Ecosystem processes are thought to depend on both the number and identity of the species present in an ecosystem, but mathematical theory predicting this has been lacking. Here we present three simple models of interspecific competitive interactions in communities containing various numbers of randomly chosen species. All three models predict that, on average, productivity increases asymptotically with the original biodiversity of a community. The two models that address plant nutrient competition also predict that ecosystem nutrient retention increases with biodiversity and that the effects of biodiversity on productivity and nutrient retention increase with interspecific differences in resource requirements. All three models show that both species identity and biodiversity simultaneously inf luence ecosystem functioning, but their relative importance varies greatly among the models. This theory reinforces recent experimental results and shows that effects of biodiversity on ecosystem functioning are predicted by well-known ecological processes.Recent studies have shown that several community and ecosystem processes are correlated with species diversity (1-12), but why this should occur remains mathematically largely unexplained. Here we report that three different ecological models predict that ecosystem productivity, standing crop, and resource use depend on species diversity, much as has been experimentally observed (3, 4, 6). Our models provide simple mechanisms that explain how such dependencies can arise and help resolve the controversy over the importance for ecosystem functioning of species identity versus species diversity.The functioning of ecosystems has long been known to depend on the identities of the species the ecosystems contain (13-19), and hypothesized to depend on the number of species. However, recent work, plus early observations by Darwin (20) Because the functioning of an ecosystem may depend both on the identities and the numbers of its species, it is necessary to distinguish between these two dependencies in both experimental and theoretical studies. This requires, first, that the group of all potential species, called the ''species pool,'' be defined. Then, to attribute effects to species diversity, effects must occur in comparisons of the average responses of two or more levels of diversity. At each level of diversity, there must be numerous replicate ecosystems, each with a random and independent combination of species chosen from the species pool. By having many random species combinations drawn from a large species pool, the mean response among replicate ecosystems at a given level of diversity becomes independent of particular species combinations. The differences among mean responses for different levels of diversity then measure the effect of diversity. The variance among the various species combinations at a given diversity level measures the effects of alternative species compositions.We apply this approach to two models of interspecific plant competition for nutrient...