Cross-scale feedbacks and tipping points in aggregated models of socio-ecological systems

Many researchers have called for more consideration of cross-scale dynamics in models of socio-ecological systems, but this is a fundamentally difficult thing to do. Focussing on cross-scale feedbacks and tipping points, this paper uses three example models to demonstrate and reflect on how cross-scale dynamics can be incorporated into aggregate models. Tipping points - where a small perturbation can lead to a qualitative change in a system - are generally the result of nonlinear feedback mechanisms. These feedback mechanisms often operate on different levels within or across scales. Tipping points occurring on one level or scale may cascade across to others. Interest in these types of cross-scale feedbacks and tipping points is high, but consideration of how to model them is underdeveloped. The representation of cross-scale feedbacks and tipping points in aggregated models of socio-ecological systems remains a critical challenge for modellers, with implications for the types of models and policy advice that can be developed. We present three case studies to demonstrate and reflect on how cross-scale feedbacks and tipping points can be represented and analysed in these models. Two key themes emerge from our reflections: (i) the variety and trade-offs in ways to explore and present model behaviour, using tools such as scenario analysis and phase portraits; and (ii) the subjectivity inherent in considering and implementing scale, in aggregated models.