The selection mutation equation (Q1069881)

The author extends Fisher's fundamental theorem of natural selection, that the mean fitness of a population is steadily increasing, to the selection mutation model with mutation rates \(\epsilon_{ij}=\epsilon_ i\), i.e. depending only on the target gene. The method of proof is the construction of a simple Lyapunov function. He points out that, for more general selection models, this is a hopeless task since such models generally exhibit more complicated dynamical behavior, and illustrates this fact with an example.