  We construct birth-and-death Markov evolution of states(distributions) of
point particle systems in $\mathbb{R}^d$. In this evolution, particles
reproduce themselves at distant points (disperse) and die under the influence
of each other (compete). The main result is a statement that the corresponding
correlation functions evolve in a scale of Banach spaces and remain
sub-Poissonian, and hence no clustering occurs, if the dispersion is
subordinate to the competition.
