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 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. 
Dmitri Finkelshtein, Yuri Kondratiev, Oleksandr Kutoviy
math.FA math-ph math.DS math.MP