  In social-ecological systems (SESs), social and biophysical dynamics interact
within and between structural levels separated by 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, which capture essential features
while being simple enough to yield insights into mechanisms. In a stylised
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. 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 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.
