context affect functional group diversity? Mathematical methods: We simulated the population dynamics and evolution of multiple species competing for discrete, substitutable resources. Key assumptions: Species’ competitive effect and response are based on resource-use overlap. Evolution occurs via selection on mutations of small effect. Intraspecific genetic variation is the same for each species. Predictions: Evolution of equivalence is possible when species evolve in a community context. A combination of convergence, divergence, and extinctions occurs when the number of species exceeds the number of resources. Species avoid competitive exclusion via convergence or divergence in their resource use. Ecological and evolutionary outcomes depend on an interaction between the rate of evolution and the initial similarity of competitors. The evolution of equivalence determines diversity within functional groups, but niche processes drive diversity among groups.