Abstract
The random-walk problem is adopted as a starting point for the analytical study of dispersal in living organisms. The solution is used as a basis for the study of the expanson of a growing population, and illustrative examples are given. The law of diffusion is deduced and applied to the understanding of the spatial distribution of population density in both linear and two-dimensional habitats on various assumptions as to the mode of population growth or decline. For the numerical solution of certain cases an iterative process is described and a short table of a new function is given. The equilibrium states of the various analytical models are considered in relation to the size of the habitat, and questions of stability are investigated. A mode of population growth resulting from the random scattering of the reproductive units in a population discrete in time, is deduced and used as a basis for study on interspecific competition. The extent to which the present analytical formulation is applicable to biological situations, and some of the more important biological implications are briefly considered.
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