Extending he canonical equation of adaptive dynamics to Mendelian populations with any population structure: replace the population size by the effective population size from population genetics

Last modified: 2014-06-09

#### Abstract

One of the powerful tools of adaptive dynamics is its so-called Canonical Equation, a differential equation describing how the trait vector prevailing in a population changes over evolutionary time. The CE is derived from an underlying individual-based model using two simplifying assumptions, separation of population dynamical and mutational timescales, and small mutational steps. This was done in 1996 for clonally reproducing individuals with the simplest possible life histories, with mathematical rigour added in 2003. The CE’s reach was extended to structured populations in 2008 and to Mendelian diploids in 2013. All the different extensions only differ in the value of some scalar terms. In this talk it will be argued that the product of these scalar terms multiplied with the population size exactly equal the effective population size from population genetics theory. This follows by linking the mutant invasion probabilities calculated from the branching process approximation used in the derivation of the CE with a diffusion approximation for the mutant frequency as this occurs in population genetics."