  The evolution of states of a spatial ecological model is studied. The model
describes an infinite population of point entities placed in $\mathbb{R}^d$
which reproduce themselves at distant points (disperse) and die with rate that
includes a competition term. The system's states are probability measures on
the space of configurations of entities, and their evolution is described by
means of a hierarchical chain of equations for the corresponding correlation
functions derived from the Fokker-Planck equation for measures. Under natural
conditions imposed on the model parameters it is proved that the correlation
functions evolve in a scale of Banach spaces in such a way that each
correlation function corresponds to a unique sub-Poissonian state. Some further
properties of the evolution of states constructed in this way are also
described.
