  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.
