ESTABLISHMENT AND FECUNDITY IN SPATIAL ECOLOGICAL MODELS: STATISTICAL APPROACH AND KINETIC EQUATIONS

Finkelshtein D, Kondratiev Y, Kutoviy O. ESTABLISHMENT AND FECUNDITY IN SPATIAL ECOLOGICAL MODELS: STATISTICAL APPROACH AND KINETIC EQUATIONS. Infinite Dimensional Analysis Quantum Probability And Related Topics. 2013;16(2): 1350014.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 Ref. 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