Evolution in complex systems

TL;DR

This paper proposes that slow, directed dynamics driven by strain release and record statistics are fundamental features of complex systems, demonstrated through models of superconductors and ecological evolution.

Contribution

It introduces a focus on slow, decelerating dynamics and strain release as key features of complexity, supported by analysis of two distinct systems.

Findings

Evidence of record statistics in system variables

Log-Poisson statistics for quake event times

Demonstration of ageing phenomena in models

Abstract

What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analysed to confirm this effect. The strain arises from local frustration. As the strain is released through "quakes", some system variable undergoes record statistics with accompanying log-Poisson statistics for the quake event times[4]. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology, and show how quantitative indications of ageing can be found.