A solution of the Crow-Kimura evolution model on fluctuating fitness landscape

Abstract

We consider the Crow-Kimura model in case of random transitions between different fitness landscapes. The epochs (system has constant in time fitness landscape) length is given by an exponential distribution. To solve the model exactly we need a large system of functional equations. We solve the model approximately at the limits of slow or fast transitions, calculating the first-order corrections via the transition rate or its inverse. We consider the case of slow transitions and find that the mean fitness equals the average fitness for the evolution on the static fitness landscapes, minus some quantity, which we call a load. While calculating the load, we speculate about the analogy with information thermodynamics. We also look at the model with few genes and identify exact transition points to the transient phase.