A solvable model of the evolutionary loop

TL;DR

This paper introduces and solves a model describing how finite populations evolve in rugged fitness landscapes, highlighting the dynamics of stasis and adaptive walks and their dependence on population parameters.

Contribution

It provides a solvable mathematical model capturing the evolutionary loop dynamics, including stasis and adaptation phases, in rugged fitness landscapes.

Findings

Average rarity depends on population size and mutation rate.

Duration of stasis phases varies with population parameters.

Model predicts the timing of adaptive walks in finite populations.

Abstract

A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The dependence of the average rarity of the population (a quantity related to the fitness of the most adapted individual) and of the duration of stases on population size and mutation rate is calculated.