Safe and just Earth system boundaries.

The stability and resilience of the Earth system and human well-being are inseparably linked1-3, yet their interdependencies are generally under-recognized; consequently, they are often treated independently4,5. Here, we use modelling and literature assessment to quantify safe and just Earth system boundaries (ESBs) for climate, the biosphere, water and nutrient cycles, and aerosols at global and subglobal scales. We propose ESBs for maintaining the resilience and stability of the Earth system (safe ESBs) and minimizing exposure to significant harm to humans from Earth system change (a necessary but not sufficient condition for justice)4. The stricter of the safe or just boundaries sets the integrated safe and just ESB. Our findings show that justice considerations constrain the integrated ESBs more than safety considerations for climate and atmospheric aerosol loading. Seven of eight globally quantified safe and just ESBs and at least two regional safe and just ESBs in over half of global land area are already exceeded. We propose that our assessment provides a quantitative foundation for safeguarding the global commons for all people now and into the future.

From single decisions to sequential choice patterns: Extending the dynamics of value-based decision-making.

Every day, we make many value-based decisions where we weigh the value of options with other properties, e.g. their time of delivery. In the laboratory, such value-based decision-making is usually studied on a trial by trial basis and each decision is assumed to represent an isolated choice process. Real-life decisions however are usually embedded in a rich context of previous choices at different time scales. A fundamental question is therefore how the dynamics of value-based decision processes unfold on a time scale across several decisions. Indeed, findings from perceptual decision making suggest that sequential decisions patterns might also be present for vale-based decision making. Here, we use a neural-inspired attractor model as an instance of dynamic models from perceptual decision making, as such models incorporate inherent activation dynamics across decisions. We use the model to predict sequential patterns, namely oscillatory switching, perseveration and dependence of perseveration on the delay between decisions. Furthermore, we predict RT effects for specific sequences of trials. We validate the predictions in two new studies and a reanalysis of existing data from a novel decision game in which participants have to perform delay discounting decisions. Applying the validated reasoning to a well-established choice questionnaire, we illustrate and discuss that taking sequential choice patterns into account may be necessary to accurately analyse and model value-based decision processes, especially when considering differences between individuals.

Cross-scale cooperation enables sustainable use of a common-pool resource.

In social-ecological systems (SESs), social and biophysical dynamics interact within and between the levels of organization at multiple spatial and temporal scales. Cross-scale interactions (CSIs) are interdependences between processes at different scales, generating behaviour unpredictable at single scales. Understanding CSIs is important for improving SES governance, but they remain understudied. Theoretical models are needed that capture essential features while being simple enough to yield insights into mechanisms. In a stylized model, we study CSIs in a two-level system of weakly interacting communities harvesting a common-pool resource. Community members adaptively conform to, or defect from, a norm of socially optimal harvesting, enforced through social sanctioning both within and between communities. We find that each subsystem's dynamics depend sensitively on the other despite interactions being much weaker between subsystems than within them. When interaction is purely biophysical, stably high cooperation in one community can cause cooperation in the other to collapse. However, even weak social interaction can prevent the collapse of cooperation and instead cause collapse of defection. We identify conditions under which subsystem-level cooperation produces desirable system-level outcomes. Our findings expand evidence that collaboration is important for sustainably managing shared resources, showing its importance even when resource sharing and social relationships are weak.

Trajectories of the Earth System in the Anthropocene.

We explore the risk that self-reinforcing feedbacks could push the Earth System toward a planetary threshold that, if crossed, could prevent stabilization of the climate at intermediate temperature rises and cause continued warming on a "Hothouse Earth" pathway even as human emissions are reduced. Crossing the threshold would lead to a much higher global average temperature than any interglacial in the past 1.2 million years and to sea levels significantly higher than at any time in the Holocene. We examine the evidence that such a threshold might exist and where it might be. If the threshold is crossed, the resulting trajectory would likely cause serious disruptions to ecosystems, society, and economies. Collective human action is required to steer the Earth System away from a potential threshold and stabilize it in a habitable interglacial-like state. Such action entails stewardship of the entire Earth System-biosphere, climate, and societies-and could include decarbonization of the global economy, enhancement of biosphere carbon sinks, behavioral changes, technological innovations, new governance arrangements, and transformed social values.

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.

Resilience offers escape from trapped thinking on poverty alleviation.

The poverty trap concept strongly influences current research and policy on poverty alleviation. Financial or technological inputs intended to "push" the rural poor out of a poverty trap have had many successes but have also failed unexpectedly with serious ecological and social consequences that can reinforce poverty. Resilience thinking can help to (i) understand how these failures emerge from the complex relationships between humans and the ecosystems on which they depend and (ii) navigate diverse poverty alleviation strategies, such as transformative change, that may instead be required. First, we review commonly observed or assumed social-ecological relationships in rural development contexts, focusing on economic, biophysical, and cultural aspects of poverty. Second, we develop a classification of poverty alleviation strategies using insights from resilience research on social-ecological change. Last, we use these advances to develop stylized, multidimensional poverty trap models. The models show that (i) interventions that ignore nature and culture can reinforce poverty (particularly in agrobiodiverse landscapes), (ii) transformative change can instead open new pathways for poverty alleviation, and (iii) asset inputs may be effective in other contexts (for example, where resource degradation and poverty are tightly interlinked). Our model-based approach and insights offer a systematic way to review the consequences of the causal mechanisms that characterize poverty traps in different agricultural contexts and identify appropriate strategies for rural development challenges.

An empirical model of the Baltic Sea reveals the importance of social dynamics for ecological regime shifts.

Regime shifts triggered by human activities and environmental changes have led to significant ecological and socioeconomic consequences in marine and terrestrial ecosystems worldwide. Ecological processes and feedbacks associated with regime shifts have received considerable attention, but human individual and collective behavior is rarely treated as an integrated component of such shifts. Here, we used generalized modeling to develop a coupled social-ecological model that integrated rich social and ecological data to investigate the role of social dynamics in the 1980s Baltic Sea cod boom and collapse. We showed that psychological, economic, and regulatory aspects of fisher decision making, in addition to ecological interactions, contributed both to the temporary persistence of the cod boom and to its subsequent collapse. These features of the social-ecological system also would have limited the effectiveness of stronger fishery regulations. Our results provide quantitative, empirical evidence that incorporating social dynamics into models of natural resources is critical for understanding how resources can be managed sustainably. We also show that generalized modeling, which is well-suited to collaborative model development and does not require detailed specification of causal relationships between system variables, can help tackle the complexities involved in creating and analyzing social-ecological models.

Fusion leads to effective segregation of damage during cell division: An analytical treatment.

High levels of cellular damage are associated with impairment of cellular function and cell death. Partitioning the damage into a fraction of cells in the population improves population fitness and survival. We have previously shown that protein aggregates, resulting from misfolded, damaged proteins, fuse with each other leading to damage partitioning during cell division. Here, using an analytical treatment of aggregate fusion in dividing cells we present analytical expressions for two measures of damage partition: aggregate mass partition asymmetry between two dividing cells and standard deviation of total aggregate mass across the population. The scaling laws obtained demonstrate how damage partition may generally depend on characteristics of the cellular processes, facilitating better understanding of damage segregation in biological cells.

Fusion of protein aggregates facilitates asymmetric damage segregation.

Asymmetric segregation of damaged proteins at cell division generates a cell that retains damage and a clean cell that supports population survival. In cells that divide asymmetrically, such as Saccharomyces cerevisiae, segregation of damaged proteins is achieved by retention and active transport. We have previously shown that in the symmetrically dividing Schizosaccharomyces pombe there is a transition between symmetric and asymmetric segregation of damaged proteins. Yet how this transition and generation of damage-free cells are achieved remained unknown. Here, by combining in vivo imaging of Hsp104-associated aggregates, a form of damage, with mathematical modeling, we find that fusion of protein aggregates facilitates asymmetric segregation. Our model predicts that, after stress, the increased number of aggregates fuse into a single large unit, which is inherited asymmetrically by one daughter cell, whereas the other one is born clean. We experimentally confirmed that fusion increases segregation asymmetry, for a range of stresses, and identified Hsp16 as a fusion factor. Our work shows that fusion of protein aggregates promotes the formation of damage-free cells. Fusion of cellular factors may represent a general mechanism for their asymmetric segregation at division.

Early warning signals for critical transitions: a generalized modeling approach.

Critical transitions are sudden, often irreversible, changes that can occur in a large variety of complex systems; signals that warn of critical transitions are therefore highly desirable. We propose a new method for early warning signals that integrates multiple sources of information and data about the system through the framework of a generalized model. We demonstrate our proposed approach through several examples, including a previously published fisheries model. We regard our method as complementary to existing early warning signals, taking an approach of intermediate complexity between model-free approaches and fully parameterized simulations. One potential advantage of our approach is that, under appropriate conditions, it may reduce the amount of time series data required for a robust early warning signal.

Effectiveness of beads for tracking small-scale molecular motor dynamics.

Investigations into molecular motor dynamics are increasingly focused on small-scale features of the motor's motion. We define performance measures of a common type of single-molecule motility assay, the bead assay, for its ability to detect such features. Using numerical models, we explore the dependence of assay performance on a number of experimentally controllable parameters, including bead size, optical force, and the method of attaching the bead to the motor. We find that the best parameter choice depends on the objective of the experiments, and give a guide to parameter selection. Comparison of the models against experimental data from a recent bead assay of myosin V exemplifies how our methods can also be used to extract additional information from bead assays, particularly that related to small-scale features. By analyzing the experimental data we find evidence for previously undetected multiple waiting states of the bead-motor complex. Furthermore, from numerical simulations we find that equilibrium bead dynamics display features previously attributed to aborted motor steps, and that bead dynamics alone can produce multiple subphases during a step.

Geometric and projection effects in Kramers-Moyal analysis.

Kramers-Moyal coefficients provide a simple and easily visualized method with which to analyze nonlinear stochastic time series. One mechanism that can affect the estimation of the coefficients is geometric projection effects. For some biologically inspired examples, these effects are predicted and explored with a nonstochastic projection operator method and compared with direct numerical simulation of the systems' Langevin equations. General features and characteristics are identified, and the utility of the Kramers-Moyal method is discussed. Projections of a system are in general non-Markovian, but here the Kramers-Moyal method remains useful, and in any case the primary examples considered are found to be close to Markovian.