We introduce a novel model of spatial evolution of mutating genotypes under selection rates. With mathematical point of view, it is a stochastic dynamics on the space of marked point configurations with an additional diffusive evolution on marks. We study the evolution of the first correlation function of the model (also called a density), and reduce the spectral analysis of the generator of the model to the analysis of 1-D Schrödinger operators. As a result we find a long-time behavior of the first correlation function and a linkage between this asymptotics and characteristics of the selection mechanism in the model.