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Current and expected decline in biodiversity have motivated a number of experiments studying how biodiversity affects ecosystem functioning. The positive relationship is usually found in experiments where species pool is manipulated; the relationship between productivity and realized species richness does not show any single trend. We constructed a simple competition model for a plant community based on the classical LotkaVolterra equations, with randomly generated parameters. We varied the species pool size and intensity of competition (range of competition coefficients). Then, we compared two measures of diversity used as predictors of productivity: (1) the size of the species pool and (2) the realized species richness, i.e. the number of species that remained in the system after competitive exclusion. Simulation results showed that productivity was always positively affected by the size of the species pool. With increasing species pool, both the selection effect and complementarity increase. The relationship between realized species richness and productivity was extremely weak within a set of simulations with a fixed species pool (i.e.where the diversity gradient was caused only by differences in the randomly generated parameters). The relationship between realized species richness and productivity was slightly positive for small species pool sizes and slightly negative for larger species pools. A species with high carrying capacity within the generated set of species usually decreases the chance of other species to survive but increases the productivity of the mixture, leading to negative diversity productivity relationship. On the contrary, presence of highly complementary species (i.e. species with low mutual competition coefficients) increases both, the realized species richness and productivity, leading to positive diversity productivity relationship. These two effects mostly counterbalance each other. These trends are not affected by the competition intensity.

Two types of mathematical models incorporating several types of competition between two species of African carnivores were constructed and analysed. The heuristic model focuses on population dynamics of both carnivores and their shared prey. The individual-based model focuses on the role of habitat heterogeneity and unique features of ecology of one of the predators, using the African wild dogs and hyaenas as a case study.