Towards a sustainability index using information theory

Abstract

We explore the use of Fisher Information as a basis for an index of sustainability. Sustainability of an ecosystem refers to the robustness of a preferred dynamic regime to human and natural disturbances. Ecosystems under perturbations of varying regularity and intensity can either remain within the current regime or transition into the neighbourhood of a regime with different (viz. less desirable) characteristics. The Fisher Information index we develop is based on the probability of finding the system in a particular state. We apply the index to a 10-compartment food web model with five functional groups: detritus, primary producers, herbivores, carnivores, and an omnivore. Fisher Information is shown to be sensitive to transients in model generated data. Such transients can be indicative of a transition to a new dynamic regime. Early detection of transitions to undesirable regimes may permit management intervention.

Introduction

While it has proven difficult to develop a consensus around the concept of sustainability, there is a growing recognition that the current growth of human activity cannot be sustained without significantly threatening Earth’s natural systems as we know them. This recognition leads to the question: Given that we depend on these natural systems for a wide range of services, what kind of future are we creating for ourselves as a species? The frequently cited definition of sustainable development given by the Brundtland Commission [1], namely development that “meets the needs and aspirations of the present without compromising the ability to meet those of the future,” is just one expression of this concern over the extent to which we will be able to rely on ecosystem services into the future and what this portends for human society.

The concept of sustainability applies to integrated systems comprising humans and nature. The structures and operation of the human component (in terms of society, economy, government etc.) must be such that these reinforce or promote the persistence of the structures and operation of the natural component (in terms of ecosystem trophic linkages, biodiversity, biogeochemical cycles, etc.), and vice versa. Thus, one of the challenges of sustainability research lies in linking measures of ecosystem functioning (as regards the uses to which it is put by humans) to the structure and operation of the ecosystem itself [2]. Research in the area of indicators such as exergy and emergy attempts to allow us to better understand ecosystem structure and operation. These thermodynamically based indicators give a holistic perspective of ecosystem properties. Exergy is a measure of the state of the system, specifically its ability to do useful work (as measured by its distance from an environmental reference state). Emergy is a measure of the system history through its many transformations of solar radiation. Both have been presented as measures of system organization and indirectly as measures of sustainability [3], [4], [5].

Another challenge of sustainability research lies in linking human demand for services to the structure and operation of human social, economic, legal and cultural systems. It would be useful to develop indicators for these systems in order to better understand the nature of human demands on ecosystems and the extent to which these can be modified. However, it is difficult to understand these systems in terms of indicators such as exergy and emergy, which are based on thermodynamic concepts. We hold out hope that the concept of information can be used to develop indicators that bridge the natural and human systems and make sense of the disparate state variables of these systems.

In this paper we examine the use of Fisher Information to assess the organizational or structural integrity of ecosystems. We develop a Fisher Information index (FII) in terms of the information contained in the time evolution of the state of a dynamic system. The time the system state spends in various sub-segments of the phase space steady state trajectory follows a characteristic pattern that is the result of the system’s organizational structure. As the ecosystem is stressed (under exploitation, for example), changes in this steady state pattern will occur. The FII hopefully will indicate differences in favorable and unfavorable changes in the pattern, or at least when such changes are occurring. Eventually we would like to link such changes to changes in structure, and ultimately to sustainability of the combination of the ecosystem and the exploiting system (e.g. human society).