  A model is proposed and studied describing an infinite population of point
migrants arriving in and departing from $X\subseteq \mathbf{R}^d$, $d\geq 1$.
Both these acts occur at random with state-dependent rates. That is, depending
on their geometry the existing migrants repel and attract the newcomers, which
makes the population a complex system. Its states are probability measures on
an appropriate configuration space, and their evolution $\mu_0 \to \mu_t$ is
obtained by solving the corresponding Fokker-Planck equation. The main result
is the conclusion that this evolution of states preserves their
sub-Poissonicity, and hence a local self-regulation (suppression of clustering)
takes place due to the inter-particle repulsion -- no matter of how small
range. Further possibilities to study the proposed model with the help of this
result are also discussed.
