Bayesian Tree–Spline Modeling of Circular Bioeconomy Potential in Regional Agricultural and Livestock Production Systems

This study investigates the structural transformation of regional livestock production systems toward an integrated Circular Bioeconomy (CBE) framework. Using an integrated Bayesian Tree–Spline approach, spatially disaggregated regional data were analyzed to evaluate the environmental, technological, and logistical determinants of sustainable livestock production. The empirical model incorporated key indicators, including infrastructure readiness, market accessibility, manure intensity, biogas conversion rates, methane emissions, alternative feed utilization, and transport-related emissions. The probabilistic classification results revealed substantial spatial heterogeneity among the analysed regions, enabling the identification of areas with high circular bioeconomy implementation potential, transitional regions, and areas requiring further technological and infrastructural development. Shannon entropy measures were applied to quantify classification uncertainty and identify transitional zones, while penalized B-splines captured non-linear saturation effects associated with alternative feed utilization and the integration of bioenergy technologies. The findings provide a data-driven basis for supporting the implementation of circular bioeconomy principles, enhancing resource-use efficiency, reducing greenhouse gas emissions, and facilitating the transition toward climate-neutral livestock production systems. Compared with the deterministic benchmark model, the proposed Bayesian Tree–Spline framework additionally quantifies classification uncertainty, captures nonlinear threshold and saturation effects, and provides probabilistic regional typologies that support more robust and evidence-based policy recommendations.