![]() ![]() Depending on the system’s internal functions (e.g., growth and harvest functions Hannesson 1983), the emerging equilibria can be either stable (e.g., Fig, 1A) or unstable (e.g., Fig. In all nonequilibrium states, the stock will increase or decrease, depending on whether there is a growth or a harvest surplus, respectively. Only when the harvest rate is equal to the natural growth rate is the fish stock size constant over time i.e., the system is in an equilibrium state. We clarify this statement with a simple example of a wild fishery from which fish are harvested (Fig. It has long been known that the direction and rate of change in many complex systems are not random, but determined by stable and unstable equilibria in the system (Holling 1973, Scheffer et al. However, due to numerous complex interactions and feedbacks in many SESs, such system understanding is usually difficult to obtain. Predicting how a SES will behave under changing conditions and what the system may look like after periods of change requires a thorough understanding of the system. 2004), but also on the functioning of the system after it has undergone a transformation (i.e., transformability Folke et al. The resilience of a SES strongly depends on how it reacts to gradual or sudden changes (Walker et al. Such shifts do not necessarily cause equally abrupt changes in the state of the system, but can gradually alter the system state over long periods of time (Walker and Meyers 2004, Biggs et al. ![]() Empirical studies on ecosystems have shown that slowly changing conditions can cause quite abrupt changes in the functioning of a system (i.e., regime shifts Scheffer and Carpenter 2003), and also in SESs such shifts have been observed (Walker and Meyers 2004). Key words: agricultural land use bifurcation diagram land-use change regime shift INTRODUCTIONĬhanging environmental, ecological, political, and socioeconomic conditions can have far-reaching consequences for the functioning of ecological, social, and coupled social-ecological systems (SESs Walker et al. Our approach does not only provide valuable insights into the resilience of our case-study region to changing conditions, but can also be applied to other (agent-based) SES models to present important model results in a condensed and understandable format. We also found that a minimum amount of direct payments was necessary for agricultural extensification to take place. The external stressors had a strong influence on the equilibrium states. With support-vector machine classifications, we created bifurcation diagrams in which the stable and unstable equilibria as a function of the values of a system stressor were depicted. We also assessed the sensitivity of these equilibria to changes in external system stressors. By iteratively running this model for different input settings, we were able to identify equilibria in intensive and extensive agriculture. We used an agent-based SES model to simulate land-use change in an alpine mountain region in the Canton of Valais, Switzerland. We developed a generic approach to identify stable and unstable equilibria states with agent-based SES models. In contrast, agent-based SES models can potentially be used to determine equilibria states, but are rarely used for this purpose. However, the equilibrium states in a SES are often unknown and difficult to identify in real systems. The state of the system rapidly or gradually changes either toward (i.e., stable equilibrium) or away from (i.e., unstable equilibrium) an equilibrium. Such behavior can be predicted if one knows the stable and unstable equilibrium states in a system and how these equilibria react to changes in the system stressors. ![]() To determine the resilience of complex social-ecological systems (SESs) it is necessary to have a thorough understanding of the system behavior under changing political, economic, and environmental conditions (i.e., external system stressors). ![]()
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