The optimization and shock waves in evolution dynamics

TL;DR

This paper analyzes the complex evolution dynamics in infinite populations, revealing exact solutions for shock wave phenomena and optimal mutation rates in smooth fitness landscapes, especially in large genome limits.

Contribution

It provides the first exact analytical solutions for discontinuous evolution dynamics and identifies optimal mutation rates in symmetric fitness landscapes.

Findings

Exact solutions for shock wave dynamics in evolution models.

Optimal mutation rates for rapid population convergence.

Single peak fitness landscapes facilitate fastest evolution.

Abstract

We consider the optimal dynamics in the infinite population evolution models with general symmetric fitness landscape. The search of optimal evolution trajectories are complicated due to sharp transitions (like shock waves) in evolution dynamics with smooth fitness landscapes, which exist even in case of popular quadratic fitness. We found exact analytical solutions for discontinuous dynamics at the large genome length limit. We found the optimal mutation rates for the fixed fitness landscape. The single peak fitness landscape gives the fastest dynamics to send the vast majority of the population from the initial sequence to the neighborhood of the final sequence.