Qingxi Huang, Jianshu Li
This study proposes a Dual-layer Ecological-Heritage Network (DEHN) framework modeling ecological connectivity and intangible cultural heritage as a coupled bi-layer graph, applied to three Hakka Cultural Ecological Protection Zones in South China (74,547 km2). Specifically, by using MSPA-lite on land cover data (2000-2023), authors built a 233-node, 799-edge ecological network coupled with a 23-node, 73-edge heritage network via a 10 km distance-decay scheme. Additionally, percolation attacks reveal critical thresholds of 0.690 for the ecological layer and 0.925 for the heritage layer, indicating the ecological network loses connectedness earlier than the ICH inventory network. A Restoration Priority Index identifies 47 Tier 1 (top-ranked) and 46 high-priority patches, with Meizhou concentrating 75% in the top tiers. Counterfactual simulations show edge-cost reduction alters collapse thresholds, while losing patches reduces them by 98.4%, necessitating topological expansion via new stepping-stone patches. The DEHN framework overall provides a density-normalized comparison (23.3 vs. 3.21), showing that the ecological layer is more resilient per unit connectivity, providing a transferable template for coupled restoration planning in protected cultural-ecological zones. The DEHN framework engages with Sustainable Development Goal 11.4 ("Strengthen efforts to protect and safeguard the world's cultural and natural heritage") and Aichi Biodiversity Target 11 (conserving at least 17% of terrestrial areas). The percolation thresholds identified (ecological f_C = 0.690, heritage f_C = 0.925) provide quantitative benchmarks for assessing whether CEPZ management has maintained network resilience above the collapse threshold. The finding that 47 patches (20% of the ecological network) constitute the Tier 1 (top-ranked), whose loss would trigger cascade failure, suggests that the CEPZ boundary designation-which does not prioritize these topologically critical patches-may be insufficient for meeting SDG 11.4 targets. Authors recommend that CEPZ management plans incorporate network resilience thresholds as monitoring indicators, reporting annually whether the consensus f_C remains above 0.50 (the operational definition of network collapse).