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...

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Our density functional theory study of hydroperoxy (OOH) intermediates on various model titanosilicalite (TS-1) Ti centers explores how microstructural aspects of Ti sites effect propylene epoxidation reactivity and shows that Ti sites located adjacent to Si vacancies in the TS-1 lattice are more reactive than fully coordinated Ti sites, which we find do not react at all. We show that propylene epoxidation near a Si-vacancy occurs through a sequential pathway where H(2)O(2) first forms a hydroperoxy intermediate Ti-OOH (15.4 kcal/mol activation energy) and then reacts with propylene by proximal oxygen abstraction (9.3 kcal/mol activation energy). The abstraction step is greatly facilitated through a simultaneous hydride transfer involving neighboring terminal silanol groups arising from the Si vacancy. The transition state for this step exhibits 6-fold oxygen coordination on Ti, and we conclude that the less constrained environment of Ti adjacent to a vacancy accounts for greater transition state stability by allowing relaxation to a more octahedral geometry. These results also show that the reactive hydroperoxy intermediates are generally characterized by smaller electron populations on the proximal oxygen atom compared to nonreactive intermediates and greater O-O polarization--providing a potential means of computationally screening novel titanosilicate structures for epoxidation reactivity.

We investigated the condensation and reverse hydrolysis reactions of several silica clusters ranging in size up to the octamer cage. Using density functional theory (DFT) at the B3LYP/6-31G(d,p) level of theory, we found that under neutral conditions the reactions proceeded through a single-step, S N 2-type mechanism with formation of a pentacoordinated transition state. Under acidic conditions, the reactions of the smaller species followed a two-step mechanism with formation of a stable pentacoordinated intermediate, while the larger species proceeded through a single-step mechanism similar to the neutral route. In vacuo energy calculations showed a decreased activation barrier for formation of the larger ringed oligomers compared to the barriers of the smaller species. Calculation also showed an increasing kinetic and thermodynamic barrier for the silica clusters to break back into smaller less-condensed constituent species as they oligomerized to form larger species. To study the influence of solvation on these reactions, we used a hybrid implicit/explicit hydration model that explicitly accounted for water in the calculations. Results on the silica dimer cluster revealed a marked change in both the mechanism and energetics of the reactions. The results suggested the presence of excess water (1) elongated the hydroxyl bonds of the cluster, (2) elongated the siloxane bonds, (3) stabilized both the reactive intermediates and transition states, and (4) acted as a proton acceptor to facilitate the reactions. The calculated rate-limiting activation barrier for the condensation reaction to form the dimer species was in excellent agreement with previous experimental and theoretical results. Application of the hybrid solvation model to calculate energy of solvation for several silica oligomers showed a decrease in solvation energy as the silica clusters grew in size.