The Outcome of Evolution when Mutations are Highly Pleiotropic

David Waxman and Joel Peck

Selection, 1, 181-191 (2000)

Centre for the Study of Evolution, School of Biological Sciences, University of Sussex, Brighton BN1 9QG, Sussex UK

A mathematical model of mutation and selection in a very large population is given. Each mutation affects Ω different phenotypic characters, each of which is subject to stabilizing selection. In the limit Ω→∞, when all other parameters are held fixed, each mutation is lethal. Thus at equilibrium, the majority of individuals have the optimal genotype. A small proportion of individuals, however, have other genotypes. These are newly arisen mutants who will not survive to the next generation. In a separate model, we again take the limit Ω→∞, but in this case we decrease the standard deviation of mutant effects on each character, so that mutations are generally not lethal. In this case we find that, at equilibrium, the distribution of genotypes and the distribution of fitnesses have unusual features. In particular, the marginal distribution of genotypic values of any single character has the form of a single sharp "spike" (Dirac delta function) corresponding to all individuals having an optimal value of the character. Despite the applicability of this for all characters, there still is variation in fitness over the population and the distribution of fitnesses consists of a series of sharp "spikes" at particular levels of fitness. This type of distribution arises at equilibrium even if a wide variety of genotypes are initially present.