A Bayesian framework linking perceived social-ecological effectiveness to stakeholder acceptance in China's Sousa chinensis protected areas

Enhancing stakeholder acceptance of marine protected areas (MPAs) is key to fulfilling the 30 × 30 Target, ocean-related Sustainable Development Goals, and the UN Decade of Ocean Science for Sustainable Development (2021-2030). These require MPAs not merely as management interventions, but also as social-ecological systems (SESs), where social-ecological effectiveness is the complex coupling of social and ecological effectiveness through interactions. However, the relationships between perceived social-ecological effectiveness and stakeholder acceptance are often indirect and mediated, while traditional models can yield statistical instabilities, risking false conclusions. This article tentatively proposes a partially informative Bayesian posterior framework with three steps and five criteria, using a theoretically based regulator formula and an inverse-Wishart prior in a penalized likelihood function for stricter estimates. Using field surveys and remote sensing data of China's Sousa chinensis MPAs, the study tentatively explores the proposed framework through stakeholder perceptions. Bayesian estimates improved model convergence, positive definiteness and nonsingularity, revealing an average 63 % underestimation of standard errors. Monte Carlo bootstrapping suggested the chain mediation and layered mechanisms, whereby perceived ecological effectiveness is related to stakeholder acceptance through perceived social effectiveness and stakeholder-MPA interaction. Practical implications include socially effective conservation, community-based activities, and stakeholder acceptance monitoring by the scientific community. The framework with more informative Bayesian methods may offer preliminary insights for broader biological conservation settings and practices, subject to contextual adaptations.