Estimate of population density and diagnosis of main factors of spatial heterogeneity in the metropolitan scale, western China.

According to the fitted equation, when the PTI is below 55.06%, population density exhibits a decreasing trend at first, but once the proportion exceeds 63.62, it sharply increases.

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The gravity centre of for the spatial patterns of population density in the research period generally showed a trend of moving from the southeast to the northwest between 2000 (30°36′4′′N, 104°9′21′′E) and 2020 (30°38′8′′N, 104°4′52′′E).

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The Moran's I values indicated an increasing trend, indicating that the degree of spatial correlation of the population density tended to increase and that cities with similar population densities tended to be more spatially concentrated.

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