The increasing intensity and scale of human activity across the globe leading to severe depletion and deterioration of the Earth's natural resources has meant that sustainability has emerged as a new paradigm of analysis and management. Sustainability, conceptually defined by the Brundtland commission [1], exhibits many dimensions related to ecology, society, economics, technology and other system aspects. The goal of a sustainable policy, then, is to promote the structure and operation of the human component of a system (society, economy, technology, etc.) in such a manner as to reinforce the persistence of the structures and operation of the natural component (i.e., the ecosystem) [2]. This requires a basic understanding of the often nonlinear and non-intuitive relationships amongst different dimensions of sustainability. 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 work illustrates the value of such an approach by analyzing an integrated ecological-economic-social model that is a concise representation of the critical aspects of the real world [3]. The work models various scenarios that replicate possible catastrophic events and studies system wide implications of such events. Once those implications are understood, the work explores the development of policy guidelines to ensure system sustainability.

2. Integrated ecological-economic model

In the model considered, resource limits are addressed by explicitly modeling the system as closed to mass. Moreover, a legal foundation is laid by identifying the mass in terms of its property type; and an explicit market system of decision making is implemented in the form of a price setting model. The result is an integrated mutually interdependent system that models both macroeconomic variables and environmental stocks and flows. The integrated model comprises of twelve compartments, including two resource pools (RP and IRP), three primary producers (plants P1, P2, and P3), three herbivores (H1, H2, and H3), two carnivores (C1 and C2), an industrial sector (IS) and humans (HH). The two resource pools, plants P2 and P3, and animals H2, H3, C1 and C2 represent natural sectors. From an economic perspective the model contains human households (HH), an industrial sector (IS), and two private firms: one a producer of plants (P1) and one a producer of herbivores (H1). These compartments are governed by a price setting model to maximize the economic benefits of each compartment. An exhaustive explanation of the various aspects related to the model can be found in Whitmore et al. [3].

3. Scenario analysis

Scenarios are plausible, challenging, and relevant stories about how the future might unfold, which can be told in both words and numbers. They are about envisioning future pathways and accounting for critical uncertainties. Previous work by the authors on this model system had analyzed the implications of possible gradual future developments on overall sustainability by modeling scenarios such as population growth and increased per capita consumption [4]. The potential developments though also include catastrophic events that cause sudden and severe changes in the system and its functioning. The response and remedies of the system to such catastrophic events is expected to be different than that for gradual changes. With this understanding, this work focuses on modeling sudden and catastrophic events and analyzing system dynamics resulting from such events. Following different scenarios are considered in this work:

• Economic depression: Modeled as a sudden drop in product prices, as typically observed, for example during the great depression of the 1920s.

• Human Pandemic: Modeled as a sudden rise in the mortality rate of humans as expected if a pandemic such a bird flue is realized.

• Species extinction: Modeled as a sudden rise in the mortality rate of selected species in the model. This scenario models the possibility of a severe disease (also including harmful environmental effects) affecting a particular class of species, which converts a live mass (either plants or animals) into dead mass (transferred to resource pool).

• Nuclear disaster: Modeled as a sudden drop in the overall mass of one or more compartments in the model where the mass is suddenly shifted to the waste compartment of the model.

5. Management strategy development

Once the implications of the possible disasters on the model are understood, the work explores the development of policy guidelines to ensure system sustainability. In the previous work, the authors have successfully used optimal control theory and dynamic optimization to develop time dependent control strategies using Fisher information based objectives [4, 5, 6, 7]. This work will implement a refinement of the formulation. Fisher information based sustainability hypothesis states that major regime shifts in the model are manifested by a drop in the Fisher information [8]. Such a drop in the Fisher information value has been illustrated for the considered model system [4]. Based on this, in addition to minimization of Fisher information variation objective (considered in the past work), this work includes an additional objective in the control problem. The multi-objective problem also tries to minimize large and consistent drop in the absolute value of the Fisher information. The results for the control problem solution will then be compared with those for the single objective problem. The results will highlight the relative importance of these different objectives and will therefore be useful pointers to developing policy guidelines.

6. Summary

Holistic consideration of the ecological, economic and social/legal dimensions of sustainability is important. Towards that objective, this work analyzes an integrated ecological-economic-social model. Scenario analysis on the model is carried out to predict implications of future catastrophic events causing sudden and severe disturbance. The work then focuses on the development of effective management strategies to ensure model sustainability using Fisher information based objectives (single as well as multiple objectives). The study is expected to put forth relevant and important issues, and suggest policy options to ensure global sustainability.

References

[1] C. Tomlinson. Our Common Future, World Commission on Environment and Development, Oxford University Press, Oxford, 1987, p 383.

[2] H. Cabezas, C. Pawlowski, A. Mayer, & N.T. Hoagland (2005). Simulated experiments with complex sustainable systems: Ecology and technology. Resources Conservation and Recycling, 44:279–291, 2005.

[3] H.Wm.Jr. Whitmore, C. Pawlowski, and H. Cabezas. Integration of an economy under imperfect competition with a twelve-cell ecological model. Technical Report EPA/600/R-06/046, USEPA, 2006.

[4] Y. Shastri, U. Diwekar, H. Cabezas and J. Williamson. Is sustainability achievable? Exploring the limits of sustainability through model system. Environmental Science & Technology, Under review

[5] Y. Shastri & U. Diwekar (2006a). Sustainable ecosystem management using optimal control theory: Part 1 (Deterministic systems). Journal of Theoretical Biology, 241: 506–521.

[6] Y. Shastri & U. Diwekar (2006b). Sustainable ecosystem management using optimal control theory: Part 2 (Stochastic systems). Journal of Theoretical Biology, 241: 522–532.

[7] Y. Shastri, U. Diwekar and H. Cabezas. Optimal control for sustainable environmental management. Environmental Science & Technology, Under review

[8] H. Cabezas & B. Fath (2002). Towards a theory of sustainable systems. Fluid Phase Equilibria, 2, 184–197.