Emergence of cascading dynamics in interacting tipping elements of ecology and climate

Multistability and intermediate tipping of the Atlantic Ocean circulation

Tipping points (TP) in climate subsystems are usually thought to occur at a well-defined, critical forcing parameter threshold, via destabilization of the system state by a single, dominant positive feedback. However, coupling to other subsystems, additional feedbacks, and spatial heterogeneity may promote further small-amplitude, abrupt reorganizations of geophysical flows at forcing levels lower than the critical threshold. Using a primitive-equation ocean model, we simulate a collapse of the Atlantic Meridional Overturning Circulation (AMOC) due to increasing glacial melt. Considerably before the collapse, various abrupt, qualitative changes in AMOC variability occur. These intermediate tipping points (ITP) are transitions between multiple stable circulation states. Using 2.75 million years of model simulations, we uncover a very rugged stability landscape featuring parameter regions of up to nine coexisting stable states. The path to an AMOC collapse via a sequence of ITPs depends on the rate of change of the meltwater input. This challenges our ability to predict and define safe limits for TPs.

Remotely sensing potential climate change tipping points across scales

Potential climate tipping points pose a growing risk for societies, and policy is calling for improved anticipation of them. Satellite remote sensing can play a unique role in identifying and anticipating tipping phenomena across scales. Where satellite records are too short for temporal early warning of tipping points, complementary spatial indicators can leverage the exceptional spatial-temporal coverage of remotely sensed data to detect changing resilience of vulnerable systems. Combining Earth observation with Earth system models can improve process-based understanding of tipping points, their interactions, and potential tipping cascades. Such fine-resolution sensing can support climate tipping point risk management across scales.

Variation in environmental stochasticity dramatically affects viability and extinction time in a predator-prey system with high prey group cohesion

Understanding how tipping points arise is critical for population protection and ecosystem robustness. This work evaluates the impact of environmental stochasticity on the emergence of tipping points in a predator-prey system subject to the Allee effect and Holling type IV functional response, modeling an environment in which the prey has high group cohesion. We analyze the relationship between stochasticity and the probability and time that predator and prey populations in our model tip between different steady states. We evaluate the safety from extinction of different population values for each species, and accordingly assign extinction warning levels to these population values. Our analysis suggests that the effects of environmental stochasticity on tipping phenomena are scenario-dependent but follow a few interpretable trends. The probability of tipping towards a steady state in which one or both species go extinct generally monotonically increased with noise intensity, while the probability of tipping towards a more favorable steady state (in which more species were viable) usually peaked at intermediate noise intensity. For tipping between two equilibria where a given species was at risk of extinction in one equilibrium but not the other, noise affecting that species had greater impact on tipping probability than noise affecting the other species. Noise in the predator population facilitated quicker tipping to extinction equilibria, whereas prey noise instead often slowed down extinction. Changes in warning level for initial population values due to noise were most apparent near attraction basin boundaries, but noise of sufficient magnitude (especially in the predator population) could alter risk even far away from these boundaries. Our model provides critical theoretical insights for the conservation of population diversity: management criteria and early warning signals can be developed based on our results to keep populations away from destructive critical thresholds.

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

Human activity is leading to changes in the mean and variability of climatic parameters in most locations around the world. The changing mean has received considerable attention from scientists and climate policy makers. However, recent work indicates that the changing variability, that is, the amplitude and the temporal autocorrelation of deviations from the mean, may have greater and more imminent impact on ecosystems. In this paper, we demonstrate that changes in climate variability alone could drive cyclic predator-prey ecosystems to extinction via so-called phase-tipping (P-tipping), a new type of instability that occurs only from certain phases of the predator-prey cycle. We construct a mathematical model of a variable climate and couple it to two self-oscillating paradigmatic predator-prey models. Most importantly, we combine realistic parameter values for the Canada lynx and snowshoe hare with actual climate data from the boreal forest. In this way, we demonstrate that critically important species in the boreal forest have increased likelihood of P-tipping to extinction under predicted changes in climate variability, and are most vulnerable during stages of the cycle when the predator population is near its maximum. Furthermore, our analysis reveals that stochastic resonance is the underlying mechanism for the increased likelihood of P-tipping to extinction.

Recurrent droughts increase risk of cascading tipping events by outpacing adaptive capacities in the Amazon rainforest

Tipping elements are nonlinear subsystems of the Earth system that have the potential to abruptly shift to another state if environmental change occurs close to a critical threshold with large consequences for human societies and ecosystems. Among these tipping elements may be the Amazon rainforest, which has been undergoing intensive anthropogenic activities and increasingly frequent droughts. Here, we assess how extreme deviations from climatological rainfall regimes may cause local forest collapse that cascades through the coupled forest-climate system. We develop a conceptual dynamic network model to isolate and uncover the role of atmospheric moisture recycling in such tipping cascades. We account for heterogeneity in critical thresholds of the forest caused by adaptation to local climatic conditions. Our results reveal that, despite this adaptation, a future climate characterized by permanent drought conditions could trigger a transition to an open canopy state particularly in the southern Amazon. The loss of atmospheric moisture recycling contributes to one-third of the tipping events. Thus, by exceeding local thresholds in forest adaptive capacity, local climate change impacts may propagate to other regions of the Amazon basin, causing a risk of forest shifts even in regions where critical thresholds have not been crossed locally.

Mean-field theory for double-well systems on degree-heterogeneous networks

Many complex dynamical systems in the real world, including ecological, climate, financial and power-grid systems, often show critical transitions, or tipping points, in which the system’s dynamics suddenly transit into a qualitatively different state. In mathematical models, tipping points happen as a control parameter gradually changes and crosses a certain threshold. Tipping elements in such systems may interact with each other as a network, and understanding the behaviour of interacting tipping elements is a challenge because of the high dimensionality originating from the network. Here, we develop a degree-based mean-field theory for a prototypical double-well system coupled on a network with the aim of understanding coupled tipping dynamics with a low-dimensional description. The method approximates both the onset of the tipping point and the position of equilibria with a reasonable accuracy. Based on the developed theory and numerical simulations, we also provide evidence for multistage tipping point transitions in networks of double-well systems.

Complex networks of interacting stochastic tipping elements: Cooperativity of phase separation in the large-system limit

Tipping elements in the Earth system have received increased scientific attention over recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element undergoes a drastic shift in its state upon an additional small parameter change when close to its tipping point. Recently, the focus of research broadened towards emergent behavior in networks of tipping elements, like global tipping cascades triggered by local perturbations. Here, we analyze the response to the perturbation of a single node in a system that initially resides in an unstable equilibrium. The evolution is described in terms of coupled nonlinear equations for the cumulants of the distribution of the elements. We show that drift terms acting on individual elements and offsets in the coupling strength are subdominant in the limit of large networks, and we derive an analytical prediction for the evolution of the expectation (i.e., the first cumulant). It behaves like a single aggregated tipping element characterized by a dimensionless parameter that accounts for the network size, its overall connectivity, and the average coupling strength. The resulting predictions are in excellent agreement with numerical data for Erdös-Rényi, Barabási-Albert, and Watts-Strogatz networks of different size and with different coupling parameters.

Phase transitions in biology: from bird flocks to population dynamics

Phase transitions are an important and extensively studied concept in physics. The insights derived from understanding phase transitions in physics have recently and successfully been applied to a number of different phenomena in biological systems. Here, we provide a brief review of phase transitions and their role in explaining biological processes ranging from collective behaviour in animal flocks to neuronal firing. We also highlight a new and exciting area where phase transition theory is particularly applicable: population collapse and extinction. We discuss how phase transition theory can give insight into a range of extinction events such as population decline due to climate change or microbial responses to stressors such as antibiotic treatment.

Public health challenges and opportunities after COVID-19

With hindsight, the main weakness behind the ineffective response to the coronavirus disease 2019 (COVID-19) pandemic in some countries has been the failure to understand, and take account of, the multilayered systemic interdependencies that spread the effects of the pandemic across social, technological, economic and health-care dimensions. For example, to respond to the COVID-19 pandemic, all people were required to rapidly adjust to social distancing and travel restrictions. Such a complex behavioural response entails adaptation to achieve a full recovery from the systemic shock. To capitalize on the positive effects of disruption to the status quo, much more complex socioeconomic modelling needs to be considered when designing and evaluating possible public health interventions that have major behavioural implications. We provide a simple example of how this reasoning may highlight generally unacknowledged connections and interdependencies and guide the construction of scenarios that can inform policy decisions to enhance the resilience of society and tackle existing societal challenges.

Dynamical landscape and multistability of a climate model

We apply two independent data analysis methodologies to locate stable climate states in an intermediate complexity climate model and analyse their interplay. First, drawing from the theory of quasi-potentials, and viewing the state space as an energy landscape with valleys and mountain ridges, we infer the relative likelihood of the identified multistable climate states and investigate the most likely transition trajectories as well as the expected transition times between them. Second, harnessing techniques from data science, and specifically manifold learning, we characterize the data landscape of the simulation output to find climate states and basin boundaries within a fully agnostic and unsupervised framework. Both approaches show remarkable agreement, and reveal, apart from the well known warm and snowball earth states, a third intermediate stable state in one of the two versions of PLASIM, the climate model used in this study. The combination of our approaches allows to identify how the negative feedback of ocean heat transport and entropy production via the hydrological cycle drastically change the topography of the dynamical landscape of Earth’s climate.

The Role of Stochasticity in Noise-Induced Tipping Point Cascades: A Master Equation Approach

Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less explored and is an important one. A study of noise-induced tipping, in particular, could provide key insights into tipping cascades. Here, we consider a specific example of a simple model system that could have cascading tipping points. This model consists of two interacting populations with underlying Allee effects and stochastic dynamics, in separate patches connected by dispersal, which can generate bistability. From an ecological standpoint, we look for rescue effects whereby one population can prevent the collapse of a second population. As a way to investigate the stochastic dynamics, we use an individual-based modeling approach rooted in chemical reaction network theory. Then, using continuous-time Markov chains and the theory of first passage times, we essentially approximate, or emulate, the original high-dimensional model by a Markov chain with just three states, where each state corresponds to a combination of population thresholds. Analysis of this reduced model shows when the system is likely to recover, as well as when tipping cascades through the whole system.