Understanding ecological complexity has stymied scientists for decades. Recent elucidation of the famously coined "devious strategies for stability in enduring natural systems" has opened up a new field of computational analyses of complex ecological networks where the nonlinear dynamics of many interacting species can be more realistically modeled and understood. Here, we describe the first extension of this field to include coupled human-natural systems. This extension elucidates new strategies for sustaining extraction of biomass (e.g., fish, forests, fiber) from ecosystems that account for ecological complexity and can pursue multiple goals such as maximizing economic profit, employment and carbon sequestration by ecosystems. Our more realistic modeling of ecosystems helps explain why simpler "maximum sustainable yield" bioeconomic models underpinning much natural resource extraction policy leads to less profit, biomass, and biodiversity than predicted by those simple models. Current research directions of this integrated natural and social science include applying artificial intelligence, cloud computing, and multiplayer online games.