Establishment and Fecundity in Spatial Ecological Models: Statistical Approach and Kinetic Equations

We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establish-ment 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 sys-tems. We analyze mesoscopic limit for stochastic dynamics under consid-eration. The corresponding Vlasov-type non-linear kinetic equations are derived and studied