Model Approach Our approach to modelling evolution is to describe the population in terms of statistical features such as the average fitness and variance in the fitnesses. In statistical mechanics language these are the macroscopic variables . Our strategy is to infer the dynamics of these variables under selection, mutation and crossover. We are interested in real evolution with finite populations.
Finite populations can behave very differently from infinite populations.
One way in which they differ is that the selection, mutation and crossover operators are stochastic for finite populations. To model this stochasticity we consider an ensemble of populations evolving. Rather than describe the evolution of a single population we describe the evolution of the ensemble. We therefore seek a set of deterministic equations for this ensemble. In this approach the dynamics have be made analytically tractable by throwing away information about the details of the populations.