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Analysis of a lottery competition model with limited nutrient availability

How a plant species utilizes a limited nutrient is important for its survival. The purpose of this work is to examine how nutrient utilization mechanisms (for seed production) affect the coexistence of competing plant species. We construct a revised lottery model that uses one of three possible kinds of nutrient utilization functions. In all cases the models suggest that two species can coexist under certain circumstances, but that three species cannot coexist, at least when the nutrient utilization functions are continuous functions of nutrient uptake. However, in the discontinuous case three species can coexist in a state of sustained oscillations. The results suggest that one need pay close attention to the differences in the nutrient utilization mechanisms among competing plant species in order to ascertain the competitive outcome.