A model with Darwinian dynamics on a rugged landscape

TL;DR

This paper models population dynamics on a rugged fitness landscape using Darwinian principles, revealing a phase diagram with a glass phase where the system optimally searches for solutions, and a phase where mutations hinder progress.

Contribution

It introduces a novel phase diagram for population dynamics on complex landscapes, linking evolutionary processes with concepts from condensed matter physics.

Findings

Identification of a glass phase with optimal search behavior

Demonstration of a phase transition influenced by population size and diffusion rate

Analogy between evolutionary dynamics and dense active matter systems

Abstract

We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase diagram in terms of the size of the population and the diffusion rate, with a glass phase inside which the dynamics keeps searching for better configurations, and outside which deleterious `mutations' spoil the performance. The phase diagram is analogous to that of dense active matter in terms of temperature and drive.