Critical rates of climate warming and abrupt collapse of ecosystems

Kaur, Taranjot; Dutta, Partha Sharathi

doi:10.1098/rspa.2022.0086

Cited by 3 publications

(2 citation statements)

References 60 publications

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“…sudden dramatic changes in population size, generally toward much lower numbers) has been well-explained in models with bistability between two stationary base states (Dakos et al, 2019). These two states could be, for example, a high population coexistence state and either a low population coexistence state or a state with extinction of one or both populations (Kaur & Sharathi, 2022;O'Keeffe & Wieczorek, 2019;Osmond & Klausmeier, 2017;Vanselow et al, 2019Vanselow et al, , 2022. However, little is known about the effects of climate change on systems whose base state is oscillatory (Bathiany et al, 2018;Sauvé et al, 2020).…”

Section: Discussionmentioning

confidence: 99%

Stochastic resonance in climate reddening increases the risk of cyclic ecosystem extinction via phase‐tipping

Alkhayuon

Marley

Wieczorek

et al. 2023

Global Change Biology

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The rate of switching between these climate regimes can be plotted to determine the expected number of years when conditions will remain either in a low productivity state, or a high productivity state. Excessively long series of years under one type of climate, such as that experienced during the extended drought of the Great Depression in North America, can occur but are unusual under typical variability. Much attention has been given to the fact that anthropogenic climate change (henceforth, climate change) is resulting in a gradual warming of global mean temperatures. Climate change, however, is also altering the climatic variability, that is, climate variations on the scale of years (also called environmental stochasticity). Existing work has shown that alterations in climatic variability can have much

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Section: Discussionmentioning

confidence: 99%

Stochastic resonance in climate reddening increases the risk of cyclic ecosystem extinction via phase‐tipping

Alkhayuon

Marley

Wieczorek

et al. 2023

Global Change Biology

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show abstract

“…Such systems may not even have any critical levels of the external input, but they may have critical rates of change of the external input: they suddenly and unexpectedly move to a different state if the external input changes faster than some critical rate. Although critical rates are less understood than critical levels, they are equally relevant and ubiquitous [6,8,9,12,14,25,62,63,74,82,85,86,88,92,96,110,114,121,[126][127][128][129]131]. In particular, critical rates are of special interest in climate science and ecology in the contexts of global warming, increasing climate variability, and ensuing failure to adapt to changing external conditions: the moving stable state is continuously available, but the system is unable to adjust to its changing position when the change happens slowly but too fast.…”

Section: Motivation: Critical Factors and R-tippingmentioning

confidence: 99%

Rate-induced tipping: thresholds, edge states and connecting orbits

2023

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Rate-induced tipping (R-tipping) occurs when time-variation of input parameters of a dynamical system interacts with system timescales to give genuine nonautonomous instabilities. Such instabilities appear as the input varies at some critical rates and cannot, in general, be understood in terms of autonomous bifurcations in the frozen system with a fixed-in-time input. This paper develops an accessible mathematical framework for R-tipping in multidimensional nonautonomous dynamical systems with an autonomous future limit. We focus on R-tipping via loss of tracking of base attractors that are equilibria in the frozen system, due to crossing what we call regular R-tipping thresholds. These thresholds are anchored at infinity by regular R-tipping edge states: compact normally hyperbolic invariant sets of the autonomous future limit system that have one unstable direction, orientable stable manifold, and lie on a basin boundary. We define R-tipping and critical rates for the nonautonomous system in terms of special solutions that limit to a compact invariant set of the autonomous future limit system that is not an attractor. We focus on the case when the limit set is a regular edge state, introduce the concept of edge tails, and rigorously classify R-tipping into reversible, irreversible, and degenerate cases. The central idea is to use the autonomous dynamics of the future limit system to analyse R-tipping in the nonautonomous system. We compactify the original nonautonomous system to include the limiting autonomous dynamics. Considering regular R-tipping edge states that are equilibria allows us to prove two results. First, we give sufficient conditions for the occurrence of R-tipping in terms of easily testable properties of the frozen system and input variation. Second, we give necessary and sufficient conditions for the occurrence of reversible and irreversible R-tipping in terms of computationally verifiable (heteroclinic) connections to regular R-tipping edge states in the autonomous compactified system.

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Rate-induced tipping in natural and human systems

Ritchie¹,

Alkhayuon²,

Cox³

et al. 2023

Earth Syst. Dynam.

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Abstract. Over the last 2 decades, tipping points in open systems subject to changing external conditions have become a topic of a heated scientific debate due to the devastating consequences that they may have on natural and human systems. Tipping points are generally believed to be associated with a system bifurcation at some critical level of external conditions. When changing external conditions across a critical level, the system undergoes an abrupt transition to an alternative, and often less desirable, state. The main message of this paper is that the rate of change in external conditions is arguably of even greater relevance in the human-dominated Anthropocene but is rarely examined as a potential sole mechanism for tipping points. Thus, we address the related phenomenon of rate-induced tipping: an instability that occurs when external conditions vary faster, or sometimes slower, than some critical rate, usually without crossing any critical levels (bifurcations). First, we explain when to expect rate-induced tipping. Then, we use three illustrative and distinctive examples of differing complexity to highlight the universal and generic properties of rate-induced tipping in a range of natural and human systems.

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Critical rates of climate warming and abrupt collapse of ecosystems

Cited by 3 publications

References 60 publications

Stochastic resonance in climate reddening increases the risk of cyclic ecosystem extinction via phase‐tipping

Stochastic resonance in climate reddening increases the risk of cyclic ecosystem extinction via phase‐tipping

Rate-induced tipping: thresholds, edge states and connecting orbits

Rate-induced tipping in natural and human systems

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