A stochastic evolutionary model of molecular sequences.

A stochastic evolutionary model of molecular sequences is proposed. The basic forces in evolution are supposed to be mutation and selection. The concept is somewhat similar to Kauffman-Levin's concept of adaptive walks and corresponding analytical expressions have been developed. The selective force is divided into two parts: a slowly-varying part and a rapidly-changing fluctuation. The latter influences the distribution of sequences and results in an equation of motion along the flow line. The former plays a more important role in the emergence of evolutionary order. It is demonstrated that the asymmetry of selective forces would lead to a definite order of the system.