Table 2 The fitting equations and precision of the spatial distribution density of population (number of people per ha) across the urban–rural gradients of 2000, 2009, and 2019 in the GBA and eleven cities.

GBA

y = 11,000x^(−0.95),***

y = 18,500x⁽⁻¹⁾,***

y = 22,500x⁽⁻¹⁾,***

Hong Kong

y = 35,500x^(−0.9)

y = 340,000x^(−1.3)

y = 210,000x^(−1.2)

Macau

–

–

–

Guangzhou

y = 28,000x^(−1.1),**

y = 35,000x^(−1.1),**

y = 45,000x^(−1.1),**

Shenzhen

y = 11,000x^(−0.95),*

y = 13,000x^(−0.9),*

y = 34,000x⁽⁻¹⁾,*

Zhuhai

y = 6850x^(−0.95)

y = 11,500x⁽⁻¹⁾

y = 8000x^(−0.9)

Dongguan

y = 210x^(−0.3)

y = 450x^(−0.4)

y = 500x^(−0.4)

Zhongshan

y = 850x^(−0.6)

y = 1050x^(−0.6)

y = 2250x^(−0.7)

Foshan

y = 6000x^(−0.9),*

y = 4100x^(−0.8),*

y = 7000x^(−0.85),*

Zhaoqing

y = 3650x^(−0.8),*

y = 2300x^(−0.7),*

y = 2500x^(−0.7),*

Jiangmen

y = 5000x^(−0.85),**

y = 4000x^(−0.8),**

y = 3200x^(−0.75),**

Huizhou

y = 2200x^(−0.8),*

y = 3300x^(−0.8),*

y = 4700x^(−0.8),*