arXiv subjects

Jonathan F. Donges

Publications and source records attributed to Jonathan F. Donges.

At least 19 recordsLinked to original sources

arXiv2026

Quantifying the safe operating space for the Amazon rainforest under climate change and deforestation

The Amazon rainforest is considered one of the core tipping elements in the climate system with a potential tipping point from rainforest to savannah between 2 and 6 °C of global warming. However, ongoing deforestation constitutes an additional major threat to the Amazon rainforest that acts simultaneously to undermine the stability of the rainforest. Both effects could synergistically compound and lower the overall threshold in global warming and deforestation when tipping points may be crossed. Here, we quantify the safe operating space of the Amazon rainforest, which we define as the joint global warming and deforestation conditions where resilience of the system as a whole is preserved. Based on the underlying environmental data from a global climate model, we use a reduced complexity model and explicitly take into account the adaptive capacities of the forest as well as the atmospheric moisture recycling. We quantify that under current conditions of around 1.4 °C of global warming and around 17 % of deforestation, more than a third of the Amazon rainforest is at high risk of crossing critical thresholds. We therefore conclude that the Amazon rainforest may have already left its safe operating space. Furthermore, we find that the historic and projected deforestation pattern could be particularly detrimental. Our results support the need for ambitious climate action to hold the Paris climate target and also nature protection to end net deforestation.

physics.ao-ph↗

arXiv2025

AI for a Planet Under Pressure

Artificial intelligence (AI) is already driving scientific breakthroughs in a variety of research fields, ranging from the life sciences to mathematics. This raises a critical question: can AI be applied both responsibly and effectively to address complex and interconnected sustainability challenges? This report is the result of a collaboration between the Stockholm resilience Centre (Stockholm University), the Potsdam Institute for Climate Impact Research (PIK), and Google DeepMind. Our work explores the potential and limitations of using AI as a research method to help tackle eight broad sustainability challenges. The results build on iterated expert dialogues and assessments, a systematic AI-supported literature overview including over 8,500 academic publications, and expert deep-dives into eight specific issue areas. The report also includes recommendations to sustainability scientists, research funders, the private sector, and philanthropies.

cs.CY↗

arXiv2025

Complex network approaches to nonlinear time series analysis

In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both nonlinear time series analysis and complex network theory are widely considered to be established fields of complex systems sciences with strong links to nonlinear dynamics and statistical physics, the thorough combination of both approaches has become an active field of nonlinear time series analysis, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of existing approaches of time series networks, covering their methodological foundations, interpretation and practical considerations with an emphasis on recent developments. After a brief outline of the state-of-the-art of nonlinear time series analysis and the theory of complex networks, we focus on three main network approaches, namely, phase space based recurrence networks, visibility graphs and Markov chain based transition networks, all of which have made their way from abstract concepts to widely used methodologies. These three concepts, as well as several variants thereof will be discussed in great detail regarding their specific properties, potentials and limitations. More importantly, we emphasize which fundamental new insights complex network approaches bring into the field of nonlinear time series analysis. In addition, we summarize examples from the wide range of recent applications of these methods, covering rather diverse fields like climatology, fluid dynamics, neurophysiology, engineering and economics, and demonstrating the great potentials of time series networks for tackling real-world contemporary scientific problems.

physics.data-an↗

arXiv2025

Causal pathway from AMOC to Southern Amazon rainforest indicates stabilising interaction between two climate tipping elements

Declines in resilience have been observed in several climate tipping elements over the past decades, including the Atlantic Meridional Overturning Circulation (AMOC) and the Amazon rainforest (AR). Large-scale nonlinear and possibly irreversible changes in system state, such as AMOC weakening or rainforest-savanna transitions in the Amazon basin, would have severe impacts on ecosystems and human societies worldwide. In order to improve future tipping risk assessments, understanding interactions between tipping elements is crucial. The AMOC is known to influence the Intertropical Convergence Zone, potentially altering precipitation patterns over the AR and affecting its stability. However, AMOC-AR interactions are currently not well understood. Here, we identify a previously unknown stabilising interaction pathway from the AMOC onto the Southern AR, applying an established causal discovery and inference approach to tipping element interactions for the first time. Analysing observational and reanalysis data from 1982-2022, we show that AMOC weakening leads to increased precipitation in the Southern AR during the critical dry season, in line with findings from recent Earth system model experiments. Specifically, we report a 4.8% increase of mean dry season precipitation in the Southern AR for every 1 Sv of AMOC weakening. This finding is consistent across multiple data sources and AMOC strength indices. We show that this stabilising interaction has offset 17% of dry season precipitation decrease in the Southern AR since 1982. Our results demonstrate the potential of causal discovery methods for analysing tipping element interactions based on reanalysis and observational data. By improving the understanding of AMOC-AR interactions, we contribute toward better constraining the risk of potential climate tipping cascades under global warming.

physics.ao-ph↗

arXiv2023

A dynamic network model of societal complexity and resilience inspired by Tainter's theory of collapse

In recent years, several global events have severely disrupted economies and social structures, undermining confidence in the resilience of modern societies. While empirical evidence on the dynamics and drivers of past societal collapse is mounting, a process-based understanding of these dynamics is still in its infancy. Here we aim to identify and illustrate the underlying drivers of such societal instability or even collapse. The inspiration for this work is Joseph Tainter's theory of the "collapse of complex societies", which postulates that the complexity of societies increases as they solve problems, leading to diminishing returns on complexity investments, and ultimately to collapse. In this work we have abstracted this theory into a low-dimensional and stylised model of two classes of networked agents, hereafter referred to as "laborers" and "administrators". We numerically modeled the dynamics of societal complexity, measured as the fraction of "administrators", which is assumed to affect the productivity of connected energy-producing "laborers". We show that collapse becomes increasingly likely as the complexity of the model society continuously increases in response to external stresses that emulate Tainter's abstract notion of problems that societies must solve. We also provide an analytical approximation of the system's dominant dynamics, which matches well with the numerical experiments, and use it to study the influence on network link density, social mobility and productivity. Our work advances the understanding of social-ecological collapse and illustrates its potentially direct link to an ever-increasing societal complexity in response to external shocks or stresses via a self-reinforcing feedback.

physics.soc-ph↗

arXiv2023

Measuring tropical rainforest resilience under non-Gaussian disturbances

The Amazon rainforest is considered one of the Earth's tipping elements and may lose stability under ongoing climate change. Recently a decrease in tropical rainforest resilience has been identified globally from remotely sensed vegetation data. However, the underlying theory assumes a Gaussian distribution of forest disturbances, which is different from most observed forest stressors such as fires, deforestation, or windthrow. Those stressors often occur in power-law-like distributions and can be approximated by $α$-stable Lévy noise. Here, we show that classical critical slowing down indicators to measure changes in forest resilience are robust under such power-law disturbances. To assess the robustness of critical slowing down indicators, we simulate pulse-like perturbations in an adapted and conceptual model of a tropical rainforest. We find few missed early warnings and few false alarms are achievable simultaneously if the following steps are carried out carefully: First, the model must be known to resolve the timescales of the perturbation. Second, perturbations need to be filtered according to their absolute temporal autocorrelation. Third, critical slowing down has to be assessed using the non-parametric Kendall-$τ$ slope. These prerequisites allow for an increase in the sensitivity of early warning signals. Hence, our findings imply improved reliability of the interpretation of empirically estimated rainforest resilience through critical slowing down indicators.

physics.ao-ph↗

arXiv2023

Resilience basins of complex systems: an application to prosumer impacts on power grids

Comparable to the traditional notion of stability in system dynamics, resilience is typically measured in a way that assesses the quality of a system's response, for example the speed of its recovery. We present a broadly applicable complementary measurement framework that quantifies resilience similarly to basin stability by estimating a "resilience basin" which reflects the extent of adverse influences that the system can recover from in a sufficient manner. In contrast to basin stability, the adverse influences considered here are not necessarily displacements in state space, but arbitrarily complex impacts to the system, quantified by adequate parameters. As a proof of concept, we present two applications: (i) the well-studied single-node power system as an easy-to-follow example and (ii) a stochastic model of a low-voltage DC power grid undergoing an unregulated energy transition consisting in the random appearance of prosumers. These act as decentral suppliers of photovoltaic power and alter the flow patterns while the grid topology remains unchanged. The resilience measurement framework is applied to evaluate the effect and efficiency of two response options: (i) upgrading the capacity of existing power lines and (ii) installing batteries in the prosumer households. The framework demonstrates that line upgrades can provide potentially unlimited resilience against energy decentralization, while household batteries are inherently limited (achieving <=70% of the resilience of line upgrades). Further, the framework aids in optimizing budget efficiency by pointing toward threshold budget values as well as budget-dependent ideal strategies for the allocation of line upgrades and for the battery charging algorithm.

physics.soc-ph↗

arXiv2022

Conceptualizing World-Earth System resilience: Exploring transformation pathways towards a safe and just operating space for humanity

We develop a framework within which to conceptualize World-Earth System resilience. Our notion of World-Earth System resilience emphasizes the need to move beyond the basin of attraction notion of resilience as we are not in a basin we can stay in. We are on a trajectory to a new basin and we have to avoid falling into undesirable basins. We thus focus on `pathway resilience', i.e. the relative number of paths that allow us to move from the transitional operating space we occupy now as we leave the Holocene basin to a safe and just operating space in the Anthropocene. We develop a mathematical model to formalize this conceptualization and demonstrate how interactions between earth system resilience (biophysical processes) and world system resilience (social processes) impact pathway resilience. Our findings show that building earth system resilience is probably our only chance to reach a safe and just operating space. We also illustrate the importance of world system dynamics by showing how the notion of fairness coupled with regional inequality affects pathway resilience.

physics.soc-ph↗

arXiv2021

A modeler's guide to studying the resilience of social-technical-environmental systems

The term 'resilience' is increasingly being used in social-technical-environmental systems sciences and particularly also in the Earth system sciences. However, the diversity of resilience concepts and a certain (sometimes intended) openness of proposed definitions can lead to misunderstandings and may impede their application to complex systems modelling. We propose a guideline that aims to ease communication as well as to support systematic development of research questions and models in the context of resilience. It can be applied independently of the modelling framework or underlying theory of choice. At the heart of this guideline is a checklist consisting of four questions to be answered: (i) Resilience of what? (ii) Resilience regarding what? (iii) Resilience against what? (iv) Resilience how? We refer to the answers to these resilience questions as the "system", the "sustainant", the "adverse influence", and the "response options". The term 'sustainant' is a neologism describing the feature of the system (state, structure, function, pathway, ...) that should be maintained (or restored quickly enough) in order to call the system resilient. The use of this proposed guideline in the field of Earth system resilience is demonstrated for the application example of a potential climate tipping element: the Amazon rainforest. The example illustrates the diversity of possible answers to the checklist's questions as well as their benefits in structuring the modelling process. The guideline supports the modeller in communicating precisely what is actually meant by 'resilience' in a specific context. This combination of freedom and precision could help to advance the resilience discourse by building a bridge between those demanding unambiguous definitions and those stressing the benefits of generality and flexibility of the resilience concept.

physics.soc-ph↗

arXiv2021

Detecting contagious spreading of urban innovations on the global city network

Only a fast and global transformation towards decarbonization and sustainability can keep the Earth in a civilization-friendly state. As hotspots for (green) innovation and experimentation, cities could play an important role in this transition. They are also known to profit from each other's ideas, with policy and technology innovations spreading to other cities. In this way, cities can be conceptualized as nodes in a globe-spanning learning network. The dynamics of this process are important for society's response to climate change and other challenges, but remain poorly understood on a macroscopic level. In this contribution, we develop an approach to identify whether network-based complex contagion effects are a feature of sustainability policy adoption by cities, based on dose-response contagion and surrogate data models. We apply this methodology to an example data set, comprising empirical data on the spreading of a public transport innovation (Bus Rapid Transit Systems) and a global inter-city connection network based on scheduled flight routes. We find evidence pointing towards a contagious spreading process which cannot be explained by either the network structure or the increase in global adoption rate alone. This suggests that the actions of a city's abstract "global neighborhood" within the network of cities may be an important factor in which policies and innovations are implemented, with potential connections to the emergence of social tipping processes. The methodology is generic, and can be used to compare the predictive power for innovation spreading of different kinds of inter-city network connections, e.g. via transport links, trade, or co-membership in political networks.

physics.soc-ph↗

arXiv2021

Dose-response functions and surrogate models for exploring social contagion in the Copenhagen Networks Study

Spreading dynamics and complex contagion processes on networks are important mechanisms underlying the emergence of critical transitions, tipping points and other nonlinear phenomena in complex human and natural systems. Increasing amounts of temporal network data are now becoming available to study such spreading processes of behaviours, opinions, ideas, diseases and innovations to test hypotheses regarding their specific properties. To this end, we here present a methodology based on dose-response functions and hypothesis testing using surrogate data models that randomise most aspects of the empirical data while conserving certain structures relevant to contagion, group or homophily dynamics. We demonstrate this methodology for synthetic temporal network data of spreading processes generated by the adaptive voter model. Furthermore, we apply it to empirical temporal network data from the Copenhagen Networks Study. This data set provides a physically-close-contact network between several hundreds of university students participating in the study over the course of three months. We study the potential spreading dynamics of the health-related behaviour "regularly going to the fitness studio" on this network. Based on a hierarchy of surrogate data models, we find that our method neither provides significant evidence for an influence of a dose-response-type network spreading process in this data set, nor significant evidence for homophily. The empirical dynamics in exercise behaviour are likely better described by individual features such as the disposition towards the behaviour, and the persistence to maintain it, as well as external influences affecting the whole group, and the non-trivial network structure. The proposed methodology is generic and promising also for applications to other temporal network data sets and traits of interest.

physics.soc-ph↗

arXiv2021

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

Tipping elements in the Earth System receive increased scientific attention over the 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 sub-dominant 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.

physics.soc-ph↗

arXiv2021

Differential imprints of distinct ENSO flavors in global patterns of very low and high seasonal precipitation

The effects of El Niño's two distinct flavors, East Pacific (EP) and Central Pacific (CP)/Modoki El Niño, on global climate variability have been studied intensively in recent years. Most of these studies have made use of linear multivariate statistics or composite analysis. Especially the former assumes the same type of linear statistical dependency to apply across different phases of the El Niño--Southern Oscillation (ENSO), which appears not necessarily a justified assumption. Here, we statistically evaluate the likelihood of co-occurrences between very high or very low seasonal precipitation sums over vast parts of the global land surface and the presence of the respective EP and CP types of both, El Niño and La Niña. By employing event coincidence analysis, we uncover differential imprints of both flavors on very low and very high seasonal precipitation patterns over distinct regions across the globe, which may severely affect, among others, agricultural and biomass production or public health. We particularly find that EP periods exhibit statistically significant event coincidence rates with hydrometeorological anomalies at larger spatial scales, whereas sparser patterns emerge along with CP periods. Our statistical analysis confirms previously reported interrelations for EP periods and uncovers additional distinct regional patterns of very high/low seasonal precipitation, such as increased rainfall over Central Asia alongside CP periods that have to our knowledge not been reported so far. Our results demonstrate that a thorough distinction of El Niño and La Niña into their two respective flavors could be crucial for understanding the emergence of strong regional hydrometeorological anomalies and anticipating their associated ecological and socioeconomic impacts.

physics.ao-ph↗

arXiv2020

Modelling nonlinear dynamics of interacting tipping elements on complex networks: the PyCascades package

Tipping elements occur in various systems such as in socio-economics, ecology and the climate system. In many cases, the individual tipping elements are not independent from each other, but they interact across scales in time and space. To model systems of interacting tipping elements, we here introduce the PyCascades open source software package for studying interacting tipping elements (doi: 10.5281/zenodo.4153102). PyCascades is an object-oriented and easily extendable package written in the programming language Python. It allows for investigating under which conditions potentially dangerous cascades can emerge between interacting dynamical systems, with a focus on tipping elements. With PyCascades it is possible to use different types of tipping elements such as double-fold and Hopf types and interactions between them. PyCascades can be applied to arbitrary complex network structures and has recently been extended to stochastic dynamical systems. This paper provides an overview of the functionality of PyCascades by introducing the basic concepts and the methodology behind it. In the end, three examples are discussed, showing three different applications of the software package. First, the moisture recycling network of the Amazon rainforest is investigated. Second, a model of interacting Earth system tipping elements is discussed. And third, the PyCascades modelling framework is applied to a global trade network.

physics.soc-ph↗

arXiv2020

Social tipping processes for sustainability: An analytical framework

Societal transformations are necessary to address critical global challenges, such as mitigation of anthropogenic climate change and reaching UN sustainable development goals. Recently, social tipping processes have received increased attention, as they present a form of social change whereby a small change can shift a sensitive social system into a qualitatively different state due to strongly self-amplifying (mathematically positive) feedback mechanisms. Social tipping processes have been suggested as key drivers of sustainability transitions emerging in the fields of technological and energy systems, political mobilization, financial markets and sociocultural norms and behaviors. Drawing from expert elicitation and comprehensive literature review, we develop a framework to identify and characterize social tipping processes critical to facilitating rapid social transformations. We find that social tipping processes are distinguishable from those of already more widely studied climate and ecological tipping dynamics. In particular, we identify human agency, social-institutional network structures, different spatial and temporal scales and increased complexity as key distinctive features underlying social tipping processes. Building on these characteristics, we propose a formal definition for social tipping processes and filtering criteria for those processes that could be decisive for future trajectories to global sustainability in the Anthropocene. We illustrate this definition with the European political system as an example of potential social tipping processes, highlighting the potential role of the FridaysForFuture movement. Accordingly, this analytical framework for social tipping processes can be utilized to illuminate mechanisms for necessary transformative climate change mitigation policies and actions.

physics.soc-ph↗

arXiv2020

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

In ecology, climate and other fields, (sub)systems have been identified that can transition into a qualitatively different state when a critical threshold or tipping point in a driving process is crossed. An understanding of those tipping elements is of great interest given the increasing influence of humans on the biophysical Earth system. Complex interactions exist between tipping elements, e.g. physical mechanisms connect subsystems of the climate system. Based on earlier work on such coupled nonlinear systems, we systematically assessed the qualitative long-term behaviour of interacting tipping elements. We developed an understanding of the consequences of interactions on the tipping behaviour allowing for tipping cascades to emerge under certain conditions. The (narrative) application of these qualitative results to real-world examples of interacting tipping elements indicates that tipping cascades with profound consequences may occur: the interacting Greenland ice sheet and thermohaline ocean circulation might tip before the tipping points of the isolated subsystems are crossed. The eutrophication of the first lake in a lake chain might propagate through the following lakes without a crossing of their individual critical nutrient input levels. The possibility of emerging cascading tipping dynamics calls for the development of a unified theory of interacting tipping elements and the quantitative analysis of interacting real-world tipping elements.

physics.geo-ph↗

arXiv2020

A network-based microfoundation of Granovetter's threshold model for social tipping

Social tipping, where minorities trigger larger populations to engage in collective action, has been suggested as one key aspect in addressing contemporary global challenges. Here, we refine Granovetter's widely acknowledged theoretical threshold model of collective behavior as a numerical modelling tool for understanding social tipping processes and resolve issues that so far have hindered such applications. Based on real-world observations and social movement theory, we group the population into certain or potential actors, such that -- in contrast to its original formulation -- the model predicts non-trivial final shares of acting individuals. Then, we use a network cascade model to explain and analytically derive that previously hypothesized broad threshold distributions emerge if individuals become active via social interaction. Thus, through intuitive parameters and low dimensionality our refined model is adaptable to explain the likelihood of engaging in collective behavior where social tipping like processes emerge as saddle-node bifurcations and hysteresis.

physics.soc-ph↗

arXiv2020

How motifs condition critical thresholds for tipping cascades in complex networks: Linking Micro- to Macro-scales

In this study, we investigate how specific micro interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erdös-Rényi networks and an exemplary moisture recycling network of the Amazon rainforest. Within these networks, decisive small-scale motifs are the feed forward loop, the secondary feed forward loop, the zero loop and the neighboring loop. Of all motifs, the feed forward loop motif stands out in tipping cascades since it decreases the critical coupling strength necessary to initiate a cascade more than the other motifs. We find that for this motif, the reduction of critical coupling strength is 11% less than the critical coupling of a pair of tipping elements. For highly connected networks, our analysis reveals that coupled feed forward loops coincide with a strong 90% decrease of the critical coupling strength. For the highly clustered moisture recycling network in the Amazon, we observe regions of very high motif occurrence for each of the four investigated motifs suggesting that these regions are more vulnerable. The occurrence of motifs is found to be one order of magnitude higher than in a random Erdös-Rényi network. This emphasizes the importance of local interaction structures for the emergence of global cascades and the stability of the network as a whole.

nlin.AO↗