Self-regulation in the Bolker-Pacala model

The Markov dynamics is studied of an infinite system of point entities placed in $\mathds{R}^d$, in which the constituents disperse and die, also due to competition. Assuming that the dispersal and competition kernels are continuous and integrable we show that the evolution of states of this model preserves their sub-Poissonicity, and hence the local self-regulation (suppression of clustering) takes place. Upper bounds for the correlation functions of all orders are also obtained for both long and short dispersals, and for all values of the intrinsic mortality rate.