Modelling Evolving Populations

A formalism is presented for modelling the evolutionary dynamics of a population of gene sequences. The formalism was originally developed for describing genetic algorithms. In this paper the formalism is elaborated by considering the evolution of an ensemble of populations. This allows the evolution to be modelled more accurately. To illustrate the formalism the problem of a population of gene sequences evolving in a multiplicative fitness landspace is considered. A comparison with simulations is made and shows very good agreement. More complicated problems have already been investigated including sexual recombination and evolution in a multi-valleyed fitness landscape. These results will be briefly reviewed.