Spatial Cox point processes is a natural framework for quantifying the various sources of variation governing the spatial distribution of rain forest trees. We introduce a general criterion for variance decomposition for spatial Cox processes and apply it to specific Cox process models with additive or log linear random intensity functions. We moreover consider a new and flexible class of pair correlation function models given in terms of Matérn covariance functions. The proposed methodology is applied to point pattern data sets of locations of tropical rain forest trees.

Keywords: additive random intensity, composite likelihood, Cox process, Matérn covariance function, pair correlation function, variance component.