Resilience in social-ecological systems: identifying stable and unstable equilibria with agent-based models

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). 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. The state of the system rapidly or gradually changes either toward (i.e., stable equilibrium) or away from (i.e., unstable equilibrium) an equilibrium. However, the equilibrium states in a SES are often unknown and difficult to identify in real systems. In contrast, agent-based SES models can potentially be used to determine equilibria states, but are rarely used for this purpose. We developed a generic approach to identify stable and unstable equilibria states with agent-based SES models. We used an agent-based SES model to simulate land-use change in an alpine mountain region in the Canton of Valais, Switzerland. By iteratively running this model for different input settings, we were able to identify equilibria in intensive and extensive agriculture. We also assessed the sensitivity of these equilibria to changes in external system stressors. 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. The external stressors had a strong influence on the equilibrium states. We also found that a minimum amount of direct payments was necessary for agricultural extensification to take place. 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.