On the relationship between mutation rates and growth rates in a changing environment
An evolutionary model is introduced in order to describe population growth under different strategies. Mutations from one growth strategy to another are possible, and the relationship between the mutation rate and the long-run growth rate of the population in a changing environment is examined. The model is described as a matrix game with two growth strategies, two environmental states and fitness payoffs. The environment is changing from one state to the other periodically. To each member of the population a strategy is assigned which determines the number of children by the corresponding payoff. However, each person might mutate with a fixed mutation rate and switch to the other strategy. The dynamic process generates a long-run rate of population growth. It is shown that, in contrast to a fixed environment case, the global maximum of this growth rate is attained at a positive mutation rate. This demonstrates the benefit of mutations when the environment is changing. However, the zero mutation rate seems to be a local maximum, as the authors confirmed in simulations, and a population with an initially low mutation rate will evolve to zero mutation.
scientific article; zbMATH DE number 493217