The response to selection equation for skew fitness distributions

The equation for the response to selection is a powerful analysis and modeling tool for genetic algorithms. In this paper, we extend the classical analysis (which is restricted to a normal distribution) to skew fitness distributions. We show that, for a small number of variables, the Gamma distribution fits the distribution of the fitness values better than a normal distribution. We compute the selection intensities for the Gamma distribution. It is shown that, with these values, the prediction for the mean fitness of the population is very accurate. Finally, we show that multi-modal functions may lead to fitness distributions having several modal values.