Error threshold in simple landscapes

TL;DR

This paper analyzes the error threshold phenomenon in simple fitness landscapes, showing it behaves like a first-order phase transition with a sudden loss of genetic overlap.

Contribution

It demonstrates that the error threshold in both master sequence and REM landscapes is analogous to a first-order thermodynamic transition.

Findings

Error threshold is a first-order transition

Overlap drops discontinuously at the threshold

Applicable to both master sequence and REM landscapes

Abstract

We consider the quasispecies description of a population evolving in both the "master sequence" landscape (where a single sequence is evolutionarily preferred over all others) and the REM landscape (where the fitness of different sequences is an independent, identically distributed, random variable). We show that, in both cases, the error threshold is analogous to a first order thermodynamical transition, where the overlap between the average genotype and the optimal one drops discontinuously to zero.