A mathematical model of evolution of demographic behavior. I: The main model. Natural selection of behavior (Q1091305)

We consider a collection of self-reproducing systems. The stochastic process of reproduction of a system is characterized by a vector of parameters - the type of demographic behavior of the system. It is shown that if the set of types is finite, then there exists a final distribution of systems by demographic behavior types. We constructively define a function of behavior types such that its maximizing type also maximizes the final distribution. The main analytical tools are the asymptotic properties of branching processes. The results are demonstrated using computer calculations.