Some insights on the COVID-19 pandemic from Fisher information.

We explored the application of Fisher information to the study of pandemics and illustrated the insights that can be gained using the COVID-19 pandemic, as a test case. To do so, we applied the Fisher information theory previously applied to periodic systems, to non-periodic dynamic systems. The resulting mathematical machinery was then used to compute the Fisher information measure, as the amount of information extracted from the time series for COVID-19 confirmed infections and deaths. The analysis was performed for the World as a whole and five nation-states: India, USA, Japan, Germany, and Chile. Several insights resulted from the study: (1) the information content of the time series varied widely for different time periods, over the course of the pandemic, (2) it is advisable not to fit model parameters or make policy decisions based on data from time periods with low Fisher information, (3) the most information about a wave of infections comes towards the end of the wave where the time series data has the most information about the dynamics of the pandemic, and (4) the quality of the time series data significantly affects the Fisher information value, and, therefore, what can be learned from studying the time series.

Network Modeling for Post-Entry Management of Invasive Pest Species in the Philippines: The Case of the Colorado Potato Beetle, Leptinotarsa decemlineata (Say, 1824) (Coleoptera: Chrysomelidae).

Crop shifting is considered as an important strategy to secure future food supply in the face of climate change. However, use of this adaptation strategy needs to consider the risk posed by changes in the geographic range of pests that feed on selected crops. Failure to account for this threat can lead to disastrous results. Models can be used to give insights on how best to manage these risks. In this paper, the socioecological process graph technique is used to develop a network model of interactions among crops, invasive pests, and biological control agents. The model is applied to a prospective analysis of the potential entry of the Colorado potato beetle into the Philippines just as efforts are being made to scale up potato cultivation as a food security measure. The modeling scenarios indicate the existence of alternative viable pest control strategies based on the use of biological control agents. Insights drawn from the model can be used as the basis to ecologically engineer agricultural systems that are resistant to pests.

Integrated model for food-energy-water (FEW) nexus to study global sustainability: The main generalized global sustainability model (GGSM).

Over the years, several global models have been proposed to forecast global sustainability, provide a framework for sustainable policy-making, or to study sustainability across the FEW nexus. An integrated model is presented here with components like food-web ecosystem dynamics, microeconomics components, including energy producers and industries, and various socio-techno-economic policy dimensions. The model consists of 15 compartments representing a simplified ecological food-web set in a macroeconomic framework along with a rudimentary legal system. The food-web is modeled by Lotka-Volterra type expressions, whereas the economy is represented by a price-setting model wherein firms and human households attempt to maximize their economic well-being. The model development is done using global-scale data for stocks and flows of food, energy, and water, which were used to parameterize this model. Appropriate proportions for some of the ecological compartments like herbivores and carnivores are used to model those compartments. The modeling of the human compartment was carried out using historical data for the global mortality rate. Historical data were used to parameterize the model. Data for key variables like the human population, GDP growth, greenhouse gases like CO2 and NOX emissions were used to validate the model. The model was then used to make long-term forecasts and to study global sustainability over an extended time. The purpose of this study was to create a global model which can provide techno-socio-economic policy solutions for global sustainability. Further, scenario analysis was conducted for cases where the human population or human consumption increases rapidly to observe the impact on the sustainability of the planet over the next century. The results indicated that the planet can support increased population if the per capita consumption levels do not rise. However, increased consumption resulted in exhaustion of natural resources and increased the CO2 emissions by a multiple of 100.

Integrated model for Food-Energy-Water (FEW) nexus to study global sustainability: The water compartments and water stress analysis.

Analysis of global sustainability is incomplete without an examination of the FEW nexus. Here, we modify the Generalized Global Sustainability Model (GGSM) to incorporate the global water system and project water stress on the global and regional levels. Five key water-consuming sectors considered here are agricultural, municipal, energy, industry, and livestock. The regions are created based on the continents, namely, Africa, Asia, Europe, North America, Oceania, and South America. The sectoral water use intensities and geographical distribution of the water demand were parameterized using historical data. A more realistic and novel indicator is proposed to assess the water situation: net water stress. It considers the water whose utility can be harvested, within economic and technological considerations, rather than the total renewable water resources. Simulation results indicate that overall global water availability is adequate to support the rising water demand in the next century. However, regional heterogeneity of water availability leads to high water stress in Africa. Africa's maximum net water stress is 140%, so the water demand is expected to be more than total exploitable water resources. Africa might soon cross the 100% threshold/breakeven in 2022. For a population explosion scenario, the intensity of the water crisis for Africa and Asia is expected to rise further, and the maximum net water stress would reach 149% and 97%, respectively. The water use efficiency improvement for the agricultural sector, which reduces the water demand by 30%, could help to delay this crisis significantly.

Socio-ecological network structures from process graphs.

We propose a process graph (P-graph) approach to develop ecosystem networks from knowledge of the properties of the component species. Originally developed as a process engineering tool for designing industrial plants, the P-graph framework has key advantages over conventional ecological network analysis techniques based on input-output models. A P-graph is a bipartite graph consisting of two types of nodes, which we propose to represent components of an ecosystem. Compartments within ecosystems (e.g., organism species) are represented by one class of nodes, while the roles or functions that they play relative to other compartments are represented by a second class of nodes. This bipartite graph representation enables a powerful, unambiguous representation of relationships among ecosystem compartments, which can come in tangible (e.g., mass flow in predation) or intangible form (e.g., symbiosis). For example, within a P-graph, the distinct roles of bees as pollinators for some plants and as prey for some animals can be explicitly represented, which would not otherwise be possible using conventional ecological network analysis. After a discussion of the mapping of ecosystems into P-graph, we also discuss how this framework can be used to guide understanding of complex networks that exist in nature. Two component algorithms of P-graph, namely maximal structure generation (MSG) and solution structure generation (SSG), are shown to be particularly useful for ecological network analysis. These algorithms enable candidate ecosystem networks to be deduced based on current scientific knowledge on the individual ecosystem components. This method can be used to determine the (a) effects of loss of specific ecosystem compartments due to extinction, (b) potential efficacy of ecosystem reconstruction efforts, and (c) maximum sustainable exploitation of human ecosystem services by humans. We illustrate the use of P-graph for the analysis of ecosystem compartment loss using a small-scale stylized case study, and further propose a new criticality index that can be easily derived from SSG results.

An information theory-based approach to assessing spatial patterns in complex systems.

Given the intensity and frequency of environmental change, the linked and cross-scale nature of social-ecological systems, and the proliferation of big data, methods that can help synthesize complex system behavior over a geographical area are of great value. Fisher information evaluates order in data and has been established as a robust and effective tool for capturing changes in system dynamics, including the detection of regimes and regime shifts. Methods developed to compute Fisher information can accommodate multivariate data of various types and requires no a priori decisions about system drivers, making it a unique and powerful tool. However, the approach has primarily been used to evaluate temporal patterns. In its sole application to spatial data, Fisher information successfully detected regimes in terrestrial and aquatic systems over transects. Although the selection of adjacently positioned sampling stations provided a natural means of ordering the data, such an approach limits the types of questions that can be answered in a spatial context. Here, we expand the approach to develop a method for more fully capturing spatial dynamics. Results reflect changes in the index that correspond with geographical patterns and demonstrate the utility of the method in uncovering hidden spatial trends in complex systems.

Using Fisher information to assess stability in the performance of public transportation systems.

Public transportation systems (PTS) are large and complex systems that consist of many modes operated by different agencies to service entire regions. Assessing their performance can therefore be difficult. In this work, we use concepts of Fisher information (FI) to analyse the stability in the performance of PTS in the 372 US urbanized areas (UZA) reported by the National Transit Database. The key advantage of FI is its ability to handle multiple variables simultaneously to provide information about overall trends of a system. It can therefore detect whether a system is stable or heading towards instability, and whether any regime shifts have occurred or are approaching. A regime shift is a fundamental change in the dynamics of the system, e.g. major and lasting change in service. Here, we first provide a brief background on FI and then compute and analyse FI for all US PTS using monthly data from 2002 to 2016; datasets include unlinked passenger trips (i.e. demand) and vehicle revenue miles (i.e. supply). We detect eight different patterns from the results. We find that most PTS are seeking stability, although some PTS have gone through regime shifts. We also observe that several PTS have consistently decreasing FI results, which is a cause for concern. FI results with detailed explanations are provided for eight major UZA.

A supplementary tool to existing approaches for assessing ecosystem community structure.

Measures of biological or species diversity are central to ecology and conservation biology. Although there are several commonly used indices, each has shortcomings and all vary in the relative emphasis they place on the number of species and their relative abundance. We propose utilizing Fisher Information, not as a replacement for existing indices, but as a supplement to other indices because it is sensitive to community structure. We demonstrate how Shannon's and Simpson's diversity indices quantify the diversity of two different systems and how Fisher Information can enhance the analyses by comparing, as example, body size, and phylogenetic diversity of the different communities. Fisher Information is sensitive to the order in which species are entered into the analysis, and therefore, it can detect differences in community structure. Thus, the Fisher Information index can be useful in helping understand and analyze biodiversity of ecosystems and in comparing ecological communities.

Toward a leading indicator of catastrophic shifts in complex systems: Assessing changing conditions in nation states.

The 20th century was characterized by substantial change on a global scale. There were multiple wars and unrest, social and political transitions, technological innovation and widespread development that impacted every corner of the earth. In order to assess the sustainability implications of these changes, we conducted a study of three advanced nations particularly affected during this time: France, Germany and the United States (USA). All three nation states withstood these changes and yet continued to thrive, which speaks to their resilience. However, we were interested in determining whether any of these countries underwent a regime shift during this period and if they did, whether there was advanced warning that transition was imminent. This study seeks to evaluate systemic trends in each country by exploring key variables that describe its condition over time. We use Fisher Information to assess changing conditions in the nation states based on trends in social, economic and environmental variables and employ Bayes Theorem as an objective means of determining whether declines in Fisher information provide early warning signals of critical transitions. Results indicate that while the United States was relatively stable and France experienced a great deal of change during this period, only Germany appeared to undergo a regime shift. Further, each country exhibited decreasing Fisher information when approaching significant events (e.g., World Wars, Great Depression), and reflected unique mechanisms linked to dynamic changes in each nation state. This study highlights the potential of using trends in Fisher information as a sentinel for evaluating dynamic change and assessing resilience in coupled human and natural systems.

Using Fisher information to track stability in multivariate systems.

With the current proliferation of data, the proficient use of statistical and mining techniques offer substantial benefits to capture useful information from any dataset. As numerous approaches make use of information theory concepts, here, we discuss how Fisher information (FI) can be applied to sustainability science problems and used in data mining applications by analysing patterns in data. FI was developed as a measure of information content in data, and it has been adapted to assess order in complex system behaviour. The main advantage of the approach is the ability to collapse multiple variables into an index that can be used to assess stability and track overall trends in a system, including its regimes and regime shifts. Here, we provide a brief overview of FI theory, followed by a simple step-by-step numerical example on how to compute FI. Furthermore, we introduce an open source Python library that can be freely downloaded from GitHub and we use it in a simple case study to evaluate the evolution of FI for the global-mean temperature from 1880 to 2015. Results indicate significant declines in FI starting in 1978, suggesting a possible regime shift.

Using Green Chemistry and Engineering Principles To Design, Assess, and Retrofit Chemical Processes for Sustainability.

The concepts of green chemistry and engineering (GC&E) have been promoted as an effective qualitative framework for developing more sustainable chemical syntheses, processes, and material management techniques. This has been demonstrated by many theoretical and practical cases. In addition, there are several approaches and frameworks focused on demonstrating that improvements were achieved through GC&E technologies. However, the application of these principles is not always straightforward. We propose using systematic frameworks and tools that help practitioners when deciding which principles can be applied, the levels of implementation, prospective of obtaining simultaneous improvements in all sustainability aspects, and ways to deal with multiobjective problems. Therefore, this contribution aims to provide a systematic combination of three different and complementary design tools for assisting designers in evaluating, developing, and improving chemical manufacturing and materials management systems under GC&E perspectives. The WAR Algorithm, GREENSCOPE, and SustainPro were employed for this synergistic approach of incorporating sustainability at early stages of process development. In this demonstration, simulated ammonia production is used as a case study to illustrate this advancement. Results show how to identify process design areas for improvements, key factors, multicriteria decision-making solutions, and optimal trade-offs. Finally, conclusions were presented regarding the tools' use in more robust sustainable process and material management designs.

Assessing sustainability in real urban systems: the Greater Cincinnati Metropolitan Area in Ohio, Kentucky, and Indiana.

Urban systems have a number of factors (i.e., economic, social, and environmental) that can potentially impact growth, change, and transition. As such, assessing and managing these systems is a complex challenge. While, tracking trends of key variables may provide some insight, identifying the critical characteristics that truly impact the dynamic behavior of these systems is difficult. As an integrated approach to evaluate real urban systems, this work contributes to the research on scientific techniques for assessing sustainability. Specifically, it proposes a practical methodology based on the estimation of dynamic order, for identifying stable and unstable periods of sustainable or unsustainable trends with Fisher Information (FI) metric. As a test case, the dynamic behavior of the City, Suburbs, and Metropolitan Statistical Area (MSA) of Cincinnati was evaluated by using 29 social and 11 economic variables to characterize each system from 1970 to 2009. Air quality variables were also selected to describe the MSA's environmental component (1980-2009). Results indicate systems dynamic started to change from about 1995 for the social variables and about 2000 for the economic and environmental characteristics.

Evaluating the sustainability of a regional system using Fisher information in the San Luis Basin, Colorado.

This paper describes the theory, data, and methodology necessary for using Fisher information to assess the sustainability of the San Luis Basin (SLB) regional system over time. Fisher information was originally developed as a measure of the information content in data and is an important method in information theory. Our adaptation of Fisher information provides a means of monitoring the variables of a system to characterize dynamic order, and, therefore, its regimes and regime shifts. This work is part of the SLB Sustainability Metrics Project, which aimed to evaluate movement over time towards or away from regional sustainability. One of the key goals of this project was to use readily available data to assess the sustainability of the system including its environmental, social and economic aspects. For this study, Fisher information was calculated for fifty-three variables which characterize the consumption of food and energy, agricultural production, environmental characteristics, demographic properties and changes in land use for the SLB system from 1980 to 2005. Our analysis revealed that while the system displayed small changes in dynamic order over time with a slight decreasing trend near the end of the period, there is no indication of a regime shift. Therefore, the SLB system is stable with very slight movement away from sustainability in more recent years.

Is sustainability achievable? Exploring the limits of sustainability with model systems.

Successful implementation of sustainability ideas in ecosystem management requires a basic understanding of the often nonlinear and nonintuitive relationships among different dimensions of sustainability, particularly the system-wide implications of human actions. This basic understanding further includes a sense of the time scale of possible future events and the limits of what is and is not likely to be possible. With this understanding, systematic approaches can then be used to develop policy guidelines for the system. This article presents an illustration of these ideas by analyzing an integrated ecological-economic-social model, which comprises various ecological (natural) and domesticated compartments representing species along with a macroeconomic price setting model. The stable and qualitatively realistic model is used to analyze different relevant scenarios. Apart from highlighting complex relationships within the system, it identifies potentially unsustainable future developments such as increased human per capita consumption rates. Dynamic optimization is then used to develop time-dependent policy guidelines for the unsustainable scenarios using objective functions that aim to minimize fluctuations in the system's Fisher information. The results can help to identify effective policy parameters and highlight the tradeoff between natural and domesticated compartments while managing such integrated systems. The results should also qualitatively guide further investigations in the area of system level studies and policy development.

Optimal control theory for sustainable environmental management.

Sustainable ecosystem management aims to promote the structure and operation of the human components of the system while simultaneously ensuring the persistence of the structures and operation of the natural component. Given the complexity of this task owing to the diverse temporal and spatial scales and multidisciplinary interactions, a systems theory approach based on sound mathematical techniques is essential. Two important aspects of this approach are formulation of sustainability-based objectives and development of the management strategies. Fisher information can be used as the basis of a sustainability hypothesis to formulate relevant mathematical objectives for disparate systems, and optimal control theory provides the means to derive time-dependent management strategies. Partial correlation coefficient analysis is an efficient technique to identify the appropriate control variables for policy development. This paper represents a proof of concept for this approach using a model system that includes an ecosystem, humans, a very rudimentary industrial process, and a very simple agricultural system. Formulation and solution of the control problems help in identifying the effective management options which offer guidelines for policies in real systems. The results also emphasize that management using multiple parameters of different nature can be distinctly effective.

Regime changes in ecological systems: an information theory approach.

We present our efforts at developing an ecological system index using information theory. Specifically, we derive an expression for Fisher Information based on sampling of the system trajectory as it evolves in the space defined by the state variables of the system, i.e. its state space. The Fisher Information index, as we have derived it, is a measure of system order, and captures the characteristic variation in speed and acceleration along the system's periodic steady-state trajectories. When calculated repeatedly over the system period, this index tracks steady states and transient behavior. We believe that such an index could be useful in detecting system 'flips' associated with a regime change, i.e. determining when systems are in a transient between one steady state and another. We illustrate the concepts using model ecosystems.