Density behavior of spatial birth-and-death stochastic evolution of mutating genotypes under selection rates
Dmitri Finkelshtein, Yuri Kondratiev, Oleksandr Kutoviy, Stanislav Molchanov, Elena Zhizhina
(Submitted on 5 Jun 2013)

We consider birth-and-death stochastic evolution of genotypes with different lengths. The genotypes might mutate that provides a stochastic changing of lengthes by a free diffusion law. The birth and death rates are length dependent which corresponds to a selection effect. We study an asymptotic behavior of a density for an infinite collection of genotypes. The cases of space homogeneous and space heterogeneous densities are considered.