Abstract
A stochastic model is developed for competition among organisms living in a patchy and varying environment. The model is designed to be suitable for species with sedentary adults and widely dispersing larvae or propagules, and applies best to marine systems but may also be adequate for some terrestrial systems. Three kinds of environmental variation are incorporated simultaneously in the model. These are pure spatial variation, pure temporal variation, and the space × time interaction. All three kinds of variation can promote coexistence, and when variation is restricted to immigration rates, all three kinds act very similarly. Moreover, for long-lived organisms their action is nearly identical, and their effects, when present together, combine equivalently. For short-lived organisms, however, pure temporal variation is a less effective promoter of coexistence. Variation in death rates acts quite differently from variation in birth rates for it may demote coexistence in some circumstances, while promoting coexistence in other circumstances. Furthermore, pure spatial variation in death rates has quite different effects than other kinds of death-rate variation. In addition to conditions for coexistence, information is given on population fluctuations, convergence to stationary distributions, and asymptotic distributions for long-lived organisms. While the model is presented as an ecological model, a genetical interpretation is also possible. This leads to new suggested mechanisms for the maintenance of polymorphisms in populations.
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