Evolve Networks Towards Better Performance: a Compromise between Mutation and Selection

TL;DR

This paper investigates how the interplay between mutation and selection influences network evolution, revealing a balance point and conditions under which either mutation or selection dominates, affecting network performance and structure.

Contribution

It introduces a simple model to analyze the balance between mutation and selection in network evolution, highlighting how timescales influence the dominant mechanism and network properties.

Findings

When optimal networks deviate from mutation-only steady states, evolution balances mutation and selection.

If mutation timescale is comparable to dynamical processes, mutation mainly determines the steady state.

Longer mutation timescales lead to selection-dominated evolution with improved performance and heterogeneity.

Abstract

The interaction between natural selection and random mutation is frequently debated in recent years. Does similar dilemma also exist in the evolution of real networks such as biological networks? In this paper, we try to discuss this issue by a simple model system, in which the topological structure of networks is repeatedly modified and selected in order to make them have better performance in dynamical processes. Interestingly, when the networks with optimal performance deviate from the steady state networks under pure mutations, we find the evolution behaves as a balance between mutation and selection. Furthermore, when the timescales of mutations and dynamical processes are comparable with each other, the steady state of evolution is mainly determined by mutation. On the opposite side, when the timescale of mutations is much longer than that of dynamical processes, selection dominates the evolution and the steady-state networks turn to have much improved performance and highly heterogeneous structures. Despite the simplicity of our model system, this finding could give useful indication to detect the underlying mechanisms that rein the evolution of real systems.