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

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 TS, and the genotypes evolve under temperature TJ, according to the evolutionary fitness. It is found that adaptation occurs at TS < TRSS, and a replica symmetric phase emerges at TRSBS < TS < TRSS. The replica symmetric phase implies canalization, and replica symmetry breaking at lower temperatures indicates loss of robustness.