The analysis of a population model demonstrating the importance of dispersal in a heterogeneous environment

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Abstract
In a previous paper (Roff, 1974) a simulation model was presented demonstrating the importance of dispersal in a spatially heterogeneous environment. In the present paper this model is analysed in detail. It is shown that the qualitative properties of the model can be understood within the framework of a more general mathematical model. The effect of dispersal in a heterogeneous environment is to reduce the variance in the environmental fluctuations. How the subpopulations are connected with respect to dispersers may be the primary factor in determining the change in population size with changes in environmental fluctuations. Both the type of dispersal pattern and the number of subpopulations may influence the persistence of a population without affecting the mean subpopulation size. Finally, it is noted that the “value” of a dispersal pattern changes with changes in parameter values and a shift from one parameter value to another may lead to a qualitative change in the type of dispersal pattern “favoured”.