Criticality in Simple Models of Evolution

TL;DR

This paper reexamines two models of biological evolution claimed to show self-organized criticality, revealing their differences, limitations of mean field analysis, and proposing clearer criteria for defining self-organized criticality.

Contribution

It provides a detailed reanalysis of two evolution models, introduces new analytic results, and discusses the need for a more precise definition of self-organized criticality.

Findings

Models are qualitatively different upon reanalysis

Mean field description has limitations

Proposes criteria for self-organized criticality

Abstract

We consider two, apparently similar, models of biological evolution which have been claimed to exhibit self-organized critical behaviour. A careful reanalysis of these models, including several new analytic results for one of them, suggests that they are qualitatively different. We demonstrate the limitations of the mean field description of these systems. We argue that a more precise definition of self-organized criticality is desirable and establish several criteria in this connection.