  We consider spatial population dynamics given by Markov birth-and-death
process with constant mortality and birth influenced by establishment or
fecundity mechanisms. The independent and density dependent dispersion of
spreading are studied. On the base of general methods of [14], we construct the
state evolution of considered microscopic ecological systems. We analyze
mesoscopic limit for stochastic dynamics under consideration. The corresponding
Vlasov-type non-linear kinetic equations are derived and studied.
