Space–time dependence dynamics for birth–death point processes

This paper analyses the space–time interdependency of a spatially explicit birth–death process based on the intensity function. Based on intensity functions, these formulations can be, to some extent, analytically solved to obtain the explicit formulae of, for instance, the total point population size contained in the unit torus at equilibrium. The definition of continuous space–time processes based on point intensities opens up new promising lines of research to analyse ecological dynamics: our spatially explicit birth–death process can be easily expanded to mimic other realistic ecological scenarios. Note that although space–time stochastic processes are (generally) intractable, theoretical development of their corresponding intensity function provides useful insights into these complex dynamics. Hence, the analytical analysis of the point intensity provides a complementary method to simulation-based analyses of complex space–time processes.