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Spatial point processes may be analysed at two levels. Quadrat and distance methods were designed for the sampling of a population in the field. In this paper we consider those situations in which a map of a spatial pattern has been produced at some cost and we wish to extract the maximum possible information. We review the stochastic models which have been proposed for spatial point patterns and discuss methods by which the fit of such a model can be tested. Certain models are shown to be the equilibrium distributions of spatial-temporal stochastic processes. The theory is illustrated by several case studies.