Applicability of spatial early warning signals to complex network dynamics

TL;DR

This study evaluates the effectiveness of spatial early warning signals across different network types, revealing their variable performance depending on network structure and tipping scenarios, with better reliability on complex networks than regular lattices.

Contribution

It provides a comprehensive analysis of six spatial EWSs on diverse networks, highlighting their differing performances and the influence of network topology on warning signal reliability.

Findings

Spatial EWSs outperform in complex networks compared to lattice networks.

Coefficient of variation and spatial skewness are the most effective EWSs.

Performance of EWSs varies with tipping scenarios.

Abstract

Early warning signals (EWSs) for complex dynamical systems aim to anticipate tipping points before they occur. While signals computed from time series data, such as temporal variance, are useful for this task, they are costly to obtain in practice because they need many samples over time to calculate. Spatial EWSs use just a single sample per spatial location and aggregate the samples over space rather than time to try to mitigate this limitation. However, although many complex systems in nature and society form diverse networks, the performance of spatial EWSs is mostly unknown for general networks because the vast majority of studies of spatial EWSs have been on regular lattice networks. Therefore, we have carried out a comprehensive investigation of six major spatial EWSs on various networks. We find that the winning EWS depends on tipping scenarios, although the coefficient of variation and spatial skewness tend to outperform alternative EWSs. We also find that spatial EWSs behave in a drastically different manner between the square lattice and complex networks and tend to be more reliable for the latter than the former. The present results encourage further studies of spatial EWSs on complex networks.