Quantitative modeling of coupled natural/human systems: simulation of societal constraints on environmental action drawing on Luhmann's social theory

Abstract We draw upon Luhmann's social theory to suggest a framework for quantitative modeling of coupled natural/human systems that may be useful in simulating the effect of societal constraints on environmental action. We (1) provide a brief summary of the key aspects of Luhmann's social theory, (2) develop a quantitative model based on this theory and evaluate model sensitivity to changes in parameters representing important aspects of the theory, (3) propose a structural linkage between the social model and biophysical models, and (4) link the social model to a simple ecological model to simulate societal constraints on environmental action. The model consists of six submodels, each representing one of the six subsystems of modern society identified by Luhmann: economy, politics, law, religion, science, and education. State variables within each submodel represent either active entities that randomly exchange units of information daily or repositories of inactive information. The daily probability that inactive information becomes active increases, and the probability that active information becomes inactive decreases, as the strength of the subsystem increases. Strength is determined by the relative distribution of active information units among the state variables, with maximum strength attained with uniform distribution. Communication among the six subsystems depends on the relative strengths of the subsystems and the frequency with which they resonate with other subsystems. Subsystems communicate externally at the following frequencies: politics once yearly, economics and education once every 3 months, legal once a month, and religion and science once daily. We investigated model behavior by running a series of replicate stochastic simulations and monitoring system and subsystem strength and robustness and over a period of 10 years. The simulated society was both stable and robust. Both stability and robustness of subsystems were inversely related to the frequency of communication with other subsystems, and both strength and robustness were more variable for subsystems with higher external communication frequencies. System strength and robustness were most sensitive to changes in factors affecting the resonance among subsystems. Subsystems open to communication with others on a daily basis (religion and science) exhibited more frequent occurrence of extinction than did subsystems open to external communication less frequently. We explored the model's usefulness in simulating societal constraints on environmental action by coupling it to a simple ecological model that simulates use of a common forage resource. We coupled the models by linking the economic, political, and legal subsystems of society to the environment via a community of resource managers composed of six pairs of ranchers, with each pair sharing a common forage resource. We structured the linkages of the economic and political subsystems with the environment to represent the Prisoner's Dilemma; and the linkages between the legal subsystem and the environment to represent the concept of mutual coercion. We ran two series of simulations in which we ‘unlinked’ and then ‘re-linked’ the environment to the legal subsystem. Results from the first series of simulations demonstrated the classic ecological tragedy of the commons. Results from the second series of simulations demonstrated the effect of periodically imposed (by mutual coercion) legal restrictions on stocking rates, which allowed recovery of forage resources and supported sustainable profits for ranchers. We also examined the sensitivity of simulation results to changes in the values of key parameters affecting the dynamics of premises as they are communicated between the environment and society and among the subsystems of society.