SIMULATION OF POPULATION EXPANSION AND SPATIAL PATTERN WHEN INDIVIDUAL DISPERSAL DISTRIBUTIONS DO NOT DECLINE EXPONENTIALLY WITH DISTANCE

Many biological transport mechanisms, especially passive transport in fluids, give rise to dispersal distributions which do not decline exponentially with distance, i.e. no single dispersal scale can be characterized. Simulation of such situations in population biology can be awkward because of the wide range of scales that need to be included. It is possible to get round these problems to some extent by storing points individually, each associated with a location. By maintaining points in spatial groups with a dynamically created index to the groups, population characteristics such as dioecy or density dependence can be incorporated in a simulation at relatively low cost. As an example of this technique, the expansion of a plant disease from a single focus is studied. With dispersal distributions which do not decline exponentially with distance, a description in terms of an expanding wave is not appropriate. The distribution of individuals produced is approximately self-similar across a wide range of scales, and the fractal dimension changes systematically with scale in a way which may be characteristic of the dispersal distribution.