Towards a theory of sustainable systems

doi:10.1016/S0378-3812(01)00677-X

Fluid Phase Equilibria

Volumes 194–197, 30 March 2002, Pages 3-14

https://doi.org/10.1016/S0378-3812(01)00677-X Get rights and content

Abstract

While there is tremendous interest in sustainability, a fundamental theory of sustainability does not exist. We present our efforts at constructing a theory from Information Theory and Ecological Models. We discuss the state of complex systems that incorporate ecological and other components in terms of dynamic behavior in a phase space defined by the system state variables. From sampling the system trajectory, a distribution function for the probability of observing the system in a given state is constructed, and an expression for the Fisher information is derived. Fisher information is the maximum amount of information available from a set of observations, in this case, states of the system. Fisher information is a function of the variability of the observations such that low variability leads to high Fisher information and high variability leads to low Fisher information. Systems in stable dynamic states have constant Fisher information. Systems losing organization migrate toward higher variability and lose Fisher information. Self-organizing systems decrease their variability and acquire Fisher information. These considerations lead us to propose a sustainability hypothesis: “sustainable systems do not lose or gain Fisher information over time.” We illustrate these concepts using simulated ecological systems in stable and unstable states, and we discuss the underlying dynamics.

Introduction

The topic of sutainability is, perhaps, operationally and conceptually one of the most complex that modern science has faced. Possibly, the two most widely known statements on sustainability are those of the World Commission on Environment and Development [1] and the National Research Council [2]. The World Commission on Environment and Development states “…development that meets the needs of the present without compromising the ability of future generations to meet their own need”. The National Research Council states “the reconciliation of society’s development goals with the planet’s environmental limits over the long term”.

As one can imagine, the topic of sustainability must at least embody in some form elements of physics, engineering, ecology, law, economics, sociology, and politics. This gives rise to severe operational difficulties in cross-disciplinary communication, and multidisciplinary research teams have by consequence a difficult history. One does know how to easily connect economic demand curves to ecosystem function and to legal issues. Yet, sustainability is an area that cannot be successfully investigated within the confines of any single discipline. The conceptual difficulties arise in part due to the lack of a general underlying theory in the area of sustainability. This gives rise to many problems. For instance, it is unclear what are the appropriate measures of sustainability, and various metrics have been proposed over the years that include species diversity, profitability, human income levels, etc. in various forms. The criteria that identify a sustainable from an unsustainable system are also unknown. In fact, even the principles on which any sustainability criteria could be based are themselves only dimly understood.

To begin to address as many of these issues as possible, we have invoked the concept of information in its mathematical form as the centerpiece of our research work. The reason is that essentially any type of data or model can be converted to information regardless of disciplinary origin. Information can, therefore, serve as common interdisciplinary bridge. We also hypothesize that information theory can serve as an appropriate basis for the construction of a basic theory of sustainability. Information is a very fundamental quantity from which many other known laws of nature can be derived as shown by Frieden [3]. The objective of this article is then to demonstrate our beginning steps in the development of a theory of sustainable systems using ecological models as a starting point. This includes a sustainability hypothesis and illustrations using predator–prey models. In a way, the long term goal of this work is fundamentally to translate into mathematical form the aforementioned statements of sustainability from World Commission on Environment and Development and the National Research Council, and this article documents our initial steps in this effort.

Section snippets

Information theory in ecology

Information theory has had four primary applications in biological and ecological research: as an index of physical or structural diversity, as a measure of evolutionary processes, as a measure of distance from thermodynamic equilibrium, and as a measure of transaction propensity in networks [4]. A fifth, more qualitative approach, treating ecosystems as semiotic systems has been recently advanced by Hoffmeyer [5] and Emmeche [6].

The most common application has been the use of Shannon

Fisher information: general

The work of Ronald Fisher [16] introduced a statistical measure of indeterminacy now called Fisher information. Fisher information can be interpreted as a measure of the ability to estimate a parameter, as the amount of information that can be extracted from a set of measurements, and also as a measure of the state of order or organization of a system or phenomenon [3]. It is the later interpretation that has the most relevance to issues of sustainability. Fisher information, I, for one

Stable dynamic states

The state of the system is defined by its state variables. That is, if one knows the values of the state variables, then one “knows” the state of the system. The behavior of these state variables determines the stability of the system. A static steady-state is reached when the state variables all maintain a constant value. A dynamic steady-state occurs when the state variables oscillate repeatedly over a fixed region in phase space. We call this latter a stable dynamic state. Both cases are

Fisher information: ecological systems

The system’s state variables determine a probability distribution function for that system based on the probability of finding the system in a particular state, i.e. a given set values for the state variables. In this manner, there is only one PDF for the entire system. For simple systems that reach steady-state or have a stable limit cycle, it is possible to create a histogram corresponding to the possible outcome space. However, when dealing with dynamic systems it may not be possible to

Sustainable systems hypothesis

Using Fisher information as a basis, we have constructed a hypothesis for a sustainability criterion. The sustainability hypothesis states that: the time-averaged Fisher information of a system in a sustainable state does not change with time. There are, in addition, two corollaries to the sustainability hypothesis which state: (1) if the Fisher information of a system is increasing with time, then the system is maintaining a state of self-organization and (2) if the Fisher information of a

Illustration: predator–prey models

Our objective is to develop a methodology to calculate the Fisher information for a dynamical ecological system. As stated above, Fisher developed a fundamental method to relate observed information with intrinsic information as estimation error. The result can be interpreted as a way to quantify the degree of system organization. We extend the use of Fisher information to measuring the probability of observing a system in a particular state (as defined by its state variables) by substituting

Fisher information and stability

Once we have a general method for calculating the Fisher information of the state of the system, we perform a sensitivity analysis to test the relationship between the system stability and Fisher information. The stability of the system is best viewed in the phase space diagram because it shows the spread of the distribution of the variables (Fig. 4). We chose to alter the dynamics of the system by changing the mortality rate of the prey species (b). For a baseline case, b=3, the phase plot is

Summary

The principal contributions in this paper are the sustainability hypothesis and its two corollaries. The sustainability hypothesis states that Fisher information of dynamic systems in a sustainable state does not change with time. This is important because it establishes a possible criterion for sustainability. The two corollaries state that increasing Fisher information leads the system on a path through self-organized states while decreasing Fisher information leads the system to a loss of

Acknowledgements

The authors wish to acknowledge the support of the National Risk Management Research Laboratory and Sustainable Technology Division. In particular we acknowledge the support and encouragement of Dr. Subhas K. Sikdar, the director of the Sustainable Technology Division. BDF is a research associate with the US Environmental Protection Agency Postdoctoral Research Program.

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¹: Present address: Department of Biology, Towson University, Towson, MD 21252, USA.

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