Preferential attachment renders an evolving network of populations robust against crashes

TL;DR

This paper demonstrates that preferential attachment in evolving networks of chemical populations leads to the rapid formation of autocatalytic sets and significantly enhances stability against crashes compared to random attachment, due to a dense core structure.

Contribution

It introduces a model combining population dynamics and preferential attachment, showing improved stability and autocatalytic set formation in evolving chemical networks.

Findings

Preferential attachment accelerates autocatalytic set formation.

Networks with preferential attachment are more crash-resistant.

A dense core with loops underpins network stability.

Abstract

We study a model for the evolution of chemical species under a combination of population dynamics on a short time scale and a selection mechanism on a longer time scale. Least fit nodes are replaced by new nodes whose links are attached to the nodes of the given network via preferential attachment. In contrast to a random attachment of newly incoming nodes that was used in previous work, this preferential attachment mechanism accelerates the generation of a so-called autocatalytic set after a start from a random geometry and the growth of this structure until it saturates in a stationary phase in which the whole system is an autocatalytic set. Moreover, the system in the stationary phase becomes much more stable against crashes in the population size as compared to random attachment. We explain in detail in terms of graph theoretical notions which structure of the resulting network is responsible for this stability. Essentially it is a very dense core with many loops and less nodes playing the role of a keystone that prevents the system against crashes almost completely.