Understanding feedbacks in social–ecological systems using non-recursive structural equation models

• We integrate Ostrom’s SES ontology with SEM to quantify and understand system interactions. • Non-recursive SEMs capture simultaneous bidirectional relationships in SES. • Feedback strength and direction are explicitly estimated. • Non-recursive models identify equilibrium under mutual dependence. • A generalizable framework to assess resilience and stability in complex systems. Addressing contemporary sustainability challenges requires an analytical approach capable of capturing the complex, reciprocal dependencies between human societies and natural environments. While Elinor Ostrom’s Social-Ecological Systems (SES) framework provides a robust diagnostic ontology, transitioning from descriptive mapping to the quantitative modelling of non-linear dynamics and feedback loops remains a methodological hurdle. Traditional statistical approaches often assume unidirectional causal relationships, limiting their capacity to represent the reciprocal interactions that characterize SES. This study proposes the application of non-recursive Structural Equation Modelling (SEM) to explicitly model equilibrium feedback loops within SES. Unlike recursive models, the non-recursive approach allows for the estimation of reciprocal effects, where social governance and ecological integrity mutually influence each other simultaneously. Using a simulation-based approach grounded in SES dynamics, we demonstrate how non-recursive SEM can identify the strength and direction of feedback mechanisms that drive systemic stability or collapse. Our results indicate that accounting for bidirectional feedbacks significantly alters the estimation of causal effects compared to traditional recursive specifications, providing a more accurate representation of the adaptive feedback structures that contribute to resilience in SES. This methodological framework offers a scalable tool for researchers to move beyond linear causality, facilitating a deeper understanding of the internal governing dynamics of complex adaptive systems.