ABSTRACT
The distribution of animal population density varies with the mean density in a systematic fashion, known as Taylor’s power law. It has been proposed that the specificity and repeatability of this relationship is a consequence of the specific behavior of the members of the population. Assuming that this is so, investigations of the population dynamic consequences of behavioral interactions between individuals, or small groups, should have simulated organisms placed in relation to each other in realistic juxtapositions. This requires an individually-based simulation in which each individual’s Cartesian coordinates may be generated according to a prescribed power law exponent. Generating realistic spatial distributions which cover the full range of densities encountered in Nature is not easy, even for such a “simple” spatial distribution as the Poisson. An algorithm is presented which places organisms on a plane in realistic spatial distributions according to any defined power law exponent within the observed range (.5 < β < 3.5). Difficulty in generating extremely aggregated distributions suggests that distributions with extremely high spatial variances at high density may be the result of an “amplification” process (West and Shlesinger 1990).
