A Study on Spatial and Temporal Changes and Synergies/Trade-Offs of the Production-Living-Ecological Functions in Mountainous Areas Based on the Niche Width Model

As a typical ecologically fragile mountainous area, Liangshan Yi Autonomous Prefecture in Sichuan Province faces challenges of irrational land resource allocation and uncoordinated urbanization. This study employs an ecological niche width model to quantify the functional status of “production-living-ecological” functions (PLEFs) between 2010–2020. Methodologically, we integrated spatial autocorrelation analysis and Spearman’s correlation coefficients to systematically evaluate spatiotemporal synergies and trade-offs among PLEFs. Based on this, spatial clustering patterns were further analyzed using Maxwell’s triangle and K-means algorithms to delineate functional zones. Key findings include: (1) Production function (PF) and living function (LF) exhibit a “core-periphery” spatial pattern (high-value clusters in the south, low-value contiguous areas in the north), while ecological function (EF) displays a “high-low-high” ring-shaped pattern (high values in the northwest and southeast, declining in the central region due to development pressure); (2) synergy and trade-off relationships coexist in the study area. Synergies and trade-offs coexist among PLEFs. The synergistic effect between PF and EF strengthens significantly, the trade-off relationship between PF and LF weakens slightly, and the trade-off between LF and EF remains prominent; high-low (HL) clusters and low-high (LH) clusters exceed 55%; (3) based on synergy/trade-off relationships, the study area is divided into six functional zones (e.g., economic priority zones, ecological protection zones), with proposed optimization strategies such as “intensive valley development, eco-cultural tourism in border areas, and urban-rural coordination in central regions,” providing scientific support for sustainable territorial spatial utilization in mountainous areas.