  There exists a wide variety of works on the dynamics of large populations
ranging from simple heuristic modeling to those based on advanced computer
supported methods. Their interconnections, however, remain mostly vague, which
significantly limits the effectiveness of using computer methods in this
domain. The aim of the present publication is to propose a concept based on the
experience elaborated in the nonequilibrium statistical mechanics of
interacting physical particles. Its key aspect is to explicitly describe
micro-states of populations of interacting entities as probability measures and
then to link this description to its macroscopic counterpart based on
kinetic-like equations, suitable for solving numerically. The pivotal notion
introduced here is a sub-Poissonian state where the large n asymptotic of the
probability of finding n particles in a given vessel is similar to that for
noninteracting entities, for which macro- and microscopic descriptions are
equivalent. To illustrate the concept, an individual based model of an infinite
population of interacting entities is proposed and analyzed. For this
population, its evolution preserves sub-Poissonian states, that allows one to
describe it through the correlation functions of such states for which a chain
of evolution equations is obtained. The corresponding kinetic equation is
derived and numerically solved and analyzed.
