Scale dependence and nonlinear threshold effects of recreation service supply–demand coupling in large river basins

The matching of recreation service supply and demand affects regional sustainability and human well-being, yet the multi-scale coupling mechanisms and threshold effects of driving factors remain unclear. Taking the Yellow River Basin, this study developed a “grid–county–city” three-scale framework and integrated the MaxEnt model, coupling coordination degree model, random forest permutation test, and segmented threshold identification algorithm to analyze the scale-dependent patterns and driving thresholds of the coupling coordination degree of recreation ecosystem service supply and demand (CCD_RES). Results showed that: (1) Spatial heterogeneity of CCD_RES decreased with increasing scale, ranging from 0.985 at grid and county scales to 0.722 at the city scale; its pattern shifted from scattered in the southern basin (grid scale) to clustering around Xi'an and Zhengzhou (county scale), stabilizing over these core cities (city scale). (2) Driver importance transitioned from “natural constraints” to “social support”: at grid scale, slope (increase in MSE ≈ 100%) and fractional vegetation cover (≈150%) dominated; at county scale, road network density (≈40%) and GDP (≈35%); at city scale, population density (≈25%) and GDP (≈25%). (3) Key drivers showed nonlinear threshold effects: population density thresholds were 208.89 people/km 2 (city) and 206.53 people/km 2 (county), and fractional vegetation cover threshold at grid scale was 0.8. This study reveals scale dependence and nonlinear thresholds of CCD_RES drivers, offering a scientific basis for differentiated spatial management in large river basins.