Replica symmetry breaking in an adiabatic spin-glass model of adaptive evolution

TL;DR

This paper models adaptive evolution using a spin-glass framework, revealing how robustness and canalization emerge through replica symmetry phases and their breaking at different temperatures.

Contribution

It introduces a novel spin-glass model with dynamic spins and interactions to study evolutionary canalization and robustness.

Findings

Adaptation occurs at temperature T_S below T_S^{RS}

A replica symmetric phase indicates canalization

Replica symmetry breaking signifies loss of robustness

Abstract

We study evolutionary canalization using a spin-glass model with replica theory, where spins and their interactions are dynamic variables whose configurations correspond to phenotypes and genotypes, respectively. The spins are updated under temperature T_S, and the genotypes evolve under temperature T_J, according to the evolutionary fitness. It is found that adaptation occurs at T_S < T_S^{RS}, and a replica symmetric phase emerges at T_S^{RSB} < T_S < T_S^{RS}. The replica symmetric phase implies canalization, and replica symmetry breaking at lower temperatures indicates loss of robustness.