Spatial gradients of supply and demand of ecosystem services within cities

The supply and demand of ecosystem services (ES) present apparent spatial heterogeneities within cities, with a higher demand but limited supply in urban centers, and vice versa in suburban and rural areas. However, there is still a lack of theory and relevant quantitative tools to quantify the distribution patterns and spatial mismatches of ES supply and demand across space, e.g., along urban-rural gradients. Here, we adopt a modified sigmoid function to quantify spatial gradients of ES supply and demand of six cities within the Danjiangkou Basin in Hubei Province, China. ES supply and demand are calculated using the value equivalent method and the land development index model, respectively. Results show that as the distance from the city center increases, there is a decrease in ES demand, while ES supply exhibits a gradual increase through the gradient analysis. We then utilized the modified sigmoid model to accurately quantify the S-shape curve for ES supply and the inverse Sshape curve for ES demand. We further observed that the balance point (the intersection of the ES supply and demand curves) of ES supply and demand gradually moved towards the outskirts of the city as it expanded. Our study introduces a quantitative tool for analyzing the spatial gradients of ES supply and demand within cities.