Spatial Agglomeration and Diffusion of Population Based on a Regional Density Function Approach: A Case Study of Shandong Province in China


  • Xiaohan Zhao

    College of Geography and Environment, Shandong Normal University, Jinan, Shandong, 250358, China

  • Yanbin Chen

    College of Geography and Environment, Shandong Normal University, Jinan, Shandong, 250358, China

5 July 2023 | Revised: 10 August 2023 | Accepted: 14 August 2023 | Published Online: 18 August 2023


Population density functions have long been used to describe the spatial structure of regional population distributions. Several studies have been conducted to examine the population distribution in Shandong Province, China, but few have applied regional density functions to the analysis. Therefore, based on the 2000, 2010, and 2020 population censuses, this study used monocentric and polycentric regional density functions to study the characteristics of population agglomeration and diffusion in Shandong. This is followed by an in-depth discussion based on population growth rate data and hot- and cold-spot analyses. The results showed that the Shandong Province population was spatially unevenly distributed. Population growth rates were higher in urban centers and counties, with more significant changes in population size in the eastern coastal areas than in the inland areas. As verified in this study, the logarithmic form of the single-center regional density function R2 was greater than 0.8, which was in line with the population spatial structure of Shandong Province. During the study period, the estimated population density of the regional center and the absolute value of the regional population density gradient both increased, indicating a clear and increasing trend of centripetal agglomeration of regional centers over the study period. Overall, the R2 value of the multicenter region density function was higher than that of the single-center region density function. The polycentric regional density function showed that the population density gradient of some centers had a downward trend, which reflected the spatial development trend of outward diffusion in these centers. Meanwhile, the variation in the estimated population density and the population density gradient exhibited differences in the central population distribution patterns at different levels.


Regional density functions; Population spatial structure; Shandong Province


[1] Bontje, M., 2001. Dealing with deconcentration: population deconcentration and planning response in polynucleated urban regions in Northwest Europe. Urban Studies. 38(4), 769-785. DOI:

[2] Salvati, L., Carlucci, M., 2016. In-between stability and subtle changes: Urban growth, population structure, and the city life cycle in Rome. Population Space and Place. 22(3), 216-227. DOI:

[3] Kabisch, N., Haase, D., Haase, A., 2012. Urban Population development in Europe, 1991-2008: The examples of Poland and the UK. International Journal of Urban and Regional Research. 36(6), 1326-1348. DOI:

[4] Wang, F.H., 2001. Regional density functions and growth patterns in major plains of China, 1982-1990. Papers in Regional Science. 80(2), 231-240. DOI:

[5] Jia, P., Qiu, Y.L., Gaughan, A.E., 2014. A fine scale spatial population distribution on the high-resolution gridded population surface and application in Alachua County, Florida. Applied Geography. 50, 99-107. DOI:

[6] Murray, A.T., Davis, R., Stimson, R.J., et al., 1998. Public transportation access. Transportation Research Part D: Transport and Environment. 3(5), 319-328. DOI:

[7] Li, J.G., Li, J.W., Yuan, Y.Z., et al., 2019. Spatiotemporal distribution characteristics and mechanism analysis of urban population density: A case of Xi’an, Shaanxi, China. Cities. 86, 62-70. DOI:

[8] Clark, C., 1951. Urban population densities. Journal of Royal Statistics Society. 114(4), 490-496. DOI:

[9] Cheng, L., 2014. Zhong guo qu yu ren kou mi du mo xing ji jing ji zeng zhang de kong jian mo shi (Chinese) [Regional population density function and spatial patterns of economic growth in China] [Ph.D.’s thesis]. Changchun: Northeast Normal University. p. 8-9.

[10] Parr, J.B., 1985. A population—density approach to regional spatial structure. Urban Studies. 22(4), 289-303. DOI:

[11] Barkley, D.L., Henry, M.S., Bao, S., 1996. Identifying “Spread” versus “Backwash” effects in regional economic areas: A density functions approach. Land Economics. (72), 336-357.

[12] Limtanakool, N., Dijst, M., Schwanen, T., 2007. A theoretical framework and methodology for characterising national urban systems on the basis of flows of people: Empirical evidence for France and Germany. Urban Studies. 44(11), 2123-2145. DOI:

[13] Subasinghe, S., Wang, R., Murayama, Y., 2022. Modelling spatial pattern of population distribution in 50 largest cities in the world: A geospatial approach. IOP Conference Series: Earth and Environmental Science. 1109(1), 012065. DOI:

[14] Heikkila, E., Gordon, P., Kim, J., et al., 1989. What happened to the CBD—distance gradient? Land values in a polycentric city. Environment and Planningn A. 21(2), 221-232.

[15] Small, K.A., Song, S., 1994. Population and employment densities: Structure and change. Journal of Urban Economics. 36, 292-313. DOI:

[16] McMillen, D.P., McDonald, J.F., 1998. Suburban subcenters and employment density in metropolitan Chicago. Journal of Urban Economics. 43(2), 157-180. DOI:

[17] Joseph, M., Wang, F.H., 2010. Population density patterns in Port-au-Prince, Haiti: A model of Latin American city? Cities. 27(3), 127-136. DOI:

[18] Zhou, Ch.S., Xu, X.Q., 1997. Guang zhou shi ren kou kong jian fen bu te zheng ji yan bian qu shi fen xi (Chinese) [Population distribution and its change in Guangzhou city]. Tropical Geography. 17(1), 53-60.

[19] Wang, F.H., Zhou, Y.X., 1999. Modelling urban population densities in Beijing 1982-90: Subur banisation and its causes.Urban Studies. 36(2), 271-287. DOI:

[20] Luo, J., Wei, Y.D., 2006. Population distribution and spatial structure in transitional Chinese cities: A study of Nanjing. Eurasian Geography and Economics. 47(5), 585-603. DOI:

[21] Wang, F.H., Meng, Y., 1999. Analyzing urban population change patterns in Shenyang, China 1982-90: Density function and spatial association approaches. Geographic Information Sciences. 5(2), 121-130. DOI:

[22] Feng, J., Zhou, Y.X., 2003. Jin 20 nian lai bei jing dou shi qu ren kou zeng zhang yu fen bu (Chinese) [The growth and distribution of population in Beijing Metropolitan Area (1982-2000)]. Journal of Geographical Sciences. 58(6), 903-916. DOI:

[23] Wu, W.Y., Ma, X.Y., 2006. Duo zhong xin cheng shi ren kou mo xing ji mo ni: Yi shang hai wei li (Chinese) [Polycentric population density functions and modelling: The case of Shanghai]. Modern Urban Research. 21(12), 39-44. DOI:

[24] Jiang, L., Wu F.L., 2013. Guang zhou ren kou kong jian fen bu bian dong yu duo zhong xin cheng shi kong jian jie gou yan hua ce du (Chinese) [Guangzhou population spatial distribution and polycentricity spatial structure evolution]. Tropical Geography. 33(2), 147-155. DOI:

[25] Sun, T.Sh., Li, G.P., Lu, M.H., 2009. Jing jin ji dou shi quan ren kou ji ju yu kuo san ji qi ying xiang yin su: Ji yu qu yu mi du han shu de shi zheng yan jiu (Chinese) [Concentration and de centralization of population in the Beijing-Tian jin-Hebei metropolitan region and its determi nants: A regional density function approach]. Acta Geographica Sinica. 64(8), 956-966. DOI:

[26] Liu, N.Q., Deng, M., 2018. Duo zhong xin jie gou mo shi yu zhang san jiao cheng shi qun ren kou kong jian fen bu you hua (Chinese) [Urban spatial structure and optimization of population distribution in Yangtze River Delta Region]. Review of Industrial Economics. 27(4), 91-103. DOI:

[27] Hong, Sh.M., Hao, J.M., 2018. Huang huai hai ping yuan ren kou kong jian jie gou ji qi yan bian te zheng yan jiu (Chinese) [Spatial structure of population and characteristics of evolution in Huang-Huai-Hai Plain]. Resource Development & Market. 34(11), 1526-1532+1557. DOI:

[28] Dong, L.F., Wang, L.L., Shao, J.H., et al., 2012. Jin 20 nian lai shan dong sheng ren kou fen bu kong jian ge ju ji qi yan bian te zheng fen xi (Chinese) [Population spatial distribution pattern and evolution characteristics of Shandong province in recent 20 years]. Territory & Natural Resources Study. 138(3), 11-13. DOI:

[29] Li, W.X., Sun, X.H., 2007. Ji yu GIS de shan dong sheng ren kou zhong xin qian yi yan jiu (Chinese) [Study of the migration of population gravity center in Shandong Province based on GIS]. Journal of Shandong Normal University. 99(3), 83-86. DOI:

[30] Wang, J., Yang, X.H., Shi, R.X., 2012. Shan dong sheng ren kou kong jian fen bu ge ju de duo chi du fen xi (Chinese) [Spatial distribution of the population in Shandong Province at multi scales]. Progress in Geography. 31(2), 176-182. DOI:

[31] McDonald, J.F., 1989. Econometric studies of urban population density: A survey. Journal of Urban Economics. 26(3), 361-385. DOI:

[32] Liu, Zh.D., Luo, Sh.F., Lin, Zh.W., et al., 2021. Shan dong sheng ren kou cheng zhen hua de shi kong te zheng ji kong jian xiao ying yan jiu (Chinese) [Study on spatial-temporal characteristics and spatial effects of population urbanization in Shandong Province]. Qu Journal of Qufu Normal University (Natural Science). 47(4), 112-119.

[33] Li, Ch.P., 2015. Xin xi liu shi jiao de shan dong sheng cheng shi wang luo te zheng yan jiu (Chinese) [City network structure of Shandong Province based on information flow]. Journal of Arid Land Resources and Environment. 29(12), 51-56. DOI:

[34] Yang, Q., 1990. Qu yu ke liu fen bu mo xing de yan jiu (Chinese) [A model for interregional trip distribution in China]. Acta Geographica Sinica. 45(3), 264-274. DOI:

[35] Wang, F.H., 2014. Quantitative methods and socio-economic applications in GIS. CRC Press: Boca Raton. pp. 127.

[36] Ohlert, P.L., Bach, M., Breuer, L., 2023. Accuracy assessment of inverse distance weighting interpolation of groundwater nitrate concentrations in Bavaria (Germany). Environmental Science and Pollution Research. 30(4), 9445-9455. DOI:

[37] Ghorbani, Z., Sexton, A., Van Loon, L.L., et al., 2023. Biogeochemical prospecting for gold at the Yellowknife City Gold Project, Northwest Territories, Canada: Part 2-Robust statistical analysis. Applied Geochemistry. 149, 105559. DOI:

[38] Ashraf, M., Loftis, J.C., Hubbard, K.G., 1997. Application of geostatistics to evaluate partial weather station networks. Agricultural and Forest Meteorology. 84(3), 255-271. DOI:

[39] Zhang, K., Wang, Zh.R., 2023. LTPP data-based investigation on asphalt pavement performance using geospatial hot spot analysis and decision tree models. International Journal of Transportation Science and Technology. 12(2), 606-627. DOI:

[40] Ord, J.K., Getis, A., 1992. The analysis of spatial association. Geogrphical Analysis. 24(3), 189-206. DOI:

[41] Tan, M.H, Li, X.B., Lu, C.H., et al., 2008. Urban population densities and their policy implications in China. Habitat International. 32(4), 471-484. DOI:

[42] Li, P., Xu, Y.T., 2011. Shan dong sheng ren kou kong jian fen bu te zheng fen xi (Chinese) [Characteristic study on the spatial distribution of Shandong Population]. Ludong University Journal (Natural Science Edition). 27(3), 274-278. DOI:

[43] Mao, Q.Zh., Long, Y., Wu, K., 2015. Zhong guo ren kou mi du shi kong yan bian yu cheng zhen hua ge ju chu tan—cong 2000 nian dao 2010 nian (Chinese) [Spatial-temporal changes of population density and exploration on urbanization pattern in China: 2000-2010]. City Planning Review. 39(2), 38-43.

[44] Zhang, P.F., Xu, Y.T., 2019. Ji yu GIS de shan dong sheng ren kou fen bu shi kong ge ju ji ying xiang yin su fen xi (Chinese) [Spatial temporal pattern and influencing factors of population distribution in Shandong Province based on GIS]. Anhui Agricultural Science Bulletin. 25(9), 158-162. DOI:

[45] Pang, Y., Lian, H., Wang, L., 2019. De zhou shi xian yu cheng zhen hua shui ping ce du ji qi fen yi yan jiu (Chinese) [Study on the measurement and dissimilarity of urbanization level of De zhou County]. City. 227(2), 53-60.

[46] Zhu, Y., 2021. Ke xue gou jian jiao dong ban dao jing ji quan yi ti hua zhan lue ge ju (Chinese) [Scientifically constructing an integrated strategic pattern of the Jiaodong Peninsula economic circle]. China Journal of Commerce. 830(7), 12-14. DOI:

[47] Gao, Q., 2019. De zhou cheng zhen hua fa zhan bu ping heng bu chong fen wen ti qian xi (Chinese) [Analysis of unbalanced and inadequate urbanization development in Dezhou]. Modern Economic Information. 14, 498.

[48] Cai, Y.J., 2021. Ji yu duo yuan shu ju de ji nan dou shi quan tong cheng hua jin cheng ji qi ying xiang yin su yan jiu (Chinese) [Research on the process and influencing factors of urban integration of Jinan Metropolitan Area based on multisource data] [Master’s thesis]. Jinan: Shandong Normal University. p. 22.


How to Cite

Zhao, X., & Chen, Y. (2023). Spatial Agglomeration and Diffusion of Population Based on a Regional Density Function Approach: A Case Study of Shandong Province in China. Journal of Geographical Research, 6(3), 61–80.


Article Type