The food-biodiversity nexus is a concept that defines and characterizes the complex interactions between agricultural systems and biodiversity conservation. Here we use a social-ecological systems approach that combines fuzzy cognitive mapping and graph theoretic analyses to uncover system properties that determine food security and biodiversity outcomes at a landscape scale. We studied a rice-based agricultural landscape system situated in Mbeliling district of West Flores, Indonesia. A graphical representation of the Mbeliling district food-biodiversity nexus was created by local experts. The representation revealed system properties that help reconcile the trade-offs between food security and biodiversity conservation. The graph represented a diverse set of food security and biodiversity nodes, and showed that there is not a simple dichotomy between 'production and protection'. The analysis captured greater complexity than popular academic concepts such as land sparing-land sharing or sustainable intensification. Three major themes emerged from the graph. We found distinct clusters of factors influencing biodiversity and food security. We named these sources of influence (1) Modernisation and sustainable farming; (2) Knowledge and management; and (3) Governance and processes. Component 2 was the most representative of emergent system properties that contribute positively to managing a sustainable food-biodiversity nexus in the Mbeliling landscape. The key determinants of outcomes were: improving agronomic practices, diversifying production, maintaining forest cover and connectivity, and using knowledge and natural resource management processes to mitigate the main drivers of change. Our approach highlights the complexities in the food-biodiversity nexus, and could have wide application in other locations.