Fisher's Geometrical Model of Evolutionary Adaptation - Beyond Spherical Geometry

D. Waxman

Journal of Theoretical Biology: 241: 887-895 (2006)

Centre for the Study of Evolution, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QG, United Kingdom.

Fisher's geometrical model of evolutionary adaptation has recently been used in a variety of contexts of interest to evolutionary biologists. The renewed interest in this model strongly motivates generalisations that make it a more realistic description of evolutionary adaptation. Previously, the distribution of mutant effects has, for analytical tractability, rather than biological realism, been taken as spherically symmetric. Here we substantially extend Fisher's model, by allowing a wider class of mutational distributions that incorporate mutational bias and more general deviations from spherical symmetry such as correlations between mutant effects. We also incorporate work on generalised fitness landscapes, thereby reducing the number of artificial assumptions underlying the model. The generalised model exhibits a substantially increased flexibility and a far richer underlying geometry. We find that the distribution characterising selection coefficients of new mutations is expressed in terms of a number of geometrical invariants associated with mutation, selection and the parental phenotype.