Universality of noise-induced resilience restoration in spatially-extended ecological systems

AbstractMany systems may switch to an undesired state due to internal failures or external perturbations, of which critical transitions toward degraded ecosystem states are prominent examples. Resilience restoration focuses on the ability of spatially-extended systems and the required time to recover to their desired states under stochastic environmental conditions. The difficulty is rooted in the lack of mathematical tools to analyze systems with high dimensionality, nonlinearity, and stochastic effects. Here we show that nucleation theory can be employed to advance resilience restoration in spatially-embedded ecological systems. We find that systems may exhibit single-cluster or multi-cluster phases depending on their sizes and noise strengths. We also discover a scaling law governing the restoration time for arbitrary system sizes and noise strengths in two-dimensional systems. This approach is not limited to ecosystems and has applications in various dynamical systems, from biology to infrastructural systems.

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Detecting, anticipating, and predicting critical transitions in spatially extended systems

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.5022189 ◽

2018 ◽

Vol 28 (3) ◽

pp. 033614 ◽

Cited By ~ 4

Author(s):

Frank Kwasniok

Keyword(s):

Extended Systems ◽

Critical Transitions ◽

Spatially Extended ◽

Spatially Extended Systems

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Critical transitions in Chinese dunes during the past 12,000 years

Science Advances ◽

10.1126/sciadv.aay8020 ◽

2020 ◽

Vol 6 (9) ◽

pp. eaay8020 ◽

Cited By ~ 5

Author(s):

Zhiwei Xu ◽

Joseph A. Mason ◽

Chi Xu ◽

Shuangwen Yi ◽

Sebastian Bathiany ◽

...

Keyword(s):

Alternative Stable States ◽

Northern China ◽

Hysteretic Behavior ◽

Stable States ◽

The Past ◽

Critical Transitions ◽

Smooth Change ◽

Spatially Extended ◽

Spatially Extended Systems ◽

Dune Dynamics

Dune systems can have alternative stable states that coexist under certain environmental conditions: a vegetated, stabilized state and a bare active state. This behavior implies the possibility of abrupt transitions from one state to another in response to gradual environmental change. Here, we synthesize stratigraphic records covering 12,000 years of dynamics of this system at 144 localities across three dune fields in northern China. We find side-by-side coexistence of active and stabilized states, and occasional sharp shifts in time between those contrasting states. Those shifts occur asynchronously despite the fact that the entire landscape has been subject to the same gradual changes in monsoon rainfall and other conditions. At larger scale, the spatial heterogeneity in dune dynamics averages out to produce relatively smooth change. However, our results do show different paths of recovery and collapse of vegetation at system-wide scales, implying that hysteretic behavior occurs in spatially extended systems.

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