Fixation Probability of a Mutant in the Wright–Fisher Model under Strong Selection and Fluctuating Fitness Landscape

The goal of this work is to calculate the fixation probability of a mutant on a fluctuating landscape, in particular, for the intermediate regime of parameters when selection and landscape fluctuations compete against each other. We derive the master equation for the fluctuating landscape, similar to the discrete version of a cross-diffusive process. Assuming an exponential ansatz for the fixation probability as a function of the number of new mutants at the start of evolution, we calculate the allele fixation probability for fluctuating fitness landscapes using a third order algebraic equation.