Critical Exponent of Species-Size Distribution in Evolution

TL;DR

This paper investigates the emergence of scale-free distributions in evolving populations of self-replicating genomes, identifying critical exponents related to avalanches in systems with phase transitions.

Contribution

It reveals how a power-law distribution arises in complex landscapes with separated time scales and determines the critical exponent for avalanche sizes in such systems.

Findings

Scale-free distributions emerge in certain evolutionary regimes.

The critical exponent of avalanche sizes is quantitatively determined.

A separation of time scales underpins the emergence of power-law behavior.

Abstract

We analyze the geometry of the species- and genotype-size distribution in evolving and adapting populations of single-stranded self-replicating genomes: here programs in the Avida world. We find that a scale-free distribution (power law) emerges in complex landscapes that achieve a separation of two fundamental time scales: the relaxation time (time for population to return to equilibrium after a perturbation) and the time between mutations that produce fitter genotypes. The latter can be dialed by changing the mutation rate. In the scaling regime, we determine the critical exponent of the distribution of sizes and strengths of avalanches in a system without coevolution, described by first-order phase transitions in single finite niches.