(223e) Analysis and Management of An Integrated Ecological-Economic-Social Model: A Sustainability Perspective

Sustainability is recognized as a highly multi-disciplinary concept. Whitmore et al. [1] propose three important dimensions of sustainability: ecological, economic, and social/legal. These dimensions represent important and at the same time interrelated aspects of sustainability. The goal of a sustainable management strategy is to promote the structure and operation of the human component of a system in such a manner as to reinforce the persistence of the structures and operation of the natural component (i.e., the ecosystem) [2]. However, in an integrated system, disturbances along any dimension can have repercussions elsewhere, and hence, sustenance of individual sub-systems does not ensure overall sustainability. Therefore, an integrated analysis of sustainability is essential. Towards that objective this work analyzes a generalized dynamic mathematical model of a combined economic-ecological-social system that has been developed by the USEPA [1]. The goal of the work is to perform an extensive analysis of the model from a sustainability perspective. The work can mainly be divided into two parts. The first part deals with elaborate parameter search work to derive a model setting that represents a functioning ecosystem. In the second part, the model is analyzed from a management perspective. This includes scenario analysis to identify potential catastrophes, and suggestion of management options (policies) through the solution of a control problem. The overall goal is to illustrate the idea of using systems theory tools for policy making for complex integrated systems.

2. Integrated ecological-economic model

The integrated model comprises 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 system flows throughout are specified in terms of mass. In the model considered in this work, resource limits are addressed by explicitly modeling the system as closed to mass (i.e. mass is conserved) and open to energy. Further, individual compartments, including those composed of private property, observe conservation of mass. Moreover, a legal foundation is laid by identifying the mass in terms of its property type; and an explicit market system for 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. Primary producers make resources available from an accessible resource pool (RP) to the rest of the food web. All but the IRP recycles some mass back to the RP representing death of biological mass. Mass from the IRP is recycled very slowly back to the system by P2 and P3; thus, it is ?biologically inaccessible? albeit temporarily. 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 another a producer of herbivores (H1). The mass in these compartments is governed by the price setting model that individually maximizes the economic benefits of each compartment under the given constraints[1].

3. Model modification

The integrated model shows interesting dynamics for the model parameters published in Whitmore et al. [1]. When the model is simulated without the optimization of the economic sector (compartment P1, H1, IS and humans), the overall model is dynamically stable and hence sustainable. However, introduction of the price setting model equations that govern the behavior of the economic compartments causes model instability. The instability is manifested by the total loss of mass (extinction) in some of the ecological compartments and by non-functioning systems, i.e. dead systems. To construct a model that is functional and dynamically (relatively) stable, it is necessary to modify the model and to adjust the model parameters. Moreover, it is also essential to insure that the model parameters and variables values are realistic. The natural compartments typically show cyclic variation in mass, representing low growth and high growth seasons. The initial work on the model, therefore, can be classified into following three different steps:

? An exhaustive search of parameter values through a combination of sampling analysis and partial rank correlation coefficient (PRCC) analysis to identify model parameters leading to relatively stable model dynamics. ? Inclusion of cyclic variation (through a sinusoidal forcing function) in compartments P1, P2 and P3 to depict the natural low growth and high growth seasons. ? Modification of the human compartment so that human population, human mortality rate and birth rate have values that are closer to reality. ? Placing a cost per unit of mass on the industrial sector for the generation of waste flowing into IRP.

4. 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 also about envisioning future pathways and accounting for critical uncertainties. It is important to understand that scenarios are not forecasts, projections, predictions, or recommendations. The actual future development can be a combination of multiple scenarios, and different scenarios might be realized for different ecosystems in the world. For the integrated ecological-economic-social model, following different scenarios are identified:

? Population explosion ? Increase in per capita consumption by humans ? Population explosion along with increased per capita consumption by humans (combination of the first two scenarios) ? Increased productivity of plants (possibly as a result of Global warming). ? Reduction in the regeneration capacity of the natural compartments (possibly due to the adverse effect of pollution)

To understand the impact of each scenario, a base case scenario is identified. This base case scenario predicts future development if the current population and consumption patterns are maintained. Although such a scenario is not possible in reality, it is very useful in understanding the impacts of the considered scenarios through a comparative study. The results indicate that population explosion does not lead to any serious instability in the model. On the contrary, increased per capita consumption leads to mass extinctions in P1, IS, and more significantly, in human compartment. The scenario of population explosion is more certain as future reality. The simulation results, therefore, conclude that the predicted population rise can be handled by the ecosystem as long as the per capita consumption rates are maintained at the current level. Policy, therefore, should to the extend that the model mirros reality focus more on reducing human consumption rates. Disturbance in natural compartments illustrate that severe perturbations can lead to instability or catastrophe in the model compartments. The economic parameters in the model along with the domesticated sectors, however, are insensitive to the disturbances in the natural compartments.

5. Management strategy development

This work proposes to use optimal control theory to derive time dependent management strategies for the integrated model. To formulate the control problem, it is important to identify a time dependent objective function. Cabezas and Fath [3] have proposed the sustainable regimes hypothesis for natural systems using Fisher information (FI) as a sustainability index. Past work by the authors [4] has illustrated the effectiveness of using Fisher information based objectives for the control problem formulation. Hence, the initial work in this area aims to compute FI variation for the various scenarios mentioned in the previous section by using different set of parameters for FI computation.

The second part deals with the formulation and solution of the optimal control problem to derive effective management strategies for the model. In this work, model parameters that can be effectively regulated in a real system are identified as potential control variables. Since the model is quite complex, with multiple logical conditions, a rigorous mathematical treatment of the control problem is difficult. Hence, pattern search algorithm is used to optimize the FI based objective function and determine the time dependent profile of the selected control variable.

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/legal model. The model development stage involves parameter identification and model modifications to ensure a realistic representation. Scenario analysis on the model is carried out to predict future developments and identify potential catastrophes. The last part deals with the development of effective management strategies to ensure model sustainability, for which Fisher information based sustainable regimes hypothesis and optimal control theory is implemented. The study is expected to illustrate and put forth relevant and important issues, and suggest policy options to ensure global sustainability.

References

[1] 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.

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

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