Regime shifts in a social-ecological system

Crop booms as regime shifts

A crop boom is a sudden, nonlinear and intense expansion of a new crop. Despite their large impacts, boom-bust dynamics are not well understood; booms are largely unpredictable and difficult to steer once they unfold. Based on the striking resemblances between land regime shifts and crop booms, we apply complex systems theory, highlighting the potential for regime shifts, to provide new insights about crop boom dynamics. We analyse qualitative and quantitative data of rubber and banana plantation expansion in two forest frontier regions of northern Laos. We show that preconditions, including previous booms, explain the occurrence (why) of booms, and triggers like policy and market changes explain their timing (when). Yet, the most important features of booms, their intensity and nonlinearity (how), strongly depended on internal self-reinforcing feedbacks. We identify built-in feedbacks (neighbourhood effects and imitation) and emergent feedbacks (land rush) and show that they were social in nature, multi-scale from plot to region and subject to thresholds. We suggest that these are regular features of booms and propose a definition and causal-mechanistic explanation of crop booms, examining the overlap between booms and regime shifts and the role of frontiers. We then identify opportunities for management interventions before, during and after booms.

Cultural transmission, competition for prey, and the evolution of cooperative hunting

Although cooperative hunting is widespread among animals, its benefits are unclear. At low frequencies, cooperative hunting may allow predators to escape competition and access bigger prey that could not be caught by a lone cooperative predator. Cooperative hunting is a more successful strategy when it is common, but its spread can result in overhunting big prey, which may have a lower per-capita growth rate than small prey. We construct a one-predator species, two-prey species model in which predators either learn to hunt small prey alone or learn to hunt big prey cooperatively. Predators first learn vertically from parents, then horizontally (i.e. socially) from random individuals or siblings. After horizontal transmission, they hunt with their learning partner if both are cooperative, and otherwise they hunt alone. Cooperative hunting cannot evolve when initially rare unless predators (a) interact with siblings, or (b) horizontally transmit the cooperative behavior to potential hunting partners. Whereas competition for small prey favors cooperative hunting when this cooperation is initially rare, the frequency of cooperative hunting cannot reach 100% unless big prey is abundant. Furthermore, a mutant that increases horizontal learning can invade if cooperative hunting is present, but not at 100%, because horizontal learning allows pairs of predators to have the same strategy. Our results reveal that the interactions between prey availability, social learning, and degree of cooperation among predators may have important effects on ecosystems.

Resilience and high compositional variability reflect the complex response of river waters to global drivers: The Eastern Siberian River Chemistry database

The chemical composition of river waters represents an important matter of investigation to understand environment modifications in response to climate changes and global warming. Prolonged dry periods, heavy flood events, degradation of the lands and ice thawing, modify the chemical composition of river waters influencing the drivers governing the complex dynamics of river catchments where everything comes together. In this framework, Compositional Data Analysis (CoDA) offers methods in which the complex structure of the river water composition and the interrelationships among the various components are put into the proper context for their statistical analysis. In this research, we propose a new CoDA approach combining the robust Mahalanobis distance (D) calculus of ilr-transformed chemical variables and the perturbation difference, both with respect to a pristine compositional benchmark. The aim was to trace the change in the chemical composition of the Eastern Siberian River Chemistry Database where degradation of the permafrost for global warming produces important effects on natural waters. The findings indicate complex multiplicative laws and feedback mechanisms governing solutes in Eastern Siberian rivers, with high values of D found where permafrost is more discontinuous. Perturbations clearly discriminate chemical components more resilient to stresses induced by global changes (Ca2+, Mg2+ and HCO3-) from those whose variability is not maintained under control (Cl-, Na+, SO42-). These outcomes open up a new scenario in searching for spatiotemporal resilience metrics to reveal rivers response to environmental changes.

Integrating evolutionary theory and social-ecological systems research to address the sustainability challenges of the Anthropocene

The rapid, human-induced changes in the Earth system during the Anthropocene present humanity with critical sustainability challenges. Social-ecological systems (SES) research provides multiple approaches for understanding the complex interactions between humans, social systems, and environments and how we might direct them towards healthier and more resilient futures. However, general theories of SES change have yet to be fully developed. Formal evolutionary theory has been applied as a dynamic theory of change of complex phenomena in biology and the social sciences, but rarely in SES research. In this paper, we explore the connections between both fields, hoping to foster collaboration. After sketching out the distinct intellectual traditions of SES research and evolutionary theory, we map some of their terminological and theoretical connections. We then provide examples of how evolutionary theory might be incorporated into SES research through the use of systems mapping to identify evolutionary processes in SES, the application of concepts from evolutionary developmental biology to understand the connections between systems changes and evolutionary changes, and how evolutionary thinking may help design interventions for beneficial change. Integrating evolutionary theory and SES research can lead to a better understanding of SES changes and positive interventions for a more sustainable Anthropocene. This article is part of the theme issue 'Evolution and sustainability: gathering the strands for an Anthropocene synthesis'.

Data on how abundance of resource inflows and punishment types affect resource extraction behavior

The data is collected through laboratory experiments on a dynamic common pool resource game, where, in an infinitely repeated number of rounds (i.e., game ended randomly), individuals made decisions about whether to exert a high or a low effort level to extract resources. Experiments were conducted using the student sample (consent provided and ethics approved) at the University of Hawai'i at Mānoa. A total of 8 sessions, 2 for each of the 4 treatments, were run with exactly 20 participants within a session. Individuals made decisions in groups of 10. Communication between any participant was not allowed. A session is randomly assigned (1) to vary whether the inflow of resources at the beginning of each round is high or low, and (2) to allow participants to either financially punish or socially punish defectors. A financial punishment resulted to a loss in profit for the punished while a social punishment displayed the words "You have extracted too much! You're being greedy!" on the computer screen of the punished. Individuals were assigned subject ID numbers and interacted using their subject IDs. The data is useful in understanding how resource inflow and type of punishment affects individual resource extraction behavior. The data could also be combined with other publicly available common pool resource datasets for a meta-analysis on individual behavior in the commons.

Evading tipping points in socio-mutualistic networks via structure mediated optimal strategy

The threat of large-scale pollinator decline is increasing globally under stress from multiple anthropogenic pressures. Traditional approaches have focused on managing endangered species at an individual level, in which the effect of complex interactions such as mutualism and competition are amiss. Here, we develop a coupled socio-mutualistic network model that captures the change in pollinator dynamics with human conservation opinion in a deteriorating environment. We show that the application of social norm (or conservation) at the pollinator nodes is fit to prevent sudden community collapse in representative networks of varied topology. Whilst primitive strategies have focused on regulating abundance as a mitigation strategy, the role of network structure has been largely overlooked. Here, we develop a novel network structure-mediated conservation strategy to find the optimal set of nodes on which norm implementation successfully prevents community collapse. We find that networks of intermediate nestedness require conservation at a minimum number of nodes to prevent a community collapse. We claim the robustness of the optimal conservation strategy (OCS) after validation on several simulated and empirical networks of varied complexity against a broad range of system parameters. Dynamical analysis of the reduced model shows that incorporating social norms allows the pollinator abundance to grow that would have otherwise crossed a tipping point and undergo extinction. Together, this novel means OCS provides a potential plan of action for conserving plant-pollinator networks bridging the gap between research in mutualistic networks and conservation ecology.

Sustainable Development Goals and risks: The Yin and the Yang of the paths towards sustainability

The United Nations 2030 Agenda and Sustainable Development Goals (SDGs) define a path towards a sustainable future, but given that uncertainty characterises the outcomes of any SDG-related actions, risks in the implementation of the Agenda need to be addressed. At the same time, most risk assessments are narrowed to sectoral approaches and do not refer to SDGs. Here, on the basis of a literature review and workshops, it is analysed how SDGs and risks relate to each other's in different communities. Then, it is formally demonstrated that, as soon as the mathematical definition of risks is broadened to embrace a more systemic perspective, acting to maintain socio-environmental systems within their sustainability domain can be done by risk minimisation. This makes Sustainable Development Goals and risks "the Yin and the Yang of the paths towards sustainability". Eventually, the usefulness of the SDG-risk nexus for both sustainability and risk management is emphasized.

Modelling coupled human-environment complexity for the future of the biosphere: strengths, gaps and promising directions

Humans and the environment form a single complex system where humans not only influence ecosystems but also react to them. Despite this, there are far fewer coupled human-environment system (CHES) mathematical models than models of uncoupled ecosystems. We argue that these coupled models are essential to understand the impacts of social interventions and their potential to avoid catastrophic environmental events and support sustainable trajectories on multi-decadal timescales. A brief history of CHES modelling is presented, followed by a review spanning recent CHES models of systems including forests and land use, coral reefs and fishing and climate change mitigation. The ability of CHES modelling to capture dynamic two-way feedback confers advantages, such as the ability to represent ecosystem dynamics more realistically at longer timescales, and allowing insights that cannot be generated using ecological models. We discuss examples of such key insights from recent research. However, this strength brings with it challenges of model complexity and tractability, and the need for appropriate data to parameterize and validate CHES models. Finally, we suggest opportunities for CHES models to improve human-environment sustainability in future research spanning topics such as natural disturbances, social structure, social media data, model discovery and early warning signals. This article is part of the theme issue 'Ecological complexity and the biosphere: the next 30 years'.

Generalized Structural Kinetic Modeling: A Survey and Guide

Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional dynamical models of complex systems are rarely mathematically tractable and their numerical exploration suffers both from computational and data limitations. Here we review generalized modeling, an alternative approach for formulating dynamical models to gain insights into dynamics and bifurcations of uncertain systems. We argue that this approach deals elegantly with the uncertainties that exist in real world data and enables analytical insight or highly efficient numerical investigation. We provide a survey of recent successes of generalized modeling and a guide to the application of this modeling approach in future studies such as complex integrative ecological models.

Stochasticity-induced persistence in coupled social-ecological systems

Stochasticity is often associated with negative consequences for population dynamics since a population may die out due to random chance during periods when population size is very low (stochastic fade-out). Here we develop a coupled social-ecological model based on stochastic differential equations that includes natural expansion and harvesting of a forest ecosystem, and dynamics of conservation opinions, social norms and social learning in a human population. Our objective was to identify mechanisms that influence long-term persistence of the forest ecosystem in the presence of noise. We found that most of the model parameters had a significant influence on the time to extinction of the forest ecosystem. Increasing the social learning rate and the net benefits of conservation significantly increased the time to extinction, for instance. Most interestingly, we found a parameter regime where an increase in the amount of system stochasticity caused an increase in the mean time to extinction, instead of causing stochastic fade-out. This effect occurs for a subset of realizations, but the effect is large enough to increase the mean time to extinction across all realizations. Such "stochasticity-induced persistence" occurs when stochastic dynamics in the social system generates benefits in the forest system at crucial points in its temporal dynamics. We conclude that studying relatively simple social-ecological models has the benefit of facilitating characterization of dynamical states and thereby enabling us to formulate new hypothesis about mechanisms that could be operating in empirical social-ecological systems.

Ecological features benefiting sustainable harvesters in socio-ecological systems: a case study of Swiftlets in Malaysia

A major challenge in biodiversity management is overharvesting by unsustainable harvesters. If a scenario could be created where sustainable harvesters benefit more than the unsustainable ones, even in the short term, the issue of overharvesting would be solved. Everyone would then follow the lead of sustainable harvesters. However, creating such a scenario is not an easy task; the difficulty is intensified if the habitat is open access and there is no property rights system. Swiftlets in Sarawak, Malaysia, present a special case where sustainable harvesters are believed to be more beneficial than unsustainable harvesters. Edible nests built by adult Swiftlets are used as ingredients for a traditional luxurious soup in Chinese cuisine. A rise in nest prices has increased the instances of unsustainable harvesters wrongfully collecting nests along with the eggs and fledglings, which are then abandoned. Swiftlets live in caves and build nests on cave ceilings. It is known that Swiftlets escape from cave ceilings when these harvesters take the nests, never to return to the same place. This ecological feature appears to work as the Swiftlet's indirect punishment against unsustainable harvesters. This study constructs a stage-structured population model and examines the effect of property rights and the indirect punishment by Swiftlets on the population dynamics of the bird, and on the economic return of both sustainable and unsustainable harvesters. Our findings are as follows: the indirect punishment by Swiftlets provides sustainable harvesters a higher short-term return than unsustainable harvesters under the property rights system, as long as Swiftlets return to their original cave after escaping from the unsustainable harvesters. While previous studies regarding the management of the commons have stressed the importance of rules and regulations for sustainable harvesting without considering the ecological uniqueness of each species, this study suggests that ecological exploration and the discovery of ecological features are also essential for designing a sustainable framework.

Stable leaders pave the way for cooperation under time-dependent exploration rates

The exploration of different behaviours is part of the adaptation repertoire of individuals to new environments. Here, we explore how the evolution of cooperative behaviour is affected by the interplay between exploration dynamics and social learning, in particular when individuals engage on prisoner's dilemma along the edges of a social network. We show that when the population undergoes a transition from strong to weak exploration rates a decline in the overall levels of cooperation is observed. However, if the rate of decay is lower in highly connected individuals (Leaders) than for the less connected individuals (Followers) then the population is able to achieve higher levels of cooperation. Finally, we show that minor differences in selection intensities (the degree of determinism in social learning) and individual exploration rates, can translate into major differences in the observed collective dynamics.

Effects of stochasticity and social norms on complex dynamics of fisheries

Recreational fishing is a highly socioecological process. Although recreational fisheries are self-regulating and resilient, changing anthropogenic pressure drives these fisheries to overharvest and collapse. Here, we evaluate the effect of demographic and environmental stochasticity for a social-ecological two-species fish model. In the presence of noise, we find that an increase in harvesting rate drives a critical transition from high-yield-low-price fisheries to low-yield-high-price fisheries. To calculate stochastic trajectories for demographic noise, we derive the master equation corresponding to the model and perform a Monte Carlo simulation. Moreover, the analysis of the probabilistic potential and mean first-passage time reveals the resilience of alternative steady states. We also describe the efficacy of a few generic indicators in forecasting sudden transitions. Furthermore, we show that incorporating social norms on the model allows a moderate fish density to maintain despite higher harvesting rates. Overall, our study highlights the occurrence of critical transitions in a stochastic social-ecological model and suggests ways to mitigate them.

Evolution and effects of the social-ecological system over a millennium in China's Loess Plateau

Understanding the regime shifts of social-ecological systems (SES) and their local and spillover effects over a long time frame is important for future sustainability. We provide a perspective of processes unfolding over time to identify the regime shifts of a SES based on changes in the relationships between SES components while also addressing their drivers and local and spillover effects. The applicability of this approach has been demonstrated by analyzing the evolution over the past 1000 years of the SES in China's Loess Plateau (LP). Five evolutionary phases were identified: "fast expansion of cultivation," "slow expansion of cultivation," "landscape engineering for higher production," "transition from cultivation to ecological conservation," and "revegetation for environment." Our study establishes empirical links between the state (phase) of a SES to its drivers and effects. Lessons of single-goal driven and locally focused SES management in the LP, which did not consider these links, have important implications to long-term planning and policy formulation of SES.

Comparison between best-response dynamics and replicator dynamics in a social-ecological model of lake eutrophication

Social-ecological models are often used to investigate the mutual interactions between an ecological system and human behaviour at a collective level. The social system is widely represented either by the replicator dynamics or by the best-response dynamics. We investigate the consequences of choosing one or the other with the example of a social-ecological model for eutrophication in shallow lakes, where the anthropogenic discharge of pollutants into the water is determined by a behavioural model using the replicator or a best-response dynamics. We discuss a fundamental difference between the replicator dynamics and the logit formulation of the best-response dynamics. This fundamental difference results in a different number of equilibria. We show that the replicator equation is a limit case of the best-response model, when agents are assumed to behave with infinite rationality. If agents act less rationally in the model using the best-response dynamics, the correspondence with the model using the replicator dynamics decreases. Finally, we show that sustained oscillations observed in both cases may differ substantially. The replicator dynamics makes the amplitude of the limit cycle become larger and makes the system come closer to full cooperation or full defection. Thus, the dynamics along the limit cycle imply a different risk for the system to be pushed by a perturbation into a desirable or an undesirable outcome depending on the socioeconomic dynamics assumed in the model. When analyzing social-ecological models, the choice of a socioeconomic dynamics is often little justified but our results show that it may have dramatic impacts on the coupled human-environment system.

The first rapid forest inventory and resource use assessment of Dashtijum Nature Reserve, Tajikistan: a mixed methods approach

There is critical need for more information on the status of forests in Central Asia, to inform conservation management. Here we assess the status and use of the globally important, threatened walnut–fruit forests of Dashtijum Nature Reserve, Tajikistan. We use a mixed methods approach combining a semi-structured interview based socio-economic survey with statistical analysis. Thirty-three tree species were recorded, with Rosaceae the most common family. The mean basal area of the forest was 20.8 m2 per ha and most tree species exhibited stable population structures. Resource use was prevalent throughout the community; most households harvested at least one fruit or nut species (78%), firewood (88%) and grazed livestock (85%). Most respondents noted declines in availability of fruits, nuts and firewood and reported a decrease in the overall area and quality of grazing. Statistical analysis and machine learning identified that distance to nearest settlement significantly affected forest total basal area, tree species richness and the Shannon index, a metric of diversity sensitive to rare species. Our results suggest that conservation management by the government and NGOs is partly effective but there is a need for increased enforcement of grazing restrictions, to prevent further forest degradation.

Tipping positive change

Tipping points exist in social, ecological and climate systems and those systems are increasingly causally intertwined in the Anthropocene. Climate change and biosphere degradation have advanced to the point where we are already triggering damaging environmental tipping points, and to avoid worse ones ahead will require finding and triggering positive tipping points towards sustainability in coupled social, ecological and technological systems. To help with that I outline how tipping points can occur in continuous dynamical systems and in networks, the causal interactions that can occur between tipping events across different types and scales of system-including the conditions required to trigger tipping cascades, the potential for early warning signals of tipping points, and how they could inform deliberate tipping of positive change. In particular, the same methods that can provide early warning of damaging environmental tipping points can be used to detect when a socio-technical or socio-ecological system is most sensitive to being deliberately tipped in a desirable direction. I provide some example targets for such deliberate tipping of positive change. This article is part of the theme issue 'Climate change and ecosystems: threats, opportunities and solutions'.

The emergence and resilience of self-organized governance in coupled infrastructure systems

Studies of small-scale, self-organized social-ecological systems have contributed to our understanding of successful governance of shared resources. However, the lack of formal analytically tractable models of such coupled infrastructure systems makes it difficult to connect this understanding to such concepts as stability, robustness, and resilience, which are increasingly important in considering such systems. In this paper, we mathematically operationalize a widely used conceptual framework via a stylized dynamical model. The model yields a wide range of system outcomes: sustainability or collapse, infrastructure at full or partial capacity, and social agents seeking outside opportunities or exclusively engaging in the system. The low dimensionality of the model enables us to derive these conditions in clear relationships of biophysical and social factors describing the coupled system. Analysis of the model further reveals regime shifts, trade-offs, and potential pitfalls that one may face in governing these self-organized systems. The intuition and insights derived from the model lay ground for more rigorous treatment of robustness and resilience of self-organized coupled infrastructure systems, which can lead to more effective governance.

Evolutionary games with environmental feedbacks

Strategic interactions arise in all domains of life. This form of competition often plays out in dynamically changing environments. The strategies employed in a population may alter the state of the environment, which may in turn feedback to change the incentive structure of strategic interactions. Feedbacks between strategies and the environment are common in social-ecological systems, evolutionary-ecological systems, and even psychological-economic systems. Here we develop a framework of 'eco-evolutionary game theory' that enables the study of strategic and environmental dynamics with feedbacks. We consider environments governed either by intrinsic growth, decay, or tipping points. We show how the joint dynamics of strategies and the environment depend on the incentives for individuals to lead or follow behavioral changes, and on the relative speed of environmental versus strategic change. Our analysis unites dynamical phenomena that occur in settings as diverse as human decision-making, plant nutrient acquisition, and resource harvesting. We discuss implications in fields ranging from ecology to economics.

The importance of transient social dynamics for restoring ecosystems beyond ecological tipping points

Managing regime shifts is often associated with “turning back from the brink” assuming that once a system has transgressed a tipping point, it moves unavoidably toward the undesired state. We show that a regime shift is rather a slippery slope that can be managed and even reversed when transient dynamics and time lags in the coupled social-ecological system are taken into account. We constructed an empirically based simulation model that includes the combined effect from nonlinear ecological dynamics and human adaptation. Delayed policy response and slow implementation introduce time lags that can strongly affect lake restoration time. Our model demonstrates how time lags in municipal policy making can be compensated for by individual action mediated through social pressure.

Regime shift modeling and management generally focus on tipping points, early warning indicators, and the prevention of abrupt shifts to undesirable states. Few studies assess the potential for restoring a deteriorating ecosystem that is on a transition pathway toward an undesirable state. During the transition, feedbacks that stabilize the new regime are still weak, providing an opportunity to reverse the ongoing shift. Here, we present a social-ecological model that explores both how transient social processes affect ecological dynamics in the vicinity of a tipping point to reinforce the desired state and how social mechanisms of policy implementation affect restoration time. We simulate transitions of a lake, policy making, and behavioral change by lake polluters to study the time lags that emerge as a response to the transient, deteriorating lake state. We found that restoration time is most sensitive to the timing of policy making, but that the transient dynamics of the social processes determined outcomes in nontrivial ways. Social pressure to adopt costly technology, in our case on-site sewage treatment, was up to a degree capable of compensating for delays in municipal policy making. Our analysis of interacting social and ecological time lags in the transient phase of a shallow lake highlights opportunities for restoration that a stable state analysis would miss. We discuss management perspectives for navigating critical feedbacks in a transitioning social-ecological system. The understanding of transient dynamics and the interaction with social time lags can be more relevant than solely stable states and tipping points.

Biocultural Hysteresis Inhibits Adaptation to Environmental Change

Indigenous peoples and local communities (IPLC) often use natural resources as both a reason and mechanism for environmental management, yet a number of environmental, social, and economic drivers disrupt this relationship. Here, we argue that these drivers can also trigger a set of feedback mechanisms that further diminish the efficacy of local management. We call this process biocultural hysteresis. These feedbacks, which include knowledge loss and a breakdown of social hierarchies, prevent IPLC from adapting their management to change. Biocultural hysteresis worsens as IPLC spend an increasing amount of time outside their social-ecological context. Therefore, we argue for adaptive policies and processes that favour protecting and enabling IPLC engagement with their environment.

Cascading regime shifts within and across scales

Regime shifts are large, abrupt, and persistent critical transitions in the function and structure of ecosystems. Yet, it is unknown how these transitions will interact, whether the occurrence of one will increase the likelihood of another or simply correlate at distant places. We explored two types of cascading effects: Domino effects create one-way dependencies, whereas hidden feedbacks produce two-way interactions. We compare them with the control case of driver sharing, which can induce correlations. Using 30 regime shifts described as networks, we show that 45% of regime shift pairwise combinations present at least one plausible structural interdependence. The likelihood of cascading effects depends on cross-scale interactions but differs for each type. Management of regime shifts should account for potential connections.

Resilience as an emergent property of human-infrastructure dynamics: A multi-agent simulation model for characterizing regime shifts and tipping point behaviors in infrastructure systems

The objective of this study is to establish a framework for analyzing infrastructure dynamics affecting the long-term steady state, and hence resilience in civil infrastructure systems. To this end, a multi-agent simulation model was created to capture important phenomena affecting the dynamics of coupled human-infrastructure systems and model the long-term performance regimes of infrastructure. The proposed framework captures the following three factors that shape the dynamics of coupled human-infrastructure systems: (i) engineered physical infrastructure; (ii) human actors; and (iii) chronic and acute stressors. A complex system approach was adopted to examine the long-term resilience of infrastructure based on the understanding of performance regimes, as well as tipping points at which shifts in the performance regime of infrastructure occur under the impact of external stressors and/or change in internal dynamics. The application of the proposed framework is demonstrated in a case of urban water distribution infrastructure using the data from a numerical case study network. The developed multi-agent simulation model was then used in examining the system resilience over a 100-year horizon under stressors such as population change and funding constraints. The results identified the effects of internal dynamics and external stressors on the resilience landscape of infrastructure systems. Furthermore, the results also showed the capability of the framework in capturing and simulating the underlying mechanisms affecting human-infrastructure dynamics, as well as long-term regime shifts and tipping point behaviors. Therefore, the integrated framework proposed in this paper enables building complex system-based theories for a more advanced understanding of civil infrastructure resilience.

Early Warnings for State Transitions

New concepts have emerged in theoretical ecology with the intent to quantify complexities in ecological change that are unaccounted for in state-and-transition models and to provide applied ecologists with statistical early warning metrics able to predict and prevent state transitions. With its rich history of furthering ecological theory and its robust and broad-scale monitoring frameworks, the rangeland discipline is poised to empirically assess these newly proposed ideas while also serving as early adopters of novel statistical metrics that provide advanced warning of a pending shift to an alternative ecological regime. Were view multivariate early warning and regime shift detection metrics, identify situations where various metrics will be most useful for rangeland science, and then highlight known shortcomings. Our review of a suite of multivariate-based regime shift/early warning indicators provides a broad range of metrics applicable to a wide variety of data types or contexts, from situations where a great deal is known about the key system drivers and a regime shift is hypothesized a priori, to situations where the key drivers and the possibility of a regime shift are both unknown. These metrics can be used to answer ecological state-and-transition questions, inform policymakers, and provide quantitative decision-making tools for managers.

Finite-time scaling in local bifurcations

Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we have made use of the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete (deterministic) dynamical systems. We analytically derive finite-time scaling laws for two ubiquitous transitions given by the transcritical and the saddle-node bifurcation, obtaining exact expressions for the critical exponents and scaling functions. One of the scaling laws, corresponding to the distance of the dynamical variable to the attractor, turns out to be universal, in the sense that it holds for both bifurcations, yielding the same exponents and scaling function. Remarkably, the resulting scaling behavior in the transcritical bifurcation is precisely the same as the one in the (stochastic) Galton-Watson process. Our work establishes a new connection between thermodynamic phase transitions and bifurcations in low-dimensional dynamical systems, and opens new avenues to identify the nature of dynamical shifts in systems for which only short time series are available.

Punishment and inspection for governing the commons in a feedback-evolving game

Utilizing common resources is always a dilemma for community members. While cooperator players restrain themselves and consider the proper state of resources, defectors demand more than their supposed share for a higher payoff. To avoid the tragedy of the common state, punishing the latter group seems to be an adequate reaction. This conclusion, however, is less straightforward when we acknowledge the fact that resources are finite and even a renewable resource has limited growing capacity. To clarify the possible consequences, we consider a coevolutionary model where beside the payoff-driven competition of cooperator and defector players the level of a renewable resource depends sensitively on the fraction of cooperators and the total consumption of all players. The applied feedback-evolving game reveals that beside a delicately adjusted punishment it is also fundamental that cooperators should pay special attention to the growing capacity of renewable resources. Otherwise, even the usage of tough punishment cannot save the community from an undesired end.

Our proposed model considers not only the fundamental dilemma of individual and collective benefits but also focuses on their impacts on the environmental state. In general, there is a strong interdependence between individual actions and the actual shape of environment that can be described by means of a co-evolutionary model. Such approach recognizes the fact that even if our common-pool resources are partly renewable, they have limited growth capacities hence a depleted environment is unable to recover and reach a sustainable level again. This scenario would have a dramatic consequence on our whole society, therefore we should avoid it by punishing those who are not exercising restrain. We provide analytical and numerical evidences which highlight that punishment alone may not necessarily be a powerful tool to maintain a healthy shape of environment for the benefit of future generations. Cooperator actors, who are believed to take care of present state of our environment, should also consider carefully the growth capacity of renewable resources.

When optimization for governing human-environment tipping elements is neither sustainable nor safe

Optimizing economic welfare in environmental governance has been criticized for delivering short-term gains at the expense of long-term environmental degradation. Different from economic optimization, the concepts of sustainability and the more recent safe operating space have been used to derive policies in environmental governance. However, a formal comparison between these three policy paradigms is still missing, leaving policy makers uncertain which paradigm to apply. Here, we develop a better understanding of their interrelationships, using a stylized model of human-environment tipping elements. We find that no paradigm guarantees fulfilling requirements imposed by another paradigm and derive simple heuristics for the conditions under which these trade-offs occur. We show that the absence of such a master paradigm is of special relevance for governing real-world tipping systems such as climate, fisheries, and farming, which may reside in a parameter regime where economic optimization is neither sustainable nor safe.

Revenue-sharing clubs provide economic insurance and incentives for sustainability in common-pool resource systems

Harvesting behaviors of natural resource users, such as farmers, fishermen and aquaculturists, are shaped by season-to-season and day-to-day variability, or in other words risk. Here, we explore how risk-mitigation strategies can lead to sustainable use and improved management of common-pool natural resources. Over-exploitation of unmanaged natural resources, which lowers their long-term productivity, is a central challenge facing societies. While effective top-down management is a possible solution, it is not available if the resource is outside the jurisdictional bounds of any management entity, or if existing institutions cannot effectively impose sustainable-use rules. Under these conditions, alternative approaches to natural resource governance are required. Here, we study revenue-sharing clubs as a mechanism by which resource users can mitigate their income volatility and importantly, as a co-benefit, are also incentivized to reduce their effort, leading to reduced over-exploitation and improved resource governance. We use game theoretic analyses and agent-based modeling to determine the conditions in which revenue-sharing can be beneficial for resource management as well as resource users. We find that revenue-sharing agreements can emerge and lead to improvements in resource management when there is large variability in production/revenue and when this variability is uncorrelated across members of the revenue-sharing club. Further, we show that if members of the revenue-sharing collective can sell their product at a price premium, then the range of ecological and economic conditions under which revenue-sharing can be a tool for management greatly expands. These results have implications for the design of bottom-up management, where resource users themselves are incentivized to operate in ecologically sustainable and economically advantageous ways.

Indicators of transitions in biological systems

In the face of global biodiversity declines, predicting the fate of biological systems is a key goal in ecology. One popular approach is the search for early warning signals (EWSs) based on alternative stable states theory. In this review, we cover the theory behind nonlinearity in dynamic systems and techniques to detect the loss of resilience that can indicate state transitions. We describe the research done on generic abundance-based signals of instability that are derived from the phenomenon of critical slowing down, which represent the genesis of EWSs research. We highlight some of the issues facing the detection of such signals in biological systems - which are inherently complex and show low signal-to-noise ratios. We then document research on alternative signals of instability, including measuring shifts in spatial autocorrelation and trait dynamics, and discuss potential future directions for EWSs research based on detailed demographic and phenotypic data. We set EWSs research in the greater field of predictive ecology and weigh up the costs and benefits of simplicity vs. complexity in predictive models, and how the available data should steer the development of future methods. Finally, we identify some key unanswered questions that, if solved, could improve the applicability of these methods.

Socio-ecological dynamics of Caribbean coral reef ecosystems and conservation opinion propagation

The Caribbean coral reef ecosystem has experienced a long history of deterioration due to various stressors. For instance, over-fishing of parrotfish - an important grazer of macroalgae that can prevent destructive overgrowth of macroalgae - has threatened reef ecosystems in recent decades and stimulated conservation efforts such as the formation of marine protected areas. Here we develop a mathematical model of coupled socio-ecological interactions between reef dynamics and conservation opinion dynamics to better understand how natural and human factors interact individually and in combination to determine coral reef cover. We find that the coupling opinion and reef systems generates complex dynamics that are difficult to anticipate without use of a model. For instance, instead of converging to a stable state of constant coral cover and conservationist opinion, the system can oscillate between low and high live coral cover as human opinion oscillates in a boom-bust cycle between complacency and concern. Out of various possible parameter manipulations, we also find that raising awareness of coral reef endangerment best avoids counter-productive nonlinear feedbacks and always increases and stabilizes live coral reef cover. In conclusion, an improved understanding of coupled opinion-reef dynamics under anthrogenic stressors is possible using coupled socio-ecological models, and such models should be further researched.

Skill (or lack thereof) of data-model fusion techniques to provide an early warning signal for an approaching tipping point

Many coupled human-natural systems have the potential to exhibit a highly nonlinear threshold response to external forcings resulting in fast transitions to undesirable states (such as eutrophication in a lake). Often, there are considerable uncertainties that make identifying the threshold challenging. Thus, rapid learning is critical for guiding management actions to avoid abrupt transitions. Here, we adopt the shallow lake problem as a test case to compare the performance of four common data assimilation schemes to predict an approaching transition. In order to demonstrate the complex interactions between management strategies and the ability of the data assimilation schemes to predict eutrophication, we also analyze our results across two different management strategies governing phosphorus emissions into the shallow lake. The compared data assimilation schemes are: ensemble Kalman filtering (EnKF), particle filtering (PF), pre-calibration (PC), and Markov Chain Monte Carlo (MCMC) estimation. While differing in their core assumptions, each data assimilation scheme is based on Bayes’ theorem and updates prior beliefs about a system based on new information. For large computational investments, EnKF, PF and MCMC show similar skill in capturing the observed phosphorus in the lake (measured as expected root mean squared prediction error). EnKF, followed by PF, displays the highest learning rates at low computational cost, thus providing a more reliable signal of an impending transition. MCMC approaches the true probability of eutrophication only after a strong signal of an impending transition emerges from the observations. Overall, we find that learning rates are greatest near regions of abrupt transitions, posing a challenge to early learning and preemptive management of systems with such abrupt transitions.

European Neolithic societies showed early warning signals of population collapse

Ecosystems on the verge of major reorganization-regime shift-may exhibit declining resilience, which can be detected using a collection of generic statistical tests known as early warning signals (EWSs). This study explores whether EWSs anticipated human population collapse during the European Neolithic. It analyzes recent reconstructions of European Neolithic (8-4 kya) population trends that reveal regime shifts from a period of rapid growth following the introduction of agriculture to a period of instability and collapse. We find statistical support for EWSs in advance of population collapse. Seven of nine regional datasets exhibit increasing autocorrelation and variance leading up to collapse, suggesting that these societies began to recover from perturbation more slowly as resilience declined. We derive EWS statistics from a prehistoric population proxy based on summed archaeological radiocarbon date probability densities. We use simulation to validate our methods and show that sampling biases, atmospheric effects, radiocarbon calibration error, and taphonomic processes are unlikely to explain the observed EWS patterns. The implications of these results for understanding the dynamics of Neolithic ecosystems are discussed, and we present a general framework for analyzing societal regime shifts using EWS at large spatial and temporal scales. We suggest that our findings are consistent with an adaptive cycling model that highlights both the vulnerability and resilience of early European populations. We close by discussing the implications of the detection of EWS in human systems for archaeology and sustainability science.

Trans-heteroclinic bifurcation: a novel type of catastrophic shift

Global and local bifurcations are extremely important since they govern the transitions between different qualitative regimes in dynamical systems. These transitions or tipping points, which are ubiquitous in nature, can be smooth or catastrophic. Smooth transitions involve a continuous change in the steady state of the system until the bifurcation value is crossed, giving place to a second-order phase transition. Catastrophic transitions involve a discontinuity of the steady state at the bifurcation value, giving place to first-order phase transitions. Examples of catastrophic shifts can be found in ecosystems, climate, economic or social systems. Here we report a new type of global bifurcation responsible for a catastrophic shift. This bifurcation, identified in a family of quasi-species equations and named as trans-heteroclinic bifurcation, involves an exchange of stability between two distant and heteroclinically connected fixed points. Since the two fixed points interchange the stability without colliding, a catastrophic shift takes place. We provide an exhaustive description of this new bifurcation, also detailing the structure of the replication-mutation matrix of the quasi-species equation giving place to this bifurcation. A perturbation analysis is provided around the bifurcation value. At this value the heteroclinic connection is replaced by a line of fixed points in the quasi-species model. But it is shown that, if the replication-mutation matrix satisfies suitable conditions, then, under a small perturbation, the exchange of heteroclinic connections is preserved, except on a tiny range around the bifurcation value whose size is of the order of magnitude of the perturbation. The results presented here can help to understand better novel mechanisms behind catastrophic shifts and contribute to a finer identification of such transitions in theoretical models in evolutionary biology and other dynamical systems.

Delayed behavioural shifts undermine the sustainability of social-ecological systems

Natural habitat destruction and fragmentation generate a time-delayed loss of species and associated ecosystem services. As social-ecological systems (SESs) depend on a range of ecosystem services, lagged ecological dynamics may affect their long-term sustainability. Here, we investigate the role of consumption changes for sustainability, under a time-delayed ecological feedback on agricultural production. We use a stylized model that couples the dynamics of biodiversity, technology, human demography and compliance with a social norm prescribing sustainable consumption. Compliance with the sustainable norm reduces both the consumption footprint and the vulnerability of SESs to transient overshoot-and-collapse population crises. We show that the timing and interaction between social, demographic and ecological feedbacks govern the transient and long-term dynamics of the system. A sufficient level of social pressure (e.g. disapproval) applied on the unsustainable consumers leads to the stable coexistence of unsustainable and sustainable or mixed equilibria, where both defectors and conformers coexist. Under bistability conditions, increasing extinction debts reduces the resilience of the system, thus favouring abrupt regime shifts towards unsustainable pathways. Given recent evidence of large extinction debts, such results call for farsightedness and a better understanding of time delays when studying the sustainability of coupled SESs.

Social Cooperation and Disharmony in Communities Mediated through Common Pool Resource Exploitation

It was theorized that when a society exploits a shared resource, the system can undergo extreme phase transition from full cooperation in abiding by a social agreement, to full defection from it. This was shown to happen in an integrated society with complex social relationships. However, real-world agents tend to segregate into communities whose interactions contain features of the associated community structure. We found that such social segregation softens the abrupt extreme transition through the emergence of multiple intermediate phases composed of communities of cooperators and defectors. Phase transitions thus now occur through these intermediate phases which avert the instantaneous collapse of social cooperation within a society. While this is beneficial to society, it nonetheless costs society in two ways. First, the return to full cooperation from full defection at the phase transition is no longer immediate. Community linkages have rendered greater societal inertia such that the switch back is now typically stepwise rather than a single change. Second, there is a drastic increase in social disharmony within the society due to the greater tension in the relationship between segregated communities of defectors and cooperators. Intriguingly, these results on multiple phases with its associated phenomenon of social disharmony are found to characterize the level of cooperation within a society of Balinese farmers who exploit water for rice production.

Early warning signals of regime shifts in coupled human-environment systems

In complex systems, a critical transition is a shift in a system's dynamical regime from its current state to a strongly contrasting state as external conditions move beyond a tipping point. These transitions are often preceded by characteristic early warning signals such as increased system variability. However, early warning signals in complex, coupled human-environment systems (HESs) remain little studied. Here, we compare critical transitions and their early warning signals in a coupled HES model to an equivalent environment model uncoupled from the human system. We parameterize the HES model, using social and ecological data from old-growth forests in Oregon. We find that the coupled HES exhibits a richer variety of dynamics and regime shifts than the uncoupled environment system. Moreover, the early warning signals in the coupled HES can be ambiguous, heralding either an era of ecosystem conservationism or collapse of both forest ecosystems and conservationism. The presence of human feedback in the coupled HES can also mitigate the early warning signal, making it more difficult to detect the oncoming regime shift. We furthermore show how the coupled HES can be "doomed to criticality": Strategic human interactions cause the system to remain perpetually in the vicinity of a collapse threshold, as humans become complacent when the resource seems protected but respond rapidly when it is under immediate threat. We conclude that the opportunities, benefits, and challenges of modeling regime shifts and early warning signals in coupled HESs merit further research.