Objective As the irreplaceable basic skeleton of the urban green network, parks are a high quality green open space that people have the closest contact with, while people, as the main body of activities leading urban development, are users and demanders of parks and recreation. At the same time, the new concept of "park city", by linking "people" and "park", emphasizes that people's needs for a better life and parks are closely correlated and interactional. Scholars have explored the relationship between urban population and park area at different scales, from different perspectives and by different methods, but most relevant researches still assume only a linear relationship between urban population and park area, and use a constant standard value to determine the level of park construction. However, the interaction between population growth and park area expansion is not only linear, but also has complex characteristics such as balance, promotion or inhibition, while being of spatial and temporal heterogeneity.

Methods As a general form of threshold regression model, the smooth transition regression model can reveal the effects of urban population or park area, as a transition variable, on other variables across different threshold parameters, and measure the linear and nonlinear relationships between them. Therefore, this research adopts the smooth transition regression model to analyze the mechanisms and dynamic evolution of urban population increment and park area increment during the period from 1997 to 2020 at both the national and city scales.

Results 1) The interaction between urban population increment and park area increment in China shows nonlinear characteristics in phases, and the linear relationship between the two always exists, so it is most appropriate to use the urban population increment with a one-period lag as the conversion variable to build a nonmonotonic conversion function model. At the national scale, the linear relationship between the two always exists, with each 1% increase in population increment accompanied by a decrease of 1.020 96% in the growth of park area increment. When the population increment crosses the threshold parameter, its nonlinear effect on park area growth becomes apparent, and for each 1% increase in population increment, the park area increment may positively change by 2.907 73%. 2) At the city scale, in 2020, the population increment and park area increment show a nonlinear relationship in roughly 96.56% of cities nationwide, and the majority of cities of all types are nonlinear. However, the contribution of megacities to park area increment is much higher than that of other types of cities; from the perspective of long time series, megacities dominate urban population increment and park area increment in the long term, followed by large cities. As the share of nonlinear cities in terms of population and park area increment tends to be stable in fluctuation among megacities and large cities, the share of nonlinear cities decreases with the increase of city size in the same time period.

Conclusion 1) This research breaks the previous single assumption that there is only a linear or nonlinear relationship between population and park, and considers both the linear and nonlinear relationships between the two, while emphasizing that nonlinear research is by no means to blindly overthrow linear research, which is exactly the biggest breakthrough achieved in this research. The asymmetry nature of population change and the self-organizing ability of park construction suggest a nonlinear relationship between the two, and thus neither linear nor non-linear can be researched separately to capture the true complex pattern of change between urban population and park area. 2) There are differences in the development stages, existing problems and planning objectives of different cities, and population and park development modes need to be further considered in combination with different city sizes. Specifically, for megacities and large cities, the scale effect should be brought into play in the context of urban agglomeration construction, and the sharing and recreation of park construction should be accurately improved in accordance with the needs of population increase; for medium and small cities, the original inertia of incremental planning should be changed, blind and inefficient expansion should be abandoned, and public resources such as population and parks should be concentrated in urban areas to create a livable urban environment and promote these cities to become "park cities". 3) The research investigates the "growth effect" between urban population and park area, revealing the threshold effect and growth change relationship between urban population and park area, which can provide a reference for further refinement of relevant per capita enjoyment indicators, while providing data support and theoretical basis for the differentiated management of people-oriented green urban development and the relationship between population and park supply allocation.