Spatial signatures of resilience

Abstract

Predicting when the dynamics of a complex system will undergo a sudden transition is difficult. New experiments show that the spatial distribution of organisms can indicate when such tipping points are near. See Letter p.355 The behaviour of complex systems near tipping points, where a small change can lead to a large shift in the state of the system, is notoriously difficult to predict. Recent studies have identified temporal factors such as recovery time and changes in size and timescale of fluctuations that precede some tipping points. Lei Dai et al. grew populations of the budding yeast that were spatially connected through controlled dispersal between nearest neighbours, and looked for spatiotemporal patterns that anticipated population collapse after perturbation — the introduction of sucrose solution more highly diluted than its surroundings. As the distance from the diluted patch increased, yeast population density increased towards a steady state. The distance required for recovery by connected populations was much greater when populations were close to collapse. This work introduces the concept of 'recovery length' as a spatial counterpart to recovery time, and as boundaries between regions of different quality are ubiquitous in nature, many systems in the oceans and on land might be expected to be subject to such spatial instability.