Where should livestock go? Integrating soil erosion risk and spatial fairness in grazing management

Grassland ecosystems in alpine pastoral regions commonly face dual challenges of ecological degradation and spatial inequality in resource allocation. To address this, this study develops and applies a novel optimization framework that integrates biophysical risk assessment, socio-spatial fairness quantification, and mathematical optimization. The methodological framework first employs the Revised Universal Soil Loss Equation (RUSLE) model to simulate soil erosion and establish ecological thresholds, identifying areas of high vulnerability. Second, this study constructs a spatial fairness index (q) based on key spatial factors to quantify grazing convenience and resource accessibility. This analysis revealed a significant mismatch, where areas with lower fairness scores paradoxically bore higher realistic grazing pressures. Finally, this study utilizes a quadratic programming model to optimize livestock allocation across 97 villages. The model minimizes structural deviation from the original distribution while adhering to the dual constraints of ecological erosion thresholds (upper limit) and fairness-adjusted stocking densities (lower limit). This integrated methodology was applied to a typical alpine pastoral region. Optimization results demonstrate the framework’s efficacy: ecological pressure in high-risk areas was significantly reduced, while under grazed, low-erosion areas received compensatory increases. This redistribution was achieved while increasing the total regional stocking by 9.25% and achieving a 45% reduction in the squared deviation from the original grazing structure. This study’s primary contribution is a replicable, data-driven strategy that effectively integrates and operationalizes ecological sustainability and social equity in pastoral management. • A dual-constraint model integrates erosion risks and spatial fairness. • RUSLE and fairness scoring reveal significant spatial heterogeneity. • Optimized allocation increased regional livestock stocking by 9.25%. • The strategy achieved a 45% reduction in grazing structural deviation.