Tarsha Eason

Discontinuities, cross-scale patterns, and the organization of ecosystems

Ecological structures and processes occur at specific spatiotemporal scales, and interactions that occur across multiple scales mediate scale-specific (e.g., individual, community, local, or regional) responses to disturbance. Despite the importance of scale, explicitly incorporating a multi-scale perspective into research and management actions remains a challenge. The discontinuity hypothesis provides a fertile avenue for addressing this problem by linking measureable proxies to inherent scales of structure within ecosystems. Here we outline the conceptual framework underlying discontinuities and review the evidence supporting the discontinuity hypothesis in ecological systems. Next we explore the utility of this approach for understanding cross-scale patterns and the organization of ecosystems by describing recent advances for examining nonlinear responses to disturbance and phenomena such as extinctions, invasions, and resilience. To stimulate new research, we present methods for performing discontinuity analysis, detail outstanding knowledge gaps, and discuss potential approaches for addressing these gaps.

Prolonged instability prior to a regime shift.

Regime shifts are generally defined as the point of ‘abrupt’ change in the state of a system. However, a seemingly abrupt transition can be the product of a system reorganization that has been ongoing much longer than is evident in statistical analysis of a single component of the system. Using both univariate and multivariate statistical methods, we tested a long-term high-resolution paleoecological dataset with a known change in species assemblage for a regime shift. Analysis of this dataset with Fisher Information and multivariate time series modeling showed that there was a∼2000 year period of instability prior to the regime shift. This period of instability and the subsequent regime shift coincide with regional climate change, indicating that the system is undergoing extrinsic forcing. Paleoecological records offer a unique opportunity to test tools for the detection of thresholds and stable-states, and thus to examine the long-term stability of ecosystems over periods of multiple millennia.

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.

Management applications of discontinuity theory

Human impacts on the environment are multifaceted and can occur across distinct spatiotemporal scales. Ecological responses to environmental change are therefore difficult to predict, and entail large degrees of uncertainty. Such uncertainty requires robust tools for management to sustain ecosystem goods and services and maintain resilient ecosystems. We propose an approach based on discontinuity theory that accounts for patterns and processes at distinct spatial and temporal scales, an inherent property of ecological systems. Discontinuity theory has not been applied in natural resource management and could therefore improve ecosystem management because it explicitly accounts for ecological complexity. Synthesis and applications. We highlight the application of discontinuity approaches for meeting management goals. Specifically, discontinuity approaches have significant potential to measure and thus understand the resilience of ecosystems, to objectively identify critical scales of space and time in ecological systems at which human impact might be most severe, to provide warning indicators of regime change, to help predict and understand biological invasions and extinctions and to focus monitoring efforts. Discontinuity theory can complement current approaches, providing a broader paradigm for ecological management and conservation.

Development of a multidisciplinary approach to assess regional sustainability

There are a number of established, scientifically supported metrics of sustainability. Many of the metrics are data-intensive and require extensive effort to collect data and compute the metrics. Moreover, individual metrics do not capture all aspects of a system that are relevant to sustainability. A pilot project was initiated to create an approach to measure, monitor, and maintain prosperity and environmental quality of a regional system. The goal was to produce a straightforward, inexpensive methodology that is simple to use and interpret. This requires historical data be readily accessible, metrics must be applicable to the relevant scale, and results must meet the needs of decision-makers. Because sustainability is a multidimensional concept, the research group consisted of a multidisciplinary team that identified the major components of an environmental system. We selected metrics to capture the multidimensionality of sustainability in environmental systems and included: (1) emergy to capture the quality-normalized flow of energy through the system; (2) ecological footprint to capture the impact of humans on the system; (3) green net regional product to estimate human prosperity and well being within the system; and (4) Fisher information to capture the dynamic order of the system. We were able to compute metrics for a test geographic region using existing datasets. Preliminary analysis indicates that each metric reveals a somewhat different trend. These preliminary findings support the idea that characterization of sustainability requires a multidisciplinary approach and demonstrate the need to measure multiple aspects of an environmental system.

Managing for resilience: early detection of regime shifts in complex systems

The broad implications of catastrophic regime shifts have prompted the need to find methods that are not only able to detect regime shifts but more importantly, identify them before they occur. Rising variance, skewness, kurtosis, and critical slowing down have all been proposed as indicators of impending regime shifts. However, these approaches typically do not signal a shift until it is well underway. Further, they have primarily been used to evaluate simple systems; hence, additional work is needed to adapt these methods, if possible, to real systems which typically are complex and multivariate. Fisher information is a key method in information theory and affords the ability to characterize the dynamic behavior of systems. In this work, Fisher information is compared to traditional indicators through the assessment of model and real systems and identified as a leading indicator of impending regime shifts. Evidenced by the great deal of activity in this research area, it is understood that such work could lead to better methods for detecting and managing systems that are of significant importance to humans. Thus, we believe the results of this work offer great promise for resilience science and sustainability.

Managing for resilience: an information theory‐based approach to assessing ecosystems

Summary Ecosystems are complex and multivariate; hence, methods to assess the dynamics of ecosystems should have the capacity to evaluate multiple indicators simultaneously. Most research on identifying leading indicators of regime shifts has focused on univariate methods and simple models which have limited utility when evaluating real ecosystems, particularly because drivers are often unknown. We discuss some common univariate and multivariate approaches for detecting critical transitions in ecosystems and demonstrate their capabilities via case studies. Synthesis and applications. We illustrate the utility of an information theory-based index for assessing ecosystem dynamics. Trends in this index also provide a sentinel of both abrupt and gradual transitions in ecosystems.

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 MSAs 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.

Body size distributions signal a regime shift in a lake ecosystem

Communities of organisms, from mammals to microorganisms, have discontinuous distributions of body size. This pattern of size structuring is a conservative trait of community organization and is a product of processes that occur at multiple spatial and temporal scales. In this study, we assessed whether body size patterns serve as an indicator of a threshold between alternative regimes. Over the past 7000 years, the biological communities of Foy Lake (Montana, USA) have undergone a major regime shift owing to climate change. We used a palaeoecological record of diatom communities to estimate diatom sizes, and then analysed the discontinuous distribution of organism sizes over time. We used Bayesian classification and regression tree models to determine that all time intervals exhibited aggregations of sizes separated by gaps in the distribution and found a significant change in diatom body size distributions approximately 150 years before the identified ecosystem regime shift. We suggest that discontinuity analysis is a useful addition to the suite of tools for the detection of early warning signals of regime shifts.

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.In this era of Big Data, proficient use of data mining is the key to capture useful information from any dataset. As numerous data mining techniques make use of information theory concepts, in this paper, we discuss how Fisher information (FI) can be applied to analyze patterns in Big Data. The main advantage of FI is its ability to combine multiple variables together to inform us on the overall trends and stability of a system. It can therefore detect whether a system is losing dynamic order and stability, which may serve as a signal of an impending regime shift. In this work, we first provide a brief overview of Fisher information theory, followed by a simple step-by-step numerical example on how to compute FI. Finally, as a numerical demonstration, we calculate the evolution of FI for GDP per capita (current US Dollar) and total population of the USA from 1960 to 2013.