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

Spatiotemporal variability in Swedish lake ecosystems

Studying ecosystem dynamics is critical to monitoring and managing linked systems of humans and nature. Due to the growth of tools and techniques for collecting data, information on the condition of these systems is more widely available. While there are a variety of approaches for mining and assessing data, there is a need for methods to detect latent characteristics in ecosystems linked to temporal and spatial patterns of change. Resilience-based approaches have been effective at not only identifying environmental change but also providing warning in advance of critical transitions in social-ecological systems (SES). In this study, we examine the usefulness of one such method, Fisher Information (FI) for spatiotemporal analysis. FI is used to assess patterns in data and has been established as an effective tool for capturing complex system dynamics to include regimes and regime shifts. We employed FI to assess the biophysical condition of eighty-five Swedish lakes from 1996–2018. Results showed that FI captured spatiotemporal changes in the Swedish lakes and identified distinct spatial patterns above and below the Limes Norrlandicus, a hard ecotone boundary which separates northern and southern ecoregions in Sweden. Further, it revealed that spatial variance changed approaching this boundary. Our results demonstrate the utility of this resilience-based approach for spatiotemporal and spatial regimes analyses linked to monitoring and managing critical watersheds and waterbodies impacted by accelerating environmental change.

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.

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.