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In the vicinity of tipping points—or more precisely bifurcation points—ecosystems recover slowly from small perturbations. Such slowness may be interpreted as a sign of low resilience in the sense that the ecosystem could easily be tipped through a critical transition into a contrasting state. Indicators of this phenomenon of 'critical slowing down (CSD)' include a rise in temporal correlation and variance. Such indicators of CSD can provide an early warning signal of a nearby tipping point. Or, they may offer a possibility to rank reefs, lakes or other ecosystems according to their resilience. The fact that CSD may happen across a wide range of complex ecosystems close to tipping points implies a powerful generality. However, indicators of CSD are not manifested in all cases where regime shifts occur. This is because not all regime shifts are associated with tipping points. Here, we review the exploding literature about this issue to provide guidance on what to expect and what not to expect when it comes to the CSD-based early warning signals for critical transitions.

A statistical mechanical mean-field approach to the temporal development of biological regulation provides a phenomenological, but basic description of the dynamical behavior of genome expression in terms of autonomous self-organization with a critical transition (Self-Organized Criticality: SOC). This approach reveals the basis of self-regulation/organization of genome expression, where the extreme complexity of living matter precludes any strict mechanistic approach. The self-organization in SOC involves two critical behaviors: scaling-divergent behavior (genome avalanche) and sandpile-type critical behavior. Genome avalanche patterns—competition between order (scaling) and disorder (divergence) reflect the opposite sequence of events characterizing the self-organization process in embryo development and helper T17 terminal cell differentiation, respectively. On the other hand, the temporal development of sandpile-type criticality (the degree of SOC control) in mouse embryo suggests the existence of an SOC control landscape with a critical transition state (i.e., the erasure of zygote-state criticality). This indicates that a phase transition of the mouse genome before and after reprogramming (immediately after the late 2-cell state) occurs through a dynamical change in a control parameter. This result provides a quantitative open-thermodynamic appreciation of the still largely qualitative notion of the epigenetic landscape. Our results suggest: (i) the existence of coherent waves of condensation/de-condensation in chromatin, which are transmitted across regions of different gene-expression levels along the genome; and (ii) essentially the same critical dynamics we observed for cell-differentiation processes exist in overall RNA expression during embryo development, which is particularly relevant because it gives further proof of SOC control of overall expression as a universal feature.

Ecological resilience is the ability of a system to persist in the face of perturbations. Although resilience has been a highly influential concept, its interpretation has remained largely qualitative. Here we describe an emerging family of methods for quantifying resilience on the basis of observations. A first set of methods is based on the phenomenon of critical slowing down, which implies that recovery upon small perturbations becomes slower as a system approaches a tipping point. Such slowing down can be measured experimentally but may also be indirectly inferred from changes in natural fluctuations and spatial patterns. A second group of methods aims to characterize the resilience of alternative states in probabilistic terms based on large numbers of observations as in long time series or satellite images. These generic approaches to measuring resilience complement the system-specific knowledge needed to infer the effects of environmental change on the resilience of complex systems.

The planetary boundary (PB) concept, introduced in 2009, aimed to define the environmental limits within which humanity can safely operate. This approach has proved influential in global sustainability policy development. Steffen et al. provide an updated and extended analysis of the PB framework. Of the original nine proposed boundaries, they identify three (including climate change) that might push the Earth system into a new state if crossed and that also have a pervasive influence on the remaining boundaries. They also develop the PB framework so that it can be applied usefully in a regional context. Science , this issue 10.1126/science.1259855 Developments in the planetary boundaries concept provide a framework to support global sustainability. The planetary boundaries framework defines a safe operating space for humanity based on the intrinsic biophysical processes that regulate the stability of the Earth system. Here, we revise and update the planetary boundary framework, with a focus on the underpinning biophysical science, based on targeted input from expert research communities and on more general scientific advances over the past 5 years. Several of the boundaries now have a two-tier approach, reflecting the importance of cross-scale interactions and the regional-level heterogeneity of the processes that underpin the boundaries. Two core boundaries—climate change and biosphere integrity—have been identified, each of which has the potential on its own to drive the Earth system into a new state should they be substantially and persistently transgressed.

Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure and function has not been investigated in much detail so far. Here we study the temporal correlations between layers exhibited by real social multiplex networks. At a basic level, the presence of such correlations implies a certain degree of predictability in the contact pattern, as we quantify by an extension of the entropy and mutual information analyses proposed for the single-layer case. At a different level, we demonstrate that temporal correlations are a signature of a ‘multitasking’ behavior of network agents, characterized by a higher level of switching between different social activities than expected in a uncorrelated pattern. Moreover, temporal correlations significantly affect the dynamics of coupled epidemic processes unfolding on the network. Our work opens the way for the systematic study of temporal multiplex networks and we anticipate it will be of interest to researchers in a broad array of fields.

Multiple global crises – including the pandemic, climate change, and Russia's war on Ukraine – have recently linked together in ways that are significant in scope, devastating in effect, but poorly understood. A growing number of scholars and policymakers characterize the situation as a ‘polycrisis’. Yet this neologism remains poorly defined. We provide the concept with a substantive definition, highlight its value-added in comparison to related concepts, and develop a theoretical framework to explain the causal mechanisms currently entangling many of the world's crises. In this framework, a global crisis arises when one or more fast-moving trigger events combine with slow-moving stresses to push a global system out of its established equilibrium and into a volatile and harmful state of disequilibrium. We then identify three causal pathways – common stresses, domino effects, and inter-systemic feedbacks – that can connect multiple global systems to produce synchronized crises. Drawing on current examples, we show that the polycrisis concept is a valuable tool for understanding ongoing crises, generating actionable insights, and opening avenues for future research. Non-technical summary The term ‘polycrisis’ appears with growing frequently to capture the interconnections between global crises, but the word lacks substantive content. In this article, we convert it from an empty buzzword into a conceptual framework and research program that enables us to better understand the causal linkages between contemporary crises. We draw upon the intersection of climate change, the covid-19 pandemic, and Russia's war in Ukraine to illustrate these causal interconnections and explore key features of the world's present polycrisis. Technical summary Multiple global crises – including the pandemic, climate change, and Russia's war on Ukraine – have recently linked together in ways that are significant in scope, devastating in effect, but poorly understood. A growing number of scholars and policymakers characterize the situation as a ‘polycrisis’. Yet this neologism remains poorly defined. We provide the concept with a substantive definition, highlight its value-added in comparison to related concepts, and develop a theoretical framework to explain the causal mechanisms currently entangling many of the world's crises. In this framework, a global crisis arises when one or more fast-moving trigger events combines with slow-moving stresses to push a global system out of its established equilibrium and into a volatile and harmful state of disequilibrium. We then identify three causal pathways – common stresses, domino effects, and inter-systemic feedbacks – that can connect multiple global systems to produce synchronized crises. Drawing on current examples, we show that the polycrisis concept is a valuable tool for understanding ongoing crises, generating actionable insights, and opening avenues for future research. Social media summary No longer a mere buzzword, the ‘polycrisis’ concept highlights causal interactions among crises to help navigate a tumultuous future.

Complex systems can exhibit sudden transitions or regime shifts from one stable state to another, typically referred to as critical transitions. It becomes a great challenge to identify a robust warning sufficiently early that action can be taken to avert a regime shift. We employ landscape-flux theory from nonequilibrium statistical mechanics as a general framework to quantify the global stability of ecological systems and provide warning signals for critical transitions. We quantify the average flux as the nonequilibrium driving force and the dynamical origin of the nonequilibrium transition while the entropy production rate as the nonequilibrium thermodynamic cost and thermodynamic origin of the nonequilibrium transition. Average flux, entropy production, nonequilibrium free energy, and time irreversibility quantified by the difference in cross-correlation functions forward and backward in time can serve as early warning signals for critical transitions much earlier than other conventional predictors.Weutilize a classical shallow lake model as an exemplar for our early warning prediction. Our proposed method is general and can be readily applied to assess the resilience of many other ecological systems. The early warning signals proposed here can potentially predict critical transitions earlier than established methods and perhaps even sufficiently early to avert catastrophic shifts.

Marine ecosystems can experience regime shifts, in which they shift from being organized around one set of mutually reinforcing structures and processes to another. Anthropogenic global change has broadly increased a wide variety of processes that can drive regime shifts. To assess the vulnerability of marine ecosystems to such shifts and their potential consequences, we reviewed the scientific literature for 13 types of marine regime shifts and used networks to conduct an analysis of co-occurrence of drivers and ecosystem service impacts. We found that regime shifts are caused by multiple drivers and have multiple consequences that co-occur in a non-random pattern. Drivers related to food production, climate change and coastal development are the most common co-occurring causes of regime shifts, while cultural services, biodiversity and primary production are the most common cluster of ecosystem services affected. These clusters prioritize sets of drivers for management and highlight the need for coordinated actions across multiple drivers and scales to reduce the risk of marine regime shifts. Managerial strategies are likely to fail if they only address well-understood or data-rich variables, and international cooperation and polycentric institutions will be critical to implement and coordinate action across the scales at which different drivers operate. By better understanding these underlying patterns, we hope to inform the development of managerial strategies to reduce the risk of high-impact marine regime shifts, especially for areas of the world where data are not available or monitoring programmes are not in place.

About 17% of humanity goes through an episode of major depression at some point in their lifetime. Despite the enormous societal costs of this incapacitating disorder, it is largely unknown how the likelihood of falling into a depressive episode can be assessed. Here, we show for a large group of healthy individuals and patients that the probability of an upcoming shift between a depressed and a normal state is related to elevated temporal autocorrelation, variance, and correlation between emotions in fluctuations of autorecorded emotions. These are indicators of the general phenomenon of critical slowing down, which is expected to occur when a system approaches a tipping point. Our results support the hypothesis that mood may have alternative stable states separated by tipping points, and suggest an approach for assessing the likelihood of transitions into and out of depression.

Some disturbances can drive ecological systems to abrupt shifts between alternative stages (tipping points) when critical transitions occur. Drought‐induced tree death can be considered as a nonlinear shift in tree vigour and growth. However, at what point do trees become predisposed to drought‐related dieback and which factors determine this (tipping) point? We investigated these questions by characterizing the responses of three tree species, silver fir (Abies alba), Scots pine (Pinus sylvestris) and Aleppo pine (Pinus halepensis), to a severe drought event. We compared basal area increment (BAI) trends and responses to climate and drought in declining (very defoliated and dying) vs. non‐declining (slightly or not defoliated) trees by using generalized additive mixed models. Defoliation, BAI and sapwood production were related to functional proxies of tree vigour measured at the onset and end of the drought (non‐structural carbohydrate concentrations, needle N content and C isotopic discrimination, presence of wood‐inhabiting fungi). We evaluated whether early warning signals (increases in synchronicity among trees or in autocorrelation and standard deviation) could be extracted from the BAI series prior to tree death. Declining silver fir and Scots pine trees showed less growth than non‐declining trees one to three decades, respectively, before the drought event, whereas Aleppo pines showed growth decline irrespective of tree defoliation. At the end of the drought period, all species showed increased defoliation and a related reduction in the concentration of sapwood soluble sugars. Defoliation was constrained by the BAI of the previous 5 years and sapwood production. No specific wood‐inhabiting fungi were found in post‐drought declining trees apart from blue‐stain fungi, which extensively affected damaged Scots pines. Declining silver firs showed increases in BAI autocorrelation and variability prior to tree death. Synthesis. Early warning signals of drought‐triggered mortality seem to be species specific and reflect how different tree species cope with drought stress. Highly correlated declining growth patterns during drought can serve as a signal in silver fir, whereas changes in the content of sapwood soluble sugars are suitable vigour proxies for Scots and Aleppo pines. Longer growth and defoliation series, additional vigour parameters and multi‐species comparisons are required to understand and predict drought‐induced tree death.