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

¹ Auriga Inc. - 400 TradeCenter, Ste 5900 Woburn, MA 01801, USA
² A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation - 2 Alikhanian Brothers St., Yerevan 375036, Armenia
³ Biodesign Center for Mechanisms of Evolution, Arizona State University - Tempe, AZ, 85287, USA

^(a) E-mail: saakian@yerphi.am (corresponding author)

Received: 27 November 2022
Accepted: 17 May 2023

Abstract

The article discusses the Crow-Kimura model in the context of random transitions between different fitness landscapes. The duration of epochs, during which the fitness landscape is constant over time, is modeled by an exponential distribution. To obtain an exact solution, a system of functional equations is required. However, to approximate the model, we consider the cases of slow or fast transitions and calculate the first-order corrections using either the transition rate or its inverse. Specifically, we focus on the case of slow transitions and find that the average fitness is equal to the average fitness for evolution on static fitness landscapes, but with the addition of a load term. We also investigate the model for a small number of genes and identify the exact transition points to the transient phase.