Tipping points and user-resource system collapse in a simple model of evolutionary dynamics

Abstract

The growing demand for ecological resources puts pressure on many ecosystems and, in extreme cases, threatens the long-term survival of the associated social–ecological system. The sustainable use of resources helps to avoid the collapse of the system, but requires the balancing of two conflicting aims: the preservation of resource productivity and the provision of satisfactory returns. Although humans can consider expected future pay-offs in decision-making, the inherent variability of ecological resources makes future returns uncertain and complicates the determination of sustainable harvest behaviours. We present here an adaptive model in which human harvest behaviour is linked to a renewable resource with a randomly fluctuating growth rate. In the model, users adjust their harvest behaviour following a trade-off between the potential current harvest and the discounted future productivity of the resource. Our analyses reveal that rising resource variability increases the discount factor required for a sustainable harvest and reduces long-term pay-offs. A high discount factor, indicating certain future returns, makes the user-resource system robust against resource fluctuations albeit at the cost of a lowered maximum total harvest. By considering the user-resource system as a single co-evolving entity, our approach allows for the determination of sustainable harvest strategies in randomly fluctuating environments.