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Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described by nonlinear dynamical systems, often display complex parameter dependence and exhibit bifurcations. The dynamics of heterogeneous spatially extended systems passing through bifurcations are still relatively poorly understood, yet recent theoretical studies and experimental data highlight the resulting complex behaviors and their relevance to real-world applications. We explore the consequences of spatial heterogeneities passing through bifurcations via two examples strongly motivated by applications. These model systems illustrate that studying heterogeneity-induced behaviors in spatial systems is crucial for a better understanding of ecological transitions and functional organization in brain development., Comment: 28 pages

Mathematical models are getting increasingly detailed to better predict phenomena or gain more accurate insights into the dynamics of a system of interest, even when there are no validation or training data available. Here, we show through ANOVA and statistical theory that this practice promotes fuzzier estimates because it generally increases the model's effective dimensions, i.e., the number of influential parameters and the weight of high-order interactions. By tracking the evolution of the effective dimensions and the output uncertainty at each model upgrade stage, modelers can better ponder whether the addition of detail truly matches the model's purpose and the quality of the data fed into it., Science Advances, 8 (42), ISSN:2375-2548

Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics. Statistical physics first confronted the problem of emergent phenomena such as critical transitions in the 1800s and 1900s, culminating in the theory of phase transitions. However, although phase transitions show a strong resemblance to critical transitions, the theoretical connections between the two sets of phenomena are tenuous at best, and it would be advantageous to make them more concrete in order to take advantage of the theoretical methods developed by physicists to study phase transitions. Here we attempt to explicitly connect the theory of critical transitions to phase transitions in physics. We initially find something paradoxical, that many critical transitions closely resemble first-order phase transitions, but that many of the early warning indicators developed to anticipate critical transitions, such as critical slowing down or increasing spatial correlations, occur instead in second-order phase transitions. We attempt to reconcile these disparities by making the connection with other phenomena associated with first-order phase transitions, such as spinodal instabilities and metastable states., Comment: 16 pages, 5 figures, To appear as book chapter in Global Systemic Risk

OBJECTIVE: To prospectively delineate self-reported health-related quality of life (HRQOL) of adolescents and young adults (AYAs) 8 and 10 years after an epilepsy diagnosis and evaluate the degree of AYA-parent agreement in ratings of AYA's HRQOL. METHODS: Data came from the Health-Related Quality of Life in Children with Epilepsy Study (HERQULES), a 10-year longitudinal study of children, aged 4-12 years, with newly diagnosed epilepsy. Epilepsy-specific HRQOL was self-reported by AYA 8 and 10 years after diagnosis and by parents at multiple time points throughout the 10-year follow-up. Measurers of HRQOL over time were analyzed using a linear mixed-effect model approach. AYA-parent agreement was evaluated using intraclass correlation coefficient (ICC) and Bland-Altman plots. RESULTS: A total of 165 AYAs participated at long-term follow-up. There was considerable heterogeneity among AYA's HRQOL, and as a group, there was no significant change in HRQOL from the 8- to 10-year follow-up. Household income at the time of diagnosis, seizure control at follow-up, and a history of emotional problems (anxiety/depression) were independent predictors of HRQOL at follow-up. AYA-parent agreement on AYA's HRQOL was moderate (ICC 0.62, 95% CI 0.51-0.71), although considerable differences were observed at the individual level. AYA-parent agreement varied with AYA's and parent's age, seizure control, and family environment. SIGNIFICANCE: In the long-term after a diagnosis of epilepsy, AYAs report stable HRQOL over time at the group level, although notable individual differences exist. Seizure control, anxiety/depression, and family environment meaningfully impact AYA's long-term HRQOL. AYA and parent reports on HRQOL are similar at the group level, although they cannot be used interchangeably, given the large individual differences observed.

Additional figures and tables.

Extended discussion on the mathematical model and computer simulations.

Models of human dimensions of fisheries are important to understanding and predicting how fishing industries respond to changes in marine ecosystems and management institutions. Advances in computation have made it possible to construct agent-based models (ABMs)—which explicitly describe the behaviour of individual people, firms, or vessels in order to understand and predict their aggregate behaviours. ABMs are widely used for both academic and applied purposes in many settings including finance, urban planning, and the military, but are not yet mainstream in fisheries science and management, despite a growing literature. ABMs are well suited to understanding emergent consequences of fisher interactions, heterogeneity, and bounded rationality, especially in complex ecological, social, and institutional contexts. For these reasons, we argue that ABMs of human behaviour can contribute significantly to human dimensions of fisheries in three areas: 1) understanding interactions between multiple management institutions; 2) incorporating cognitive and behavioural sciences into fisheries science and practice; and 3) understanding and projecting the social consequences of management institutions. We provide simple examples illustrating the potential for ABMs in each of these areas, using conceptual (‘toy’) versions of the POSEIDON model. We argue that salient strategic advances in these areas could pave the way for increased tactical use of ABMs in fishery management settings. We review common ABM development and application challenges, with the aim of providing guidance to beginning ABM developers and users studying human dimensions of fisheries.

Our hypothesis is that differences in the regional connectivity within the fetal brain (the structural and functional connections between regions of the brain) can be observed with fetal fMRI as early as in the second trimester of pregnancy. If we can detect differences in an at-risk fetal brain and associate that with plancental and maternal data, we could recommend interventions, such as diet or medication changes, and then monitor the impact of treatment on the fetal brain. https://ir.lib.uwo.ca/brainscanprojectsummaries/1000/thumbnail.jpg

Aquaculture production is projected to expand from land-based operations to the open ocean as demand for seafood grows and competition increases for inputs to land-based aquaculture, such as freshwater and suitable land. In contrast to land-based production, open-ocean aquaculture is constrained by oceanographic factors, such as current speeds and seawater temperature, which are dynamic in time and space, and cannot easily be controlled. As such, the potential for offshore aquaculture to increase seafood production is tied to the physical state of the oceans. We employ a novel spatial model to estimate the potential of open-ocean finfish aquaculture globally, given physical, biological and technological constraints. Finfish growth potential for three common aquaculture species representing different thermal guilds—Atlantic salmon (Salmo salar), gilthead seabream (Sparus aurata) and cobia (Rachycentron canadum)—is compared across species and regions and with climate change, based on outputs of a high-resolution global climate model. Globally, there are ample areas that are physically suitable for fish growth and potential expansion of the nascent aquaculture industry. The effects of climate change are heterogeneous across species and regions, but areas with existing aquaculture industries are likely to see increases in growth rates. In areas where climate change results in reduced growth rates, adaptation measures, such as selective breeding, can probably offset potential production losses.

What is the ultimate limiting nutrient in the ocean? The dominant theory, which was first proposed by Redfield and later formalized by Tyrrell[1, 2], states that despite the scarcity of fixed nitrogen (N) in the surface ocean, phosphorus (P) availability ultimately determines primary productivity. Two recent findings directly challenge the assumptions of the Redfield-Tyrrell paradigm: the discovery of systematic variations of phytoplankton cellular N:P:Fe and widespread iron-limitation of phytoplankton. Here we use a simple model of nitrogen, phosphorus, and iron (Fe) cycling to show how the resource demand ratios and biogeography of phytoplankton interact with external resource supply ratios to govern nutrient cycling and primary productivity. We find that all three nutrients can limit global primary productivity, and that the ratio of geochemical supply to biological demand of each nutrient in each ocean region determines the limiting nutrients, with nitrogen N fixation providing a mechanism for the cycles to interact. These results have important consequences for our understanding of biogeochemical cycles, ocean-atmosphere interactions, marine ecology, and the response of ocean ecosystems to climate change. Our work demonstrates the importance of resource ratios and suggests that future studies of the physiological and geochemical regulation of these ratios are indispensable to building accurate theories and future predictions of nutrient cycling and primary productivity.

Appendix A. R-N phase diagrams for single site breeding migration model. (PDF 203 kb)

Marine ecosystems play an integral role in the functioning of life on earth. To predict how they will respond to global changes, and to effectively manage and maintain services upon which humans rely, we must understand how biological processes at the cellular level generate macroscopic patterns in the oceans. Here, we discuss how physics and biogeochemistry influence and constrain marine ecosystem structure and function, and outline key regularities and patterns of variability that models should aim to reproduce. We identify unanswered questions regarding how size-dependent physiological and ecological processes are linked to turbulent mixing, dealing specifically with how size structure is related to mixing over a range of spatial scales and how it is linked to the fate of primary production in the sea. Los ecosistemas marinos juegan un papel integral en el funcionamiento de la vida sobre la Tierra. Para predecir cómo van a responder a cambios globales y para mantener los servicios de los cuales los humanos dependemos, tenemos que comprender cómo los procesos biológicos a nivel celular generan patrones macroscópicos en el océano. Examinamos cómo la física y la biogeoquímica afectan y limitan la estructura y función de los ecosistemas marinos, y exponemos importantes regularidades y patrones de variabilidad que los modelos deberían reproducir. Identificamos aspectos sin resolver sobre la relación entre procesos fisiológicos y ecológicos y la mezcla turbulenta. En concreto, cómo la estructura de tamaños está relacionada con la mezcla en un rango de escalas espaciales y cómo está conectada con el destino de la producción primaria en el mar.

This report presents an overview of research horizons in sustainability science. Its motivation is to help harness science and technology to foster a transition toward sustainability – toward patterns of development that promote human well-being while conserving the life-support systems of the planet. It builds on but does not explicitly address the vast range of relevant sector-specific and cross-sectoral problem-solving work now underway in fields ranging from green technologies in energy and manufacturing to urban design to agriculture and natural resources. It focuses on the narrower but essential task of characterizing the needs for fundamental work on the core concepts, methods, models, and measurements that, if successful, would support work across all of those sectoral applications by advancing fundamental understanding of the science of sustainability. The report sets forth the workshop’s findings and recommendations on six fundamental questions now facing scholars seeking to harness science and technology to foster sustainability: 1. What are the principal tradeoffs between human well-being and the natural environment, and how are those tradeoffs mediated by the ways in which people use nature? 2. What determines the adaptability of coupled human-environment systems and, more broadly, their vulnerability and robustness/resilience in the face of external shocks and internal dynamics? 3. What shapes the long term trends and transitions that set the stage on which humanenvironment interactions are played out? 4. How can theory and models be formulated that better account for the variation in types or trends of human-environment interactions? 5. How can society most effectively guide or manage human-environment systems toward a sustainability transition? 6. How can the “sustainability†of alternative trajectories of human-environment interactions be usefully and rigorously evaluated?

Expanded Results, Theorems and remarks, A related epidemiological model with disease-induced death, Additional infection stages

Funder: H2020 European Research Council; FundRef: http://dx.doi.org/10.13039/100010663; Grant(s): Naviflu:818353, Seasonal influenza viruses create a persistent global disease burden by evolving to escape immunity induced by prior infections and vaccinations. New antigenic variants have a substantial selective advantage at the population level, but these variants are rarely selected within-host, even in previously immune individuals. Using a mathematical model, we show that the temporal asynchrony between within-host virus exponential growth and antibody-mediated selection could limit within-host antigenic evolution. If selection for new antigenic variants acts principally at the point of initial virus inoculation, where small virus populations encounter well-matched mucosal antibodies in previously-infected individuals, there can exist protection against reinfection that does not regularly produce observable new antigenic variants within individual infected hosts. Our results provide a theoretical explanation for how virus antigenic evolution can be highly selective at the global level but nearly neutral within-host. They also suggest new avenues for improving influenza control.

This file contains the sections: Expanded Results, The addition of infection stages, Evolutionary dynamics in the presence of coexistence, Analysis for theorems and remarks in main text

This file contains the sections: Expanded Results, The addition of infection stages, Evolutionary dynamics in the presence of coexistence, Analysis for theorems and remarks in main text

This file contains the sections: Expanded Results, The addition of infection stages, Evolutionary dynamics in the presence of coexistence, Analysis for theorems and remarks in main text

Expanded Results, Theorems and remarks, A related epidemiological model with disease-induced death, Additional infection stages

SARS-CoV-2 is an international public health emergency; high transmissibility and morbidity and mortality can result in the virus overwhelming health systems. Combinations of social distancing, and test, trace and isolate strategies can reduce the number of new infections per infected individual below 1, thus driving declines in case numbers, but may be both challenging and costly. These interventions must also be maintained until development and (and now likely) mass deployment of a vaccine (or therapeutics), since otherwise, many susceptible individuals are still at risk of infection. We use a simple analytical model to explore how low levels of infection, combined with vaccination, determine the trajectory to community immunity. Understanding the repercussions of the biological characteristics of the viral life cycle in this scenario is of considerable importance. We provide a simple description of this process by modelling the scenario where the effective reproduction number Reff is maintained at 1. Since the additional complexity imposed by the strength and duration of transmission-blocking immunity is not yet clear, we use our framework to probe the impact of these uncertainties. Through intuitive analytical relations, we explore how the necessary magnitude of vaccination rates and mitigation efforts depends crucially on the durations of natural and vaccinal immunity. We also show that our framework can encompass seasonality or preexisting immunity due to epidemic dynamics prior to strong mitigation measures. Taken together, our simple conceptual model illustrates the importance of individual and vaccinal immunity for community immunity, and that the quantification of individuals immunized against SARS-CoV-2 is paramount.

The world's forests and forestry sector are facing unprecedented biological, political, social, and climatic challenges. The development of appropriate, novel forest management and restoration approaches that adequately consider uncertainty and adaptability are hampered by a continuing focus on production of a few goods or objectives, strong control of forest structure and composition, and most importantly the absence of a global scientific framework and long‐term vision. Ecosystem‐based approaches represent a step in the right direction, but are limited in their ability to deal with the rapid pace of social, climatic, and environmental changes. We argue here that viewing forest ecosystems as complex adaptive system provides a better alternative for both production‐ and conservation‐oriented forests and forestry. We propose a set of broad principles and changes to increase the adaptive capacity of forests in the face of future uncertainties. These span from expanding the sustained‐yield, single‐good paradigm to developing policy incentives and interventions that promote self‐organization and integrated social‐ecological adaptation. This research was supported by the Marie Curie IRSES Newforests Project (EU‐FP7–612645).

This file contains the sections: Expanded Results, The addition of infection stages, Evolutionary dynamics in the presence of coexistence, Analysis for theorems and remarks in main text

Additional file 1. Study Specific Questionnaires and forms

Additional file 1. Study Specific Questionnaires and forms

SARS-CoV-2 is an international public health emergency; high transmissibility and morbidity and mortality can result in the virus overwhelming health systems. Combinations of social distancing, and test, trace and isolate strategies can reduce the number of new infections per infected individual below 1, thus driving declines in case numbers, but may be both challenging and costly. These interventions must also be maintained until development and (and now likely) mass deployment of a vaccine (or therapeutics), since otherwise, many susceptible individuals are still at risk of infection. We use a simple analytical model to explore how low levels of infection, combined with vaccination, determine the trajectory to community immunity. Understanding the repercussions of the biological characteristics of the viral life cycle in this scenario is of considerable importance. We provide a simple description of this process by modelling the scenario where the effective reproduction number Reff is maintained at 1. Since the additional complexity imposed by the strength and duration of transmission-blocking immunity is not yet clear, we use our framework to probe the impact of these uncertainties. Through intuitive analytical relations, we explore how the necessary magnitude of vaccination rates and mitigation efforts depends crucially on the durations of natural and vaccinal immunity. We also show that our framework can encompass seasonality or preexisting immunity due to epidemic dynamics prior to strong mitigation measures. Taken together, our simple conceptual model illustrates the importance of individual and vaccinal immunity for community immunity, and that the quantification of individuals immunized against SARS-CoV-2 is paramount.

This file contains the sections: Expanded Results, The addition of infection stages, Evolutionary dynamics in the presence of coexistence, Analysis for theorems and remarks in main text

Contemporary economic thinking does not acknowledge that the human economy is embedded in Nature; it instead treats humanity as a customer that draws on Nature. In this paper, we present a grammar for economic reasoning that is not built on that error. The grammar is based on a comparison between our demand for Nature's maintenance and regulating services and her ability to supply them on a sustainable basis. The comparison is then used to show that for measuring economic well-being, national statistical offices should estimate an inclusive measure of their economies' wealth and its distribution, not GDP and its distribution. The concept of ‘inclusive wealth’ is then used to identify policy instruments that ought to be used to manage such global public goods as the open seas and tropical rainforests. Trade liberalization without heed paid to the fate of local ecosystems from which primary products are drawn and exported by developing countries leads to a transfer of inclusive wealth from there to rich importing countries. Humanity's embeddedness in Nature has far-reaching implications for the way we should view human activities—in households, communities, nations and the world. This article is part of the theme issue ‘Detecting and attributing the causes of biodiversity change: needs, gaps and solutions’.

Climate change is a global externality that has proven difficult to address through formal institutions alone, due to the public good properties of climate change mitigation and the lack of a supranational institution for enforcing global treaties. Given these circumstances, which are arguably the most challenging for international cooperation, commitment problems and free-riding incentives for countries to delay costly mitigation efforts are major obstacles to effective environmental agreements. Starting from this premise, we examine domestic mitigation efforts, with the goal of assessing the extent to which the willingness of individuals to contribute voluntarily to the public good of climate mitigation could be scaled up to the global level. Although individual environmental actions are clearly insufficient for achieving ambitious global mitigation targets, we argue that they are nevertheless initial and essential steps in the right direction. In fact, individual and community efforts may be particularly important if local interventions encourage shifts in norms and behaviors that favor large-scale transformations. With this in mind, we discuss the importance of the visibility of norms and the role of beliefs when such visibility is lacking, and their implications for leveraging cooperative behavior to increase climate mitigation efforts locally and globally.

spatial heterogeneity, pollution flow, Solow model We seek to explain the emergence of spatial heterogeneity regarding development and pollution on the basis of interactions associated with the movement of capital and polluting activities from one economy to another. We use a simple dynamical model describing capital accumulation along the lines of a fixed-savings-ratio Solow-type model capable of producing endogenous growth and convergence behavior, and pollution accumulation in each country with pollution diffusion between countries or regions. The basic mechanism underlying the movements of capital across space is the quest for locations where the marginal productivity of capital is relatively higher than the productivity at the location of origin. The notion that capital moves to locations of relatively higher productivity but not necessarily from locations of high concentration to locations of low concentration, does not face difficulties associated with the Lucas paradox. We show that, for a wide range of capital and pollution rates of flow, spatial heterogeneity emerges even between two economies with identical fundamental structures. These results can be interpreted as suggesting that the neoclassical convergence hypothesis might not hold under differential rates of flow of capital and polluting activities among countries of the same fundamental structure.

Sustainably managing coupled ecological-economic systems requires not only an understanding of the environmental factors that affect them, but also knowledge of the interactions and feedback cycles that operate between resource dynamics and activities attributable to human intervention. The socioeconomic dynamics, in turn, call for an investigation of the behavioural drivers behind human action. We argue that a multidisciplinary approach is needed in order to tackle the increasingly pressing and intertwined environmental challenges faced by modern societies. Academic contributions to climate change policy have been constrained by methodological and terminological differences, so we discuss how programmes aimed at cross-disciplinary education and involvement in governance may help to unlock scholars' potential to propose new solutions.

Trade-offs are not the only constraints affecting the performance and impact of work by living systems. Christina De La Rocha asks us to look at the impact of one of the most fundamental kinds of work on Earth- the work of photosynthesis- from the global perspective provided from biogeochemistry. Starting with the history and basic chemistry of photosynthesis, we see how photosynthesis developed as a work process. We also find that, like many human work processes, it has a choke point, induced by a "working part" that worked just fine when it started but has been unable to change with changing times and conditions. Because this is a crucial part- a critical enzyme- and the changing conditions are the long-term fluctuations in carbon dioxide over the span of life on Earth, this choke point has come to limit photosynthesis and the work of life on Earth. De La Rocha also takes us through the ways in which carbon makes its way through the biogeochemical cycle, and we can see how the work of photosynthesis and the work of the biosphere affect us all.

This paper examines the role of other-regarding behavior as a mechanism for the establishment and maintenance of cooperation in resource use under variable social and environmental conditions. By coupling resource stock dynamics with social dynamics concerning compliance to a social norm prescribing non-excessive resource extraction in a common pool resource, we show that when reputational considerations matter and a sufficient level of social stigma affects the violators of a norm, sustainable outcomes are achieved. We find large parameter regions where norm-observing and norm-violating types coexist, and analyze to what extent such coexistence depends on the environment. © 2011 Elsevier Ltd.