Social-ecological models are often used to investigate the mutual interactions between an ecological system and human behaviour at a collective level. The social system is widely represented either by the replicator dynamics or by the best-response dynamics. We investigate the consequences of choosing one or the other with the example of a social-ecological model for eutrophication in shallow lakes, where the anthropogenic discharge of pollutants into the water is determined by a behavioural model using the replicator or a best-response dynamics. We discuss a fundamental difference between the replicator dynamics and the logit formulation of the best-response dynamics. This fundamental difference results in a different number of equilibria. We show that the replicator equation is a limit case of the best-response model, when agents are assumed to behave with infinite rationality. If agents act less rationally in the model using the best-response dynamics, the correspondence with the model using the replicator dynamics decreases. Finally, we show that sustained oscillations observed in both cases may differ substantially. The replicator dynamics makes the amplitude of the limit cycle become larger and makes the system come closer to full cooperation or full defection. Thus, the dynamics along the limit cycle imply a different risk for the system to be pushed by a perturbation into a desirable or an undesirable outcome depending on the socioeconomic dynamics assumed in the model. When analyzing social-ecological models, the choice of a socioeconomic dynamics is often little justified but our results show that it may have dramatic impacts on the coupled human-environment system.

社会生态模型通常用于在集体层面上研究生态系统与人类行为之间的相互作用。社会系统被复制者动力学或最佳响应动力学广泛地代表。我们以在浅水湖泊富营养化的社会生态模型为例，研究了选择其中一种的后果，在这种情况下，人为排放到水​​中的污染物是通过使用复制器或最佳响应动力学的行为模型确定的。我们讨论了复制器动力学和最佳响应动力学的logit公式之间的根本区别。这种根本的差异导致了不同数量的平衡。我们证明复制器方程是最佳响应模型的极限情况，假设代理商行为具有无限理性。如果代理使用最佳响应动力学在模型中的行为较不合理，则使用复制器动力学的模型与模型的对应关系将减少。最后，我们表明在两种情况下观察到的持续振荡可能有很大的不同。复制器的动力学特性使极限循环的幅度变大，并使系统更接近完全协作或完全偏离。因此，取决于模型中假设的社会经济动态，沿着极限周期的动态暗示了系统被扰动推入期望或不期望结果的不同风险。在分析社会生态模型时，