Transformation starts at the periphery of networks where pushback is less.

Complex systems ranging from societies to ecological communities and power grids may be viewed as networks of connected elements. Such systems can go through critical transitions driven by an avalanche of contagious change. Here we ask, where in a complex network such a systemic shift is most likely to start. Intuitively, a central node seems the most likely source of such change. Indeed, topological studies suggest that central nodes can be the Achilles heel for attacks. We argue that the opposite is true for the class of networks in which all nodes tend to follow the state of their neighbors, a category we call two-way pull networks. In this case, a well-connected central node is an unlikely starting point of a systemic shift due to the buffering effect of connected neighbors. As a result, change is most likely to cascade through the network if it spreads first among relatively poorly connected nodes in the periphery. The probability of such initial spread is highest when the perturbation starts from intermediately connected nodes at the periphery, or more specifically, nodes with intermediate degree and relatively low closeness centrality. Our finding is consistent with empirical observations on social innovation, and may be relevant to topics as different as the sources of originality of art, collapse of financial and ecological networks and the onset of psychiatric disorders.

A tiny fraction of all species forms most of nature: Rarity as a sticky state.

Using data from a wide range of natural communities including the human microbiome, plants, fish, mushrooms, rodents, beetles, and trees, we show that universally just a few percent of the species account for most of the biomass. This is in line with the classical observation that the vast bulk of biodiversity is very rare. Attempts to find traits allowing the tiny fraction of abundant species to escape rarity have remained unsuccessful. Here, we argue that this might be explained by the fact that hyper-dominance can emerge through stochastic processes. We demonstrate that in neutrally competing groups of species, rarity tends to become a trap if environmental fluctuations result in gains and losses proportional to abundances. This counter-intuitive phenomenon arises because absolute change tends to zero for very small abundances, causing rarity to become a "sticky state", a pseudoattractor that can be revealed numerically in classical ball-in-cup landscapes. As a result, the vast majority of species spend most of their time in rarity leaving space for just a few others to dominate the neutral community. However, fates remain stochastic. Provided that there is some response diversity, roles occasionally shift as stochastic events or natural enemies bring an abundant species down allowing a rare species to rise to dominance. Microbial time series spanning thousands of generations support this prediction. Our results suggest that near-neutrality within niches may allow numerous rare species to persist in the wings of the dominant ones. Stand-ins may serve as insurance when former key species collapse.

Toxicokinetic-Toxicodynamic Model to Assess Thermal Stress.

Temperature is a crucial environmental factor affecting the distribution and performance of ectothermic organisms. This study introduces a new temperature damage model to interpret their thermal stress. Inspired by the ecotoxicological damage model in the General Unified Threshold model for Survival (GUTS) framework, the temperature damage model assumes that damage depends on the balance between temperature-dependent accumulation and constant repair. Mortality due to temperature stress is driven by the damage level exceeding a threshold. Model calibration showed a good agreement with the measured survival of Gammarus pulex exposed to different constant temperatures. Further, model simulations, including constant temperatures, daily temperature fluctuations, and heatwaves, demonstrated the model's ability to predict temperature effects for various environmental scenarios. With this, the present study contributes to the mechanistic understanding of temperature as a single stressor while facilitating the incorporation of temperature as an additional stressor alongside chemicals in mechanistic multistressor effect models.

The vulnerability of aging states: A survival analysis across premodern societies.

How states and great powers rise and fall is an intriguing enigma of human history. Are there any patterns? Do polities become more vulnerable over time as they age? We analyze longevity in hundreds of premodern states using survival analysis to help provide initial insights into these questions. This approach is commonly used to study the risk of death in biological organisms or failure in mechanical systems. The results reveal that the risk of state termination increased steeply over approximately the first two centuries after formation and stabilized thereafter. This provides the first quantitative support for the hypothesis that the resilience of political states decreases over time. Potential mechanisms that could drive such declining resilience include environmental degradation, increasing complexity, growing inequality, and extractive institutions. While the cases are from premodern times, such dynamics and drivers of vulnerability may remain relevant today.

The potential of resilience indicators to anticipate infectious disease outbreaks, a systematic review and guide.

To reduce the consequences of infectious disease outbreaks, the timely implementation of public health measures is crucial. Currently used early-warning systems are highly context-dependent and require a long phase of model building. A proposed solution to anticipate the onset or termination of an outbreak is the use of so-called resilience indicators. These indicators are based on the generic theory of critical slowing down and require only incidence time series. Here we assess the potential for this approach to contribute to outbreak anticipation. We systematically reviewed studies that used resilience indicators to predict outbreaks or terminations of epidemics. We identified 37 studies meeting the inclusion criteria: 21 using simulated data and 16 real-world data. 36 out of 37 studies detected significant signs of critical slowing down before a critical transition (i.e., the onset or end of an outbreak), with a highly variable sensitivity (i.e., the proportion of true positive outbreak warnings) ranging from 0.03 to 1 and a lead time ranging from 10 days to 68 months. Challenges include low resolution and limited length of time series, a too rapid increase in cases, and strong seasonal patterns which may hamper the sensitivity of resilience indicators. Alternative types of data, such as Google searches or social media data, have the potential to improve predictions in some cases. Resilience indicators may be useful when the risk of disease outbreaks is changing gradually. This may happen, for instance, when pathogens become increasingly adapted to an environment or evolve gradually to escape immunity. High-resolution monitoring is needed to reach sufficient sensitivity. If those conditions are met, resilience indicators could help improve the current practice of prediction, facilitating timely outbreak response. We provide a step-by-step guide on the use of resilience indicators in infectious disease epidemiology, and guidance on the relevant situations to use this approach.

Five fundamental ways in which complex food webs may spiral out of control.

Theory suggests that increasingly long, negative feedback loops of many interacting species may destabilize food webs as complexity increases. Less attention has, however, been paid to the specific ways in which these 'delayed negative feedbacks' may affect the response of complex ecosystems to global environmental change. Here, we describe five fundamental ways in which these feedbacks might pave the way for abrupt, large-scale transitions and species losses. By combining topological and bioenergetic models, we then proceed by showing that the likelihood of such transitions increases with the number of interacting species and/or when the combined effects of stabilizing network patterns approach the minimum required for stable coexistence. Our findings thus shift the question from the classical question of what makes complex, unaltered ecosystems stable to whether the effects of, known and unknown, stabilizing food-web patterns are sufficient to prevent abrupt, large-scale transitions under global environmental change.

The Potential for Alternative Stable States in Food Webs Depends on Feedback Mechanism and Trait Diversity.

AbstractAlternative stable ecosystem states are possible under the same environmental conditions in models of two or three interacting species and an array of feedback loops. However, multispecies food webs might weaken the feedbacks loops that can create alternative stable states. To test how this potential depends on food web properties, we develop a many-species model where consumer Allee effects emerge from consumer-resource interactions. We evaluate the interactive effects of food web connectance, interspecific trait diversity, and two classes of feedbacks: specialized feedbacks, where consumption of individual resources declines at high resource abundance (e.g., from schooling or reaching size refugia), and aggregate feedbacks, where overall resource abundance reduces consumer recruitment (e.g., from resources enhancing competition or mortality experienced by recruits). We find that aggregate feedbacks maintain, and specialized feedbacks reduce, the potential for alternative states. Interspecific trait diversity decreases the prevalence of alternative stable states more for specialized than for aggregate feedbacks. Increasing food web connectance increases the potential for alternative stable states for aggregated feedbacks but decreases it for specialized feedbacks, where losing vulnerable consumers can cascade into food web collapses. Altogether, multispecies food webs can limit the set of processes that create alternative stable states and impede consumer recovery from disturbance.

Northern expansion is not compensating for southern declines in North American boreal forests.

Climate change is expected to shift the boreal biome northward through expansion at the northern and contraction at the southern boundary respectively. However, biome-scale evidence of such a shift is rare. Here, we used remotely-sensed tree cover data to quantify temporal changes across the North American boreal biome from 2000 to 2019. We reveal a strong north-south asymmetry in tree cover change, coupled with a range shrinkage of tree cover distributions. We found no evidence for tree cover expansion in the northern biome, while tree cover increased markedly in the core of the biome range. By contrast, tree cover declined along the southern biome boundary, where losses were related largely to wildfires and timber logging. We show that these contrasting trends are structural indicators for a possible onset of a biome contraction which may lead to long-term carbon declines.

Loss of Earth system resilience during early Eocene transient global warming events.

Superimposed on long-term late Paleocene-early Eocene warming (~59 to 52 million years ago), Earth's climate experienced a series of abrupt perturbations, characterized by massive carbon input into the ocean-atmosphere system and global warming. Here, we examine the three most punctuated events of this period, the Paleocene-Eocene Thermal Maximum and Eocene Thermal Maximum 2 and 3, to probe whether they were initiated by climate-driven carbon cycle tipping points. Specifically, we analyze the dynamics of climate and carbon cycle indicators acquired from marine sediments to detect changes in Earth system resilience and to identify positive feedbacks. Our analyses suggest a loss of Earth system resilience toward all three events. Moreover, dynamic convergent cross mapping reveals intensifying coupling between the carbon cycle and climate during the long-term warming trend, supporting increasingly dominant climate forcing of carbon cycle dynamics during the Early Eocene Climatic Optimum when these recurrent global warming events became more frequent.

Anticipating the occurrence and type of critical transitions.

Critical transition can occur in many real-world systems. The ability to forecast the occurrence of transition is of major interest in a range of contexts. Various early warning signals (EWSs) have been developed to anticipate the coming critical transition or distinguish types of transition. However, no effective method allows to establish practical threshold indicating the condition when the critical transition is most likely to occur. Here, we introduce a powerful EWS, named dynamical eigenvalue (DEV), that is rooted in bifurcation theory of dynamical systems to estimate the dominant eigenvalue of the system. Theoretically, the absolute value of DEV approaches 1 when the system approaches bifurcation, while its position in the complex plane indicates the type of transition. We demonstrate the efficacy of the DEV approach in model systems with known bifurcation types and also test the DEV approach on various critical transitions in real-world systems.

Explicit Consideration of Temperature Improves Predictions of Toxicokinetic-Toxicodynamic Models for Flupyradifurone and Imidacloprid in Gammarus pulex.

In the face of global climate change, where temperature fluctuations and the frequency of extreme weather events are increasing, it is needed to evaluate the impact of temperature on the ecological risk assessment of chemicals. Current state-of-the-art mechanistic effect models, such as toxicokinetic-toxicodynamic (TK-TD) models, often do not explicitly consider temperature as a modulating factor. This study implemented the effect of temperature in a widely used modeling framework, the General Unified Threshold model for Survival (GUTS). We tested the model using data from toxicokinetic and toxicity experiments with Gammarus pulex exposed to the insecticides imidacloprid and flupyradifurone. The experiments revealed increased TK rates with increasing temperature and increased toxicity under chronic exposures. Using the widely used Arrhenius equation, we could include the temperature influence into the modeling. By further testing of different model approaches, differences in the temperature scaling of TK and TD model parameters could be identified, urging further investigations of the underlying mechanisms. Finally, our results show that predictions of TK-TD models improve if we include the toxicity modulating effect of temperature explicitly.

Species abundance correlations carry limited information about microbial network interactions.

Unraveling the network of interactions in ecological communities is a daunting task. Common methods to infer interspecific interactions from cross-sectional data are based on co-occurrence measures. For instance, interactions in the human microbiome are often inferred from correlations between the abundances of bacterial phylogenetic groups across subjects. We tested whether such correlation-based methods are indeed reliable for inferring interaction networks. For this purpose, we simulated bacterial communities by means of the generalized Lotka-Volterra model, with variation in model parameters representing variability among hosts. Our results show that correlations can be indicative for presence of bacterial interactions, but only when measurement noise is low relative to the variation in interaction strengths between hosts. Indication of interaction was affected by type of interaction network, process noise and sampling under non-equilibrium conditions. The sign of a correlation mostly coincided with the nature of the strongest pairwise interaction, but this is not necessarily the case. For instance, under rare conditions of identical interaction strength, we found that competitive and exploitative interactions can result in positive as well as negative correlations. Thus, cross-sectional abundance data carry limited information on specific interaction types. Correlations in abundance may hint at interactions but require independent validation.

Exit time as a measure of ecological resilience.

Ecological resilience is the magnitude of the largest perturbation from which a system can still recover to its original state. However, a transition into another state may often be invoked by a series of minor synergistic perturbations rather than a single big one. We show how resilience can be estimated in terms of average life expectancy, accounting for this natural regime of variability. We use time series to fit a model that captures the stochastic as well as the deterministic components. The model is then used to estimate the mean exit time from the basin of attraction. This approach offers a fresh angle to anticipating the chance of a critical transition at a time when high-resolution time series are becoming increasingly available.

Understanding the critical rate of environmental change for ecosystems, cyanobacteria as an example.

Recently it has been show that in some ecosystems fast rates of change of environmental drivers may trigger a critical transition, whereas change of the same magnitude but at slower rates would not. So far, few studies describe this phenomenon of rate-induced tipping, while it is important to understand this phenomenon in the light of the ongoing rapid environmental change. Here, we demonstrate rate-induced tipping in a simple model of cyanobacteria with realistic parameter settings. We explain graphically that there is a range of initial conditions at which a gradual increase in environmental conditions can cause a collapse of the population, but only if the change is fast enough. In addition, we show that a pulse in the environmental conditions can cause a temporary collapse, but that is dependent on both the rate and the duration of the pulse. Furthermore, we study whether the autocorrelation of stochastic environmental conditions can influence the probability of inducing rate-tipping. As both the rate of environmental change, and autocorrelation of the environmental variability are increasing in parts of the climate, the probability for rate-induced tipping to occur is likely to increase. Our results imply that, even though the identification of rate sensitive ecosystems in the real world will be challenging, we should incorporate critical rates of change in our ecosystem assessments and management.

Loss of resilience preceded transformations of pre-Hispanic Pueblo societies.

Climate extremes are thought to have triggered large-scale transformations of various ancient societies, but they rarely seem to be the sole cause. It has been hypothesized that slow internal developments often made societies less resilient over time, setting them up for collapse. Here, we provide quantitative evidence for this idea. We use annual-resolution time series of building activity to demonstrate that repeated dramatic transformations of Pueblo cultures in the pre-Hispanic US Southwest were preceded by signals of critical slowing down, a dynamic hallmark of fragility. Declining stability of the status quo is consistent with archaeological evidence for increasing violence and in some cases, increasing wealth inequality toward the end of these periods. Our work thus supports the view that the cumulative impact of gradual processes may make societies more vulnerable through time, elevating the likelihood that a perturbation will trigger a large-scale transformation that includes radically rejecting the status quo and seeking alternative pathways.

Evaluating the performance of multivariate indicators of resilience loss.

Various complex systems, such as the climate, ecosystems, and physical and mental health can show large shifts in response to small changes in their environment. These 'tipping points' are notoriously hard to predict based on trends. However, in the past 20 years several indicators pointing to a loss of resilience have been developed. These indicators use fluctuations in time series to detect critical slowing down preceding a tipping point. Most of the existing indicators are based on models of one-dimensional systems. However, complex systems generally consist of multiple interacting entities. Moreover, because of technological developments and wearables, multivariate time series are becoming increasingly available in different fields of science. In order to apply the framework of resilience indicators to multivariate time series, various extensions have been proposed. Not all multivariate indicators have been tested for the same types of systems and therefore a systematic comparison between the methods is lacking. Here, we evaluate the performance of the different multivariate indicators of resilience loss in different scenarios. We show that there is not one method outperforming the others. Instead, which method is best to use depends on the type of scenario the system is subject to. We propose a set of guidelines to help future users choose which multivariate indicator of resilience is best to use for their particular system.

Global inequality remotely sensed.

Economic inequality is notoriously difficult to quantify as reliable data on household incomes are missing for most of the world. Here, we show that a proxy for inequality based on remotely sensed nighttime light data may help fill this gap. Individual households cannot be remotely sensed. However, as households tend to segregate into richer and poorer neighborhoods, the correlation between light emission and economic thriving shown in earlier studies suggests that spatial variance of remotely sensed light per person might carry a signal of economic inequality. To test this hypothesis, we quantified Gini coefficients of the spatial variation in average nighttime light emitted per person. We found a significant relationship between the resulting light-based inequality indicator and existing estimates of net income inequality. This correlation between light-based Gini coefficients and traditional estimates exists not only across countries, but also on a smaller spatial scale comparing the 50 states within the United States. The remotely sensed character makes it possible to produce high-resolution global maps of estimated inequality. The inequality proxy is entirely independent from traditional estimates as it is based on observed light emission rather than self-reported household incomes. Both are imperfect estimates of true inequality. However, their independent nature implies that the light-based proxy could be used to constrain uncertainty in traditional estimates. More importantly, the light-based Gini maps may provide an estimate of inequality where previously no data were available at all.

No warning for slow transitions.

A rise in fragility as a system approaches a tipping point may be sometimes estimated using dynamical indicators of resilience (DIORs) that measure the characteristic slowing down of recovery rates before a tipping point. A change in DIORs could be interpreted as an early warning signal for an upcoming critical transition. However, in order to be able to estimate the DIORs, observational records need to be long enough to capture the response rate of the system. As we show here, the required length of the time series depends on the response rates of the system. For instance, the current rate of anthropogenic climate forcing is fast relative to the response rate of some parts of the climate system. Therefore, we may expect difficulties estimating the resilience from modern time series. So far, there have been no systematic studies of the effects of the response rates of the dynamical systems and the rates of forcing on the detectability trends in the DIORs prior to critical transitions. Here, we quantify the performance of the resilience indicators variance and temporal autocorrelation, in systems with different response rates and for different rates of forcing. Our results show that the rapid rise of anthropogenic forcing to the Earth may make it difficult to detect changes in the resilience of ecosystems and climate elements from time series. These findings suggest that in order to determine with models whether the use of the DIORs is appropriate, we need to use realistic models that incorporate the key processes with the appropriate time constants.

Hysteresis of tropical forests in the 21st century.

Tropical forests modify the conditions they depend on through feedbacks at different spatial scales. These feedbacks shape the hysteresis (history-dependence) of tropical forests, thus controlling their resilience to deforestation and response to climate change. Here, we determine the emergent hysteresis from local-scale tipping points and regional-scale forest-rainfall feedbacks across the tropics under the recent climate and a severe climate-change scenario. By integrating remote sensing, a global hydrological model, and detailed atmospheric moisture tracking simulations, we find that forest-rainfall feedback expands the geographic range of possible forest distributions, especially in the Amazon. The Amazon forest could partially recover from complete deforestation, but may lose that resilience later this century. The Congo forest currently lacks resilience, but is predicted to gain it under climate change, whereas forests in Australasia are resilient under both current and future climates. Our results show how tropical forests shape their own distributions and create the climatic conditions that enable them.

Neutral competition boosts cycles and chaos in simulated food webs.

Similarity of competitors has been proposed to facilitate coexistence of species because it slows down competitive exclusion, thus making it easier for equalizing mechanisms to maintain diverse communities. On the other hand, previous studies suggest that chaotic ecosystems can have a higher biodiversity. Here, we link these two previously unrelated findings, by analysing the dynamics of food web models. We show that near-neutrality of competition of prey, in the presence of predators, increases the chance of developing chaotic dynamics. Moreover, we confirm that chaotic dynamics correlate with a higher biodiversity.