We introduce a new multivariate product-shot-noise Cox process which is useful for model- ing multi-species spatial point patterns with clustering intra-specific interactions and neutral, negative or positive inter-specific interactions. The auto and cross pair correlation functions of the process can be obtained in closed analytical forms and approximate simulation of the process is straightforward. We use the proposed process to model interactions within and among five tree species in the Barro Colorado Island plot.

Keywords: Cox process; Cross pair correlation function; Inter-specific interactions; Multivariate point process; Product fields.