Resilient Food-Biodiversity Outcomes Via Stochastic Control Of Multiplex Socio-Ecological Networks Under Water Stress

Food-security pressures, biodiversity loss, and chronic water scarcity interact to erode the connectivity that keeps agricultural socio-ecological systems (SES) functional. We ask: how much effort — of which type and when — is required to preserve multiplex connectivity under volatile water supplies at minimum cost? We model the agricultural SES as a multiplex network and embed its dynamics in a stochastic optimal-control problem solved in Hamiltonian form. Shadow prices of connectivity are derived via the Feynman–Kac representation, and open-loop solutions are refined with a machine learning controller. Methodologically, this integrates stochastic co-states with policy refinement for multilayer SES control. Conceptually, resilience is operationalized through network-level criteria. Numerical experiments under escalating drought show: (i) optimally configured controllers maintain strong resilience under moderate stress; (ii) beyond a critical drought threshold, only weak resilience is attainable; (iii) control effort exhibits layer asymmetry, with agri-food requiring sustained torque and biodiversity benefiting from punctuated interventions; and (iv) a governance wedge persists between technically cost-effective effort and stakeholders' willingness to implement it. These results clarify when, and how, incentive-compatible policies are needed to keep agri-food-biodiversity connectivity viable under water volatility.