We analyze a new class of models of spatial distribution, developing mathematical properties and performing empirical tests. The models are based on a simple colonization rule operating on a rectangular grid. Two special cases within the class are traditional random placement and negative binomial models. Over three large data sets, these two cases are strongly outperformed by more flexible models within the class, in particular, models that allow more general patterns of aggregation. The models are simple and broadly applicable, with only one adjustable parameter, representing aggregation. Shortcomings of the colonization rule are studied, and extensions and applications of the models are discussed.
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