Does a scaling exist in urban ecological infrastructure? A case for sustainability trade-off in China.

So far, urban scaling theory has proven that urban area, infrastructure, and economic output have a scaling relation with population. But if we consider ecological space as a part of urban infrastructure, would the same scaling characteristics exist? What is the scaling relationship between ecological spaces and economic social development in different stages of urbanization? This paper is based on this question and explores the trade-off between social economic system and ecosystem in 370 cities of China. The results show that the relationship between population and urban ecological space generally follows the scaling theory in terms of different types of ecological spaces and ecosystem services. For every 10-fold increase in population size, the total area of ecological space and ecosystem services increase by approximately 4 times. The manifestation of ecological space following the scaling laws is the aggregation behavior of better network connectivity. There is a trade-off between urban ecological space and socioeconomic development, with flow equilibrium reached at a population of 2 million and efficiency equilibrium reached at a population of 1 million. Starting from type I and type II megapolis, urban development gradually tends to stabilize, and there may even be a trend of slow decline in urban development potential. In the absence of ecological space, virtual network space can serve as a substitute for ecological space. The driving factors affect scaling behavior of ecological space, including connectivity of ecological space, spatial heterogeneity of natural conditions, and disturbance of economic and social activities. This research can help city to expand ecological space, promoting the added value of urban ecological assets and keeping the urban development potential within the optimal threshold range continuously.