Alternative stable states, tipping points, and early warning signals of ecological transitions

2020 ◽  
pp. 263-284
Author(s):  
John M. Drake ◽  
Suzanne M. O’Regan ◽  
Vasilis Dakos ◽  
Sonia Kéfi ◽  
Pejman Rohani
Keyword(s):  
Early Warning ◽  
Alternative Stable States ◽  
Intrinsic Noise ◽  
Point Theory ◽  
Ecological Systems ◽  
Tipping Point ◽  
Stable States ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Theoretical Predictions

Ecological systems are prone to dramatic shifts between alternative stable states. In reality, these shifts are often caused by slow forces external to the system that eventually push it over a tipping point. Theory predicts that when ecological systems are brought close to a tipping point, the dynamical feedback intrinsic to the system interact with intrinsic noise and extrinsic perturbations in characteristic ways. The resulting phenomena thus serve as “early warning signals” for shifts such as population collapse. In this chapter, we review the basic (qualitative) theory of such systems. We then illustrate the main ideas with a series of models that both represent fundamental ecological ideas (e.g. density-dependence) and are amenable to mathematical analysis. These analyses provide theoretical predictions about the nature of measurable fluctuations in the vicinity of a tipping point. We conclude with a review of empirical evidence from laboratory microcosms, field manipulations, and observational studies.

scholarly journals Relation between stability and resilience determines the performance of early warning signals under different environmental drivers

2015 ◽  
Vol 112 (32) ◽  
pp. 10056-10061 ◽  
Author(s):  
Lei Dai ◽  
Kirill S. Korolev ◽  
Jeff Gore
Keyword(s):  
Early Warning ◽  
Alternative Stable States ◽  
Basin Of Attraction ◽  
Environmental Drivers ◽  
Ecological Communities ◽  
Stable States ◽  
Warning Signals ◽  
Early Warning Signals ◽  
The Stability ◽  
Stability And Resilience

Shifting patterns of temporal fluctuations have been found to signal critical transitions in a variety of systems, from ecological communities to human physiology. However, failure of these early warning signals in some systems calls for a better understanding of their limitations. In particular, little is known about the generality of early warning signals in different deteriorating environments. In this study, we characterized how multiple environmental drivers influence the dynamics of laboratory yeast populations, which was previously shown to display alternative stable states [Dai et al., Science, 2012]. We observed that both the coefficient of variation and autocorrelation increased before population collapse in two slowly deteriorating environments, one with a rising death rate and the other one with decreasing nutrient availability. We compared the performance of early warning signals across multiple environments as “indicators for loss of resilience.” We find that the varying performance is determined by how a system responds to changes in a specific driver, which can be captured by a relation between stability (recovery rate) and resilience (size of the basin of attraction). Furthermore, we demonstrate that the positive correlation between stability and resilience, as the essential assumption of indicators based on critical slowing down, can break down in this system when multiple environmental drivers are changed simultaneously. Our results suggest that the stability–resilience relation needs to be better understood for the application of early warning signals in different scenarios.

scholarly journals Early warning signals of tipping points in periodically forced systems

2016 ◽  
Vol 7 (2) ◽  
pp. 313-326 ◽  
Author(s):  
Mark S. Williamson ◽  
Sebastian Bathiany ◽  
Timothy M. Lenton
Keyword(s):  
Sea Ice ◽  
Early Warning ◽  
Tipping Point ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
System Response ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Arctic Sea

Abstract. The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we use alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose timescale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. For these systems, phase lag and amplification of the system response can provide early warning signals, based on a linear dynamics approximation. Furthermore, the Fourier spectrum of the system's time series reveals harmonics of the forcing period in the system response whose amplitude is related to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators as well as a return map analysis to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation.

scholarly journals Early warnings and missed alarms for abrupt monsoon transitions

2015 ◽  
Vol 11 (12) ◽  
pp. 1621-1633 ◽  
Author(s):  
Z. A. Thomas ◽  
F. Kwasniok ◽  
C. A. Boulton ◽  
P. M. Cox ◽  
R. T. Jones ◽  
...  
Keyword(s):  
Early Warning ◽  
Asian Summer Monsoon ◽  
System Stability ◽  
Multiple Model ◽  
Glacial Cycle ◽  
Stable States ◽  
Warning Signals ◽  
Data Set ◽  
Early Warning Signals ◽  
Model Simulations

Abstract. Palaeo-records from China demonstrate that the East Asian Summer Monsoon (EASM) is dominated by abrupt and large magnitude monsoon shifts on millennial timescales, switching between periods of high and weak monsoon rains. It has been hypothesized that over these timescales, the EASM exhibits two stable states with bifurcation-type tipping points between them. Here we test this hypothesis by looking for early warning signals of past bifurcations in speleothem δ18O records from Sanbao Cave and Hulu Cave, China, spanning the penultimate glacial cycle. We find that although there are increases in both autocorrelation and variance preceding some of the monsoon transitions during this period, it is only immediately prior to the abrupt monsoon shift at the penultimate deglaciation (Termination II) that statistically significant increases are detected. To supplement our data analysis, we produce and analyse multiple model simulations that we derive from these data. We find hysteresis behaviour in our model simulations with transitions directly forced by solar insolation. However, signals of critical slowing down, which occur on the approach to a bifurcation, are only detectable in the model simulations when the change in system stability is sufficiently slow to be detected by the sampling resolution of the data set. This raises the possibility that the early warning "alarms" were missed in the speleothem data over the period 224–150 kyr and it was only at the monsoon termination that the change in the system stability was sufficiently slow to detect early warning signals.

scholarly journals Deep learning for early warning signals of regime shifts

2021 ◽  
Author(s):  
Thomas Bury ◽  
Raman Sujith ◽  
Induja Pavithran ◽  
Marten Scheffer ◽  
Timothy Lenton ◽  
...  
Keyword(s):  
Deep Learning ◽  
Early Warning ◽  
Normal Forms ◽  
Learning Algorithm ◽  
Tipping Point ◽  
Regime Shifts ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Deep Learning Algorithm

Many natural systems exhibit regime shifts where slowly changing environmental conditions suddenly shift the system to a new and sometimes very different state. As the tipping point is approached, the dynamics of complex and varied systems all simplify down to a small number of possible 'normal forms' that determine how the new regime will look. Indicators such as increasing lag-1 autocorrelation and variance provide generic early warning signals (EWS) by detecting how dynamics slow down near the tipping point. But they do not indicate what type of new regime will emerge. Here we develop a deep learning algorithm that can detect EWS in systems it was not explicitly trained on, by exploiting information about normal forms and scaling behaviour of dynamics near tipping points that are common to many dynamical systems. The algorithm detects EWS in 268 empirical and model time series from ecology, thermoacoustics, climatology, and epidemiology with much greater sensitivity and specificity than generic EWS. It can also predict the normal form that will characterize the oncoming regime shift. Such approaches can help humans better manage regime shifts. The algorithm also illustrates how a universe of possible models can be mined to recognize naturally-occurring tipping points.

scholarly journals Early-Warning Signals for the Onsets of Greenland Interstadials and the Younger Dryas–Preboreal Transition

2016 ◽  
Vol 29 (11) ◽  
pp. 4047-4056 ◽  
Author(s):  
Martin Rypdal
Keyword(s):  
Time Scales ◽  
Early Warning ◽  
High Frequency ◽  
Characteristic Time ◽  
Younger Dryas ◽  
Tipping Point ◽  
Warning Signals ◽  
Correlation Times ◽  
Early Warning Signals ◽  
Slowing Down

Abstract The climate system approaches a tipping point if the prevailing climate state loses stability, making a transition to a different state possible. A result from the theory of randomly driven dynamical systems is that the reduced stability in the vicinity of a tipping point is accompanied by increasing fluctuation levels and longer correlation times (critical slowing down) and can in principle serve as early-warning signals of an upcoming tipping point. This study demonstrates that the high-frequency band of the δ18O variations in the North Greenland Ice Core Project displays fluctuation levels that increase as one approaches the onset of an interstadial (warm) period. Similar results are found for the locally estimated Hurst exponent for the high-frequency fluctuations, signaling longer correlation times. The observed slowing down is found to be even stronger in the Younger Dryas, suggesting that both the Younger Dryas–Preboreal transition and the onsets of the Greenland interstadials are preceded by decreasing stability of the climate state. It is also verified that the temperature fluctuations during the stadial periods can be approximately modeled as a scale-invariant persistent noise, which can be approximated as an aggregation of processes that respond to perturbations on certain characteristic time scales. The results are consistent with the hypothesis that both the onsets of the Greenland interstadials and the Younger Dryas–Preboreal transition are caused by tipping points in dynamical processes with characteristic time scales on the order of decades and that the variability of other processes on longer time scales masks the early-warning signatures in the δ18O signal.

scholarly journals Early warning signals of tipping points in periodically forced systems

2015 ◽  
Vol 6 (2) ◽  
pp. 2243-2272 ◽  
Author(s):  
M. S. Williamson ◽  
S. Bathiany ◽  
T. M. Lenton
Keyword(s):  
Sea Ice ◽  
Early Warning ◽  
Tipping Point ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
System Response ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Arctic Sea

Abstract. The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much recent interest. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we find alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose time scale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. We show that the phase lag and amplification of the system response provide early warning signals, based on a linear dynamics approximation. Furthermore, the power spectrum of the system's time series reveals the generation of harmonics of the forcing period, the size of which are proportional to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation.

scholarly journals Early warning signals in complex ecosystems

2015 ◽  
Vol 6 (2) ◽  
pp. 2507-2542 ◽  
Author(s):  
I. S. Weaver ◽  
J. G. Dyke
Keyword(s):  
Early Warning ◽  
Warning Signal ◽  
Ecosystem Model ◽  
Robust Methods ◽  
Stable States ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Critical Transitions ◽  
Rapid Changes ◽  
External Driving

Abstract. Given the potential for elements of the Earth system to undergo rapid, hard to reverse changes in state, there is a pressing need to establish robust methods to produce early warning signals of such events. Here we present a conceptual ecosystem model in which a diversity of stable states emerge, along with rapid changes, referred to as critical transitions, as a consequence of external driving and non-linear ecological dynamics. We are able to produce robust early warning signals that precede critical transitions. However, we show that there is no correlation between the magnitude of the signal and magnitude or reversibility of any individual critical transition. We discuss these findings in the context of ecosystem management prior to and post critical transitions. We argue that an understanding of the dynamics of the systems is necessary both for management prior and post critical transitions and the effective interpretation of any early warning signal that may be produced for that system.

scholarly journals Spatial Correlation as an Early Warning Signal of Regime Shifts in a Multiplex Disease-Behaviour Network

2017 ◽  
Author(s):  
Peter C. Jentsch ◽  
Madhur Anand ◽  
Chris T. Bauch
Keyword(s):  
Spatial Correlation ◽  
Early Warning ◽  
Regime Shift ◽  
Tipping Point ◽  
Regime Shifts ◽  
Critical Slowing Down ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Network Layer ◽  
Slowing Down

AbstractEarly warning signals of sudden regime shifts are a widely studied phenomenon for their ability to quantify a system’s proximity to a tipping point to a new and contrasting dynamical regime. However, this effect has been little studied in the context of the complex interactions between disease dynamics and vaccinating behaviour. Our objective was to determine whether critical slowing down (CSD) occurs in a multiplex network that captures opinion propagation on one network layer and disease spread on a second network layer. We parameterized a network simulation model to represent a hypothetical self-limiting, acute, vaccine-preventable infection with shortlived natural immunity. We tested five different network types: random, lattice, small-world, scale-free, and an empirically derived network. For the first four network types, the model exhibits a regime shift as perceived vaccine risk moves beyond a tipping point from full vaccine acceptance and disease elimination to full vaccine refusal and disease endemicity. This regime shift is preceded by an increase in the spatial correlation in non-vaccinator opinions beginning well before the bifurcation point, indicating CSD. The early warning signals occur across a wide range of parameter values. However, the more gradual transition exhibited in the empirically-derived network underscores the need for further research before it can be determined whether trends in spatial correlation in real-world social networks represent critical slowing down. The potential upside of having this monitoring ability suggests that this is a worthwhile area for further research.

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