The evolution of an individual-based spatial ecological model with dispersion and competition is studied. In the model, an infinite number of individuals, point particles in R^d, reproduce themselves, compete, and die at random. These events are described by a Markov generator, which determines the evolution of states understood as probability measures on the space of particle configurations. 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.
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