A pressing challenge for coming decades is sustainable and just management of large-scale common-pool resources including the atmosphere, biodiversity and public services. This poses a difficult collective action problem because such resources may not show signs that usage restraint is needed until tragedy is almost inevitable. To solve this problem, a sufficient level of cooperation with a pro-conservation behavioural norm must be achieved, within the prevailing sociopolitical environment, in time for the action taken to be effective. Here we investigate the transient dynamics of behavioural change in an agent-based model on structured networks that are also exposed to a global external influence. We find that polarisation emerges naturally, even without bounded confidence, but that for rationally motivated agents, it is temporary. The speed of convergence to a final consensus is controlled by the rate at which the polarised clusters are dissolved. This depends strongly on the combination of external influences and the network topology. Both high connectivity and a favourable environment are needed to rapidly obtain final consensus.

In social-ecological systems (SESs), social and biophysical dynamics interact within and between the levels of organization at multiple spatial and temporal scales. Cross-scale interactions (CSIs) are interdependences between processes at different scales, generating behaviour unpredictable at single scales. Understanding CSIs is important for improving SES governance, but they remain understudied. Theoretical models are needed that capture essential features while being simple enough to yield insights into mechanisms. In a stylized model, we study CSIs in a two-level system of weakly interacting communities harvesting a common-pool resource. Community members adaptively conform to, or defect from, a norm of socially optimal harvesting, enforced through social sanctioning both within and between communities. We find that each subsystem's dynamics depend sensitively on the other despite interactions being much weaker between subsystems than within them. When interaction is purely biophysical, stably high cooperation in one community can cause cooperation in the other to collapse. However, even weak social interaction can prevent the collapse of cooperation and instead cause collapse of defection. We identify conditions under which subsystem-level cooperation produces desirable system-level outcomes. Our findings expand evidence that collaboration is important for sustainably managing shared resources, showing its importance even when resource sharing and social relationships are weak.