A stochastic model for the spatial distribution of species based on an aggregation-repulsion rule

The heterogeneity associated with the spatial distribution of organisms is an awkward problem in ecology because this heterogeneity directly depends o n the sampling scale. To specify the scope of the influence of sampling sca le on the level of species aggregation, we need data sets that entail exces sive sampling costs in situ. To find a solution for this problem, we can us e models to simulate patterns of organisms. These models are often very com plex models that take into account heterogeneity of habitats and displaceme nt or longevity of studied species. In this article, we introduce a new sto chastic model to simulate patterns for one taxon and we want this model to be parsimonious, i.e., with few parameters and able to simulate observed pa tterns. Th is model is based on an aggregation-repulsion rule. This aggrega tion-repulsion rule is defined by two parameters. On a large scale. the num ber of aggregates present on the pattern is the first parameter. On a small er scale, the level of aggregation-repulsion among individuals is determine d by a probability distribution. These two parameters are estimated from fi eld data set in a robust way so that the simulated patterns reflect the obs erved heterogeneity. We apply this model to entomological data: four Dipter a families, namely the Sciaridae, Phoridae, Cecidomyiidae, and Empididae. T he field data for the Phoridae family are used to simulate sampling using d ifferent trap sizes. We record changes in the coefficient of variation (C) as a function of the sampling scale, and we can suggest to ecologists emerg ence traps of 0.6 m(2), in other words a square 77 x 77 cm trap, to obtain a C value under 20%.