Microscopic dynamics and kinetic description of spatial ecology models

Abstract

We consider a method for the construction of Markov statistical dynamics for a class of birth-and-death ecological models in the continuum. Mesoscopic scaling limits for these dynamics lead to the kinetic equations for the density of a population. The resulting evolution equations are non-local and non-linear ones. We discuss properties of solutions to kinetic equations which strongly depend on characteristics of the models considered. The survey paper is devoted to giving an overview of our recent progress on the subject and it is not intended to be a complete review of the field.