Beyond spillovers: Constructing an efficient synergy network to balance ecological surplus-deficit in Beijing-Tianjin-Hebei urban agglomeration

The networked development of urban agglomerations (UAs) contributes to ecological footprint (EF) expansion and spillovers, yet creates opportunities for cross-regional ecological resource synergy. However, research gaps persist in constructing intercity synergy networks and planning ecological resource allocation and transfer paths within them. This study develops a novel multi-scenario approach using a Network Flow Allocation-based Particle Swarm Optimization (NFA-PSO) model to construct an efficient synergy network for balancing ecological surplus–deficit within UAs. The approach's effectiveness is empirically validated in the Beijing–Tianjin–Hebei urban agglomeration (BTHUA), China. Results show severe ecological resource supply–demand imbalance in the BTHUA, with 84%–86% of units in deficit. From 2010 to 2020, EF continuously shifted from the core metropolitan area to peripheral underdeveloped regions. Regarding the ecological synergy network, underdeveloped transportation infrastructure in ecological surplus areas imposed a high resource flow load, constraining the allocation efficiency of the ecological synergy network. Multi-scenario simulations further show that different development orientations alter ecological resource flow paths and network loads. Among S1–S5, the economy-priority scenario (S2) has the lowest network resource load and the highest efficiency. By contrast, total network load rises by 8.01%–20.57% under scenarios integrating population, vulnerability, and sustainability objectives, demonstrating that more balanced resource allocation requires higher cross-regional network flow costs. Moreover, the resource flow network exhibits structural vulnerabilities and limited spatial coverage due to over-dependence on a small number of trunk paths. This study provides novel insights and solutions for optimizing ecological synergy networks, thereby advancing the sustainable development of UAs.