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Ba sed on the urban resident population statistics from 2005 to 2018, thi s paper analyzes the distribution and evolution of city scale in China by screening city samples according to the threshold criteria and using empirical research methods such as the City Primacy Index, the Rank-Scale Rule, the Gini coefficient of city scale, Kernel Density Estimation and Markov transfer matrix. The results show that: the most populous city in China has obvious advantages. The population distribution is concentrated in high order cities and in accordance with the law of order - scale; the economic scale of cities is in a concentrated state, the gap between the economic development levels of different types of cities is large, and the megacities are more attractive, which to a certain extent limit the development of the scale of the rest of the cities; the number of China’s city population is increasing, however, the gap between the population scale of other cities and the most populous city continues to be large, and the structure of city population scale is not reasonable enough; megacities and megalopolises keep their original scale levels unchanged to a large extent, and the scale transition between the two types of cities is rather difficult. Finally, based on the explanatory framework of the dynamics of city scale evolution, policy recommendations are proposed to promote a more balanced distribution of city scale.

City scale is a core topic in city research, and an accurate understanding of the evolutionary dynamics of China’s city scale can provide strong technical support for sustainable city development and high efficiency in the use of public resources [

There are countless studies on the characteristics of city scale distribution at home and abroad. Jefferson, a foreign scholar, first introduced the city primacy in 1931 when he discussed the characteristics of regional city distribution [^{ }et al., applied a joint cubic equation model in economics and explored that the city-rural income gap also has an impact on the city scale distribution [^{ }et al., improved the land use model for city scale development by adding land constraint parameters in terms of population growth and land expansion to derive a quantitative relationship between the rate of land expansion and the rate of population growth [

However, there are fewer relevant studies using multiple research methods such as Zipf’s law [

The American geographer Jefferson (1939) considered the first city as the most populous city in a region and its number would be higher than the second city by two times, therefore, the ratio of the population scale of the first and second cities was proposed to represent the firstness, i.e., S_{2}. Later on, some scholars improved it and proposed the four-city index (S_{4}) and the eleven-city index (S_{11}) [

{ S 2 = P 1 P 2 S 4 = P 1 P 2 + P 3 + P 4 S 11 = 2 P 1 P 2 + P 3 + ⋯ + P 11 (1)

where P 1 , P 2 , P 3 , ⋯ denotes the number of population of cities in order 1^{st}, 2^{nd}, 3^{rd}, …, respectively. According to Felix Auerbach’s (1913) Theory of City Rank Scale Distribution [_{2} is 2, andS_{4},S_{11} are 1.

The American linguist George Kingsley Zipf (1935) established the city Rank-Scale Rule, known as the Zipf distribution. The general relationship equation is as follows:

P i = P 1 × R i − q (2)

To transform the expression (2), we get:

ln P i = ln P 1 − q ln R i (3)

where: P 1 is the population of the most populous city; P 2 , P 3 , P 4 , ⋯ refers to the population of the 2^{nd}, 3^{rd}, and 4^{th}, etc., cities, respectively; R i represents the order ofi city; q denotes the Zipf index.

Marshall first introduced the city Gini coefficient for the study of city scale, and the specific formula is:

G = T / 2 S ( n − 1 ) (4)

Specifically, n represents the number of cities. G represents the city Gini coefficient, which can be expressed as PG or EG. PG refers to the Gini coefficient of

city population scale, with S = ∑ i = 1 n P i and T = ∑ i , j = 1 , i ≠ j n | P i − P j | in expression (4) respectively representing the total city population in the region and the sum of the absolute values of the difference between the population scale of any two cities. EG denotes the Gini coefficient of city economic scale. S = ∑ i n G D P i and T = ∑ i , j = 1 , i ≠ j n | G D P i − G D P j | in expression (4) are the total city economic scale in

the region and the sum of the absolute values of the difference between the economic scale of any two cities, respectively.

Rosenblatt (1955) and Emanuel Parzen proposed the Kernel Density Estimation, also known as KDE, in 1962, which is a nonparametric estimation. The general expression is:

f ( x ) = 1 n h ∑ i = 1 n K ( x − x i h ) (5)

where f ( x ) is the probability density function to be estimated and k ( . ) is the kernel function, satisfying symmetry and ∫ K ( x ) d x = 1 , also, n is the number of observations and h is the bandwidth. It is worth noting that the choice of h affects the smoothness of the estimated function as well as the fitness of the model, which in principle should satisfy the minimum of the mean square error. In this paper, the commonly used Epanechnikov kernel function is selected, and the h-value is automatically adjusted in MATLAB according to the sample data characteristics to be optimal.

The city scale data are divided into k classes, and to calculate the probability of cities in each class and the probability of transferring cities between each class, this process can be approximated as a Markov process.

The Markov transfer matrix is denoted by M, M i j denotes the one-step transfer probability of a city belonging to ranki in timet converting to rank j in the next period t + 1 , i.e., M i j = n i j / n i , where n i j denotes the sum of the number of cities converting from ranki in timet to rankj in time t + 1 . n i is the sum of the number of all ranki cities in timet. The process of city scale evolution is accompanied by the rise and fall of each city scale class, i.e., the change of mobility in different classes of cities. In this paper, two mobility measures are used, the first of which is the SMI (Shorrocks Mobility Index) as defined by Shorrocks [

SMI = k − ∑ i = 1 k M i i k − 1 (6)

The scale of SMI depends on ∑ i = 1 k M i i . The smaller the SMI value, the weaker

the mobility, and the greater the probability that a city belonging to a certain class in time t will still belong to the same class in time t + 1 ; on the contrary, the larger the calculated SMI value, the stronger the mobility.

The second one is to construct a new liquidity measure DMI (Direction Mobility Index). It can be expressed as:

DMI = ∑ i = 1 k 2 | i − j | − 1 ( ∑ j = i + 1 k M i j − ∑ j = 1 i − 1 M i j ) (7)

The former part of expression (7) indicates the mobility index of cities moving to higher levels, i.e. upward mobility level, and the latter part indicates downward mobility level, where 2 | i − j | − 1 is the weight of mobility across levels, when the higher the number of levels crossed, the more hard it is to move, so it needs to be given a greater weight. DMI > 0 indicates that cities are more likely to cross to higher levels. DMI < 0 indicates that cities are more mobile downward, i.e., cities are underdeveloped in later stages and their scale levels are decreasing.

Most studies on city scale use two types of data, one is the data of “population of municipal districts” in the City Statistical Yearbook, which includes the entire population of city areas and a large number of rural areas and is easy to overestimate city scale; the other type of data is the statistical caliber of household population, using the data of “city non-agricultural population” to measure, which lacks systematic and accurate statistics of the transient and mobile population, it is easy to underestimate city scale. Accordingly, the choice of either “municipal population” or “non-agricultural population” can lead to errors in measuring the scale of cities. The city resident population of the national census data from 2005 to 2018 is selected in this paper, and in order to more accurately portray the mobility characteristics of cities, a population scale of 5 million and the National GDP per capita (billion yuan) of that year are also selected as the threshold lower bound at the same time. Defining thresholds is of high significance for the study: for one, this paper uses both the population of 5 million and the National GDP per capita as the lower threshold to filter out cities that meet both the population scale and a certain level of economic development, so that it is easy to identify them from other cities and the economic links are more obvious. The second one is that cities will gradually prosper or decay in the process of development, and setting the threshold can make the cities whose original resident population scale exceeds the threshold enter the sample, while those below the threshold in the later stage drop out of the sample.

In this paper, the population data from 2005 to 2018 are obtained from the China City Statistical Yearbook 2006-2019, China Statistical Yearbook 2006- 2019 and China Population and Employment Statistical Yearbook 2006-2019. The three major indicators of resident population and gross product, and gross product per capita are selected as the research data by combining the above yearbooks, and the characteristics and evolutionary trends of city scale distribution in China are studied by using MATLAB, ArcGIS and other measurement and statistical analysis software.

In this paper, China’s city resident population data from 2005 to 2018 are screened for sample cities based on threshold conditions, and the current city scale class is also used as the basis for classifying the city scale class. At present, the State Council stipulates the criteria for dividing city scale as: 1) megacity (population number over 10 million); 2) megalopolis (population number 5 to 10 million); 3) large city (population number 1 to 5 million, among which the population number of type I large cities is 3 to 5 million, and the population number of type II large cities is 1 to 3 million); 4) medium city (population number 500,000 to 1 million); 5) small city (population number less than 500,000, including type I small cities with population number 200,000 to 500,000, and type II small cities with population number less than 200,000), according to which the distribution of city population class scale is obtained in this paper (See

As seen in

Scale | 2005 | 2010 | 2015 | 2018 |
---|---|---|---|---|

Megacities (Population > 10 million) | 4 | 6 | 10 | 10 |

Shanghai, Beijing, Chengdu, Tianjin | Shanghai, Beijing, Tianjin, Chengdu, Guangzhou, Shijiazhuang | Chongqing, Shanghai, Beijing, Tianjin, Chengdu, Guangzhou, Shenzhen, Shijiazhuang, Suzhou, Wuhan | Chongqing, Shanghai, Beijing, Chengdu, Tianjin, Guangzhou, Shenzhen, Wuhan, Suzhou, Zhengzhou | |

33 | 35 | 33 | 33 | |

Megalopolises (5 million < Population < 10 million) | Harbin, Shijiazhuang, Wuhan, Weifang, Shenzhen, Qingdao, Jining, Xi’an, Quanzhou, Wenzhou, Guangzhou, Suzhou, Nantong, Changchun, Tangshan, Shenyang, Cangzhou, Fuzhou, Hangzhou, Dongguan, Zhengzhou, Yantai, Luoyang, Changsha, Kunming, Jinan, Nanjing, Foshan, Dalian, Taizhou, Ningbo, Dezhou, Tai’an | Suzhou, Harbin, Wuhan, Weifang, Shenzhen, Xuzhou, Qingdao, Hangzhou, Xi’an, Zhengzhou, Jining, Shenyang, Nanjing, Quanzhou, Wenzhou, Changchun, Tangshan, Ningbo, Yancheng, Nantong, Cangzhou, Yantai, Fuzhou, Changsha, Jinan, Dalian, Luoyang, Dongguan, Kunming, Wuxi, Foshan, Taizhou, Tai’an, Jinhua, Nanchang | Harbin, Zhengzhou, Weifang, Wenzhou, Qingdao, Hangzhou, Xi’an, Xuzhou, Quanzhou, Dongguan, Shenyang, Nanjing, Ningbo, Tangshan, Hefei, Changchun, Fuzhou, Foshan, Changsha, Nantong, Yancheng, Jinan, Yantai, Dalian, Luoyang, Kunming, Wuxi, Taizhou, Yueyang, Xiangyang, Tai’an, Jinhua, Nanchang | Xi’an, Hangzhou, Harbin, Weifang, Qingdao, Wenzhou, Xuzhou, Quanzhou, Nanjing, Dongguan, Shenyang, Ningbo, Changsha, Hefei, Tangshan, Foshan, Fuzhou, Changchun, Jinan, Nantong, Yancheng, Yantai, Dalian, Luoyang, Kunming, Wuxi, Taizhou, Xiangyang, Tai’an, Jinhua, Nanchang, Zhangzhou, Shaoxing |

largest resident population in China. Between 2015 and 2018, Shijiazhuang withdrew from the sample because its per capita gross product was lower than the national per capita gross product in the same year, which was due to the unhealthy industrial structure, relying mainly on light industry, and most people working in purely manual technical categories, which did not have significant advantages compared to other industries. Moreover, the foundation of the Internet industry is quite weak. The most critical thing is that Shijiazhuang has only one main line of Beijing-Guangzhou Railway in its territory, and as the capital city of the province, it has no advantages in terms of geographical location, further leading to Shijiazhuang’s lack of development momentum out of the sample.

Following the visualization of the data in

In order to directly observe the distribution areas of cities with a population of 10 million or more and a citywide GDP in the top ten of the national GDP during the sample period, we imported the city population scale and GDP data into ArcGIS 10.2 software separately for visual analysis (

Comparing

According to the population scale distribution from 2005 to 2018 in China, the percentage of the number of cities in each class is plotted (

is gradually decreasing. Combining

Order | 2005 | 2010 | 2015 | 2018 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

city | population | city | population | increase | city | population | increase | city | population | increase | |

1 | Shanghai | 1778 | Shanghai | 2256 | 0.27 | Chongqing | 3004 | 0.05 | Chongqing | 3088 | 0.03 |

2 | Beijing | 1515 | Beijing | 1858 | 0.23 | Shanghai | 2420 | 0.07 | Shanghai | 2421 | 0 |

3 | Chengdu | 1207 | Tianjin | 1263 | 0.22 | Beijing | 2161 | 0.16 | Beijing | 2162 | 0 |

4 | Tianjin | 1033 | Chengdu | 1144 | −0.05 | Tianjin | 1531 | 0.21 | Chengdu | 1618 | 0.11 |

5 | Harbin | 970 | Guangzhou | 1037 | 0.39 | Chengdu | 1454 | 0.27 | Tianjin | 1558 | 0.02 |

6 | Shijiazhuang | 956 | Shijiazhuang | 1003 | 0.05 | Guangzhou | 1329 | 0.28 | Guangzhou | 1470 | 0.11 |

7 | Wuhan | 852 | Suzhou | 992 | 0.34 | Shenzhen | 1107 | 0.24 | Shenzhen | 1277 | 0.15 |

8 | Weifang | 851 | Harbin | 992 | 0.02 | Shijiazhuang | 1065 | 0.06 | Wuhan | 1098 | 0.05 |

9 | Shenzhen | 814 | Wuhan | 944 | 0.11 | Suzhou | 1060 | 0.12 | Suzhou | 1070 | 0.01 |

10 | Qingdao | 812 | Weifang | 902 | 0.06 | Wuhan | 1047 | 0.11 | Zhengzhou | 1000 | 0.06 |

11 | Jining | 804 | Shenzhen | 896 | 0.1 | Harbin | 974 | −0.01 | Xi’an | 981 | 0.13 |

stores and consumption amount in Chengdu showed excellent development, thus Chengdu was named as “the third city of luxury in China”, ranking after Beijing and Shanghai, which shows that the population and economic scale of Chengdu are rapidly developing. When combined with

Equation (1) was further applied to calculate the trends of S_{2}, S_{4} andS_{11} from 2005 to 2018 population data (see _{2} is significantly higher than the theoretical state 2, S_{4} is close to the theoretical value 1, andS_{11} is significantly lower than the theoretical value 1 from 2005 to 2018. This happens as a result of the denominator value of the summed eleven-city index being too large, making the eleven-city index value much smaller than ideal. It means that the population scale stratification among cities is unreasonable, and the population distribution is concentrated in high order cities, and the most populous city has obvious advantages of strong attraction. Shanghai, Beijing and other high order cities have obvious population clustering effect,

and the “double core” spatial pattern is remarkable, showing the unbalanced development trend of city population scale system. In recent years, Chengdu, Shenzhen, Guangzhou, Xi’an and other high order cities have experienced rapid economic scale development, which have increased their attractiveness to other cities and further contributed to the continued expansion of population scale, coupled with the current implementation of a series of talent policies in these cities, the future eleven-city index will either stabilize or decline. At the same time, looking at the trend of changes throughout the sample period, S_{2} andS_{4} are increasing year by year, and the reason for this phenomenon is that Shanghai, the most populous city from 2005 to 2015, and Chongqing, the most populous city from 2015 to 2018, continue to expand their city scale, causing a gradual strengthening of the return effect, which has a dampening effect on the scale development of high order cities such as Beijing, Tianjin, Chengdu, and Guangzhou.

Generally speaking, Shanghai, Chongqing, Beijing, Tianjin, Chengdu, Guangzhou and other high order cities have fast economic development and strong vitality, however, it will take a long time for the national population growth to achieve a balanced evolution due to the relatively large gap in city population scale development between cities in the Midwest and Northeast and other cities.

Bringing the population data into Equation (3): ln P i = ln P 1 − q ln R i , the Zipf distribution-related indicators were calculated to derive the trend of city scale distribution by year regression results from 2005 to 2018 (

From

analysis is small from R 2 > 0.9 , indicating that the regression model based on the rank-scale rule fits the actual city population data effectively. Meanwhile, by | q | > 1 can be indicated that the city scale distribution is in the concentration stage. Also represents that high order cities such as Shanghai, Beijing, Guangzhou, Shenzhen, etc., have strong economic, technological power and significant advantages, which is why the concentration of population scale is obvious, while low order cities such as Zhangzhou, Xiangyang, Yueyang, etc., have smaller scale and lower development level. As a whole, | q | shows a rising trend, suggesting that the population scale of high order cities expands faster than that of low order cities, giving rise to a trend of large-scale dispersion and local concentration of city scale distribution. The strong attractiveness of some megacities has produced a monopoly effect in some ranges, exerting a driving effect while also producing a restrictive constraint effect, which results in a large difference in the speed of development between the high order cities and the rest, causing a disproportionate city development.

Application of Equation (4) to calculate the Gini coefficient of population scale (PG) and the Gini coefficient of economic scale (EG) from 2005 to 2018 (

First of all, according to the relevant United Nations organizations: if the Gini coefficient is less than 0.2, it refers to an absolutely balanced distribution; 0.2 to 0.3 represents a relatively balanced distribution; between 0.3 and 0.4 represents a relatively reasonable distribution; 0.4 to 0.5 represents a large gap in scale; and above 0.5 represents a significant gap in scale. The Gini coefficient of population

scale from 2005 to 2010 is lower than 0.4, which implies a relatively reasonable distribution of population scale, however, the Gini coefficient of population scale from 2010 to 2018 is higher than 0.4, indicating a large gap between the population scale of megacities and megapolises. Overall, the distribution of city population scale shows a dispersion and a continuous tendency to regional concentration. From 2005 to 2015, the most populous city, Shanghai, whose diffusion effect has not been effectively utilized, did not have the resources of other cities effectively allocated, making the development of these cities slow and hindering the coordinated development among cities, making the Gini coefficient of population scale continuously larger. Due to the implementation of the national urbanization strategy of small and medium-scaled cities, small and medium-scaled cities have been developed rapidly, while the process of development of high-order cities is slow, thereby facing the challenge of coordinated development of city scale in China.

Secondly, the city GDP is brought into Equation (4) to calculate the city economic scale Gini coefficient, and it can be found from

Eventually, a comprehensive comparison of the Gini coefficients of city population and economic scale in the same year reveals that the population and economic scale of each city are in a state of overall dispersion and small regional concentration.

We estimated kernel density for city scale data in 2005, 2010, 2015 and 2018 and obtained city scale kernel density distribution (

The first one is that the kernel density curve of city scale gradually shifts rightward with the increase of time, which represents the high urbanization rate and rapid growth of city population scale in China.

Moreover, when the peak of the kernel density curve is higher and the curve on the right side of the peak is steeper, it indicates that the distribution of the data is more concentrated [

Last but not least, the kernel density curve in the figure is mainly decentralized single-peaked, and the peaks show a tendency to spread, which demonstrates that the population tends to be more and more regionally concentrated and the scale distribution among cities is uneven, however, the change in the number of megalopolises also reflects that this uneven trend is being gradually adjusted.

In this paper, the growth characteristics of cities of different scale classes are considered on the basis of Markov matrix principles, and an in-depth dynamic analysis of the status of city scale distribution is carried out. Firstly, all cities in our selected sample are classified into two types: the first is type I for cities with a population scale of 5 - 10 million; the second is type II for cities with a population

scale of 10 million or more. After that, the probability of each city converting to a different class is calculated. Finally, the dynamics of city scale over the whole sample period is derived. Simultaneously consider the probability of entering and exiting the sample of cities in each period (

From

The mobility measure index of Markov transfer matrix (

In the beginning, the overall level of liquidity tends to increase, with an increase (0.07) in the SMI from 2015 to 2018 (0.161) compared to the SMI from 2005-2010 (0.091). Specifically, the possibility of inter-transformation between the classes of cities shows that the diagonal element of class II is 1 from 2005 to 2015, indicating that the highest class of cities, i.e. (megacities), is extremely

particular year | scale | I | II | exit |
---|---|---|---|---|

2005-2010 | I | 0.909 | 0.061 | 0.03 |

II | 0 | 1 | 0 | |

enter | 0.151 | 0 | exit | |

2010-2015 | I | 0.857 | 0.086 | 0.03 |

II | 0 | 1 | 0 | |

enter | 0.086 | 0.167 | exit | |

2015-2018 | I | 0.939 | 0.030 | 0.03 |

II | 0 | 0.9 | 0.1 | |

enter | 0.06 | 0.1 |

stable during this period, while the diagonal element of class I decreases, which implies that cities of class I scale become more mobile. Then, the diagonal element of class I becomes smaller from 2010 to 2015, illustrating those megalopolises become more mobile. Combined with

Following that, comparing the DMI index obtained from the non-diagonal elements can better illustrate the directionality of city mobility. From 2005 to 2018, city development shows a trend of upward mobility (DMI are larger than zero), and the elements on the left side of the diagonal of each class are smaller than the right side, and the left side element is always zero, therefore, city scale development maintains the trend of upward transformation i.e., there is no reverse transformation from type II to type I.

Finally, considering new entrants and exiting cities in the sample, it is found that 15.1% of new cities entered rank I from 2005 to 2010, while the rank exit rate was lower; to the extent that more than 10% of cities entered rank II (megacities) in both time periods since 2010 to 2018, there is, moreover, evidence of a different city growth pattern in the two phases.

Through a series of analyses on the characteristics and dynamic evolution of the distribution of city scale in China, the following main conclusions are finally obtained:

1) From the perspective of megacities distribution regions in China, policy regulations have largely determined the basic pattern of city scale evolution. Firstly, strategies such as Reform and Coastal Opening, together with the development of Pudong New Area, have all contributed to the concentration of population in the eastern coastal region. Secondly, the city population scale in Chengdu, Chongqing and Central Plains has developed faster under the influence of the National Western Development Strategy.

2) The Rank-Scale rule fits the data of Chinese cities well and conforms to their distribution characteristics, that is, the population distribution is concentrated in high rank-order cities and the number of low rank-order cities is small. Shanghai and Chongqing have played a central role in regional development, have an obvious effect of radiation on the surrounding city. At this stage, the distribution of city population scale in China has shown the trend of gradually increasing the most populous city, which means that the phenomenon of unreasonable city population scale distribution is becoming more serious.

3) From 2005 to 2018, the Gini index of economic scale of China’s cities is significantly higher than the Gini coefficient of city population scale, and both population and economy are in a state of regional concentration, with a high level of economic development and significant economic agglomeration benefits in megacities.

4) Judging from the nuclear density curve, the population gap between different cities is decreasing year by year, but the gap with the population scale of the most populous cities is still large, and it still takes a long time to achieve the harmonization of China’s city population scale.

5) The diagonal elements of Markov transfer matrix are all higher than 0.85, indicating that the development of cities in these two levels of scale is relatively smooth, with a high probability of maintaining the original level, and the mobility of scale levels is not strong. Among them, the possibility of transferring from type I to type II in the process of development transition is small, and there is no reverse transfer from type II to type I.

Based on the constructed explanatory framework of the dynamics mechanism of city scale evolution (

1) As for the government departments, they should formulate the city scale development measures based on the principle that the development patterns are different for different regions. The government should introduce appropriate preferential policies to encourage all cities to vigorously develop advantageous industries and improve city economies. At the same time, allow large cities to drive smaller cities to develop their economies and implement inter-city staggered development. For small cities with small populations, the government should focus on implementing talent acquisition programs to increase the scale of the population. For regions where excessive development of core cities leads to resource concentration, the government should appropriately control their development speed.

2) From the aspect of economic development. The economic development of cities must rely on industries, therefore, cities with slow development should

re-define their functional positioning and optimize the layout of industrial structure while vigorously developing special industries. Focus on cultivating secondary hubs in the region that can undertake industrial transfer in addition to the central cities and grow into new regional economic growth points, so that they can give full play to their role as bridges, allowing small cities to establish close economic ties with the central cities, promoting the flow of industrial capital between cities, realizing regional industrial upgrading and industrial transfer thus reducing city unemployment and raising city wage levels.

3) In terms of social livelihood, optimizing the service functions of the city, more employment opportunities, quality medical and educational resources, considerable income, and perfect service facilities are important factors to attract the inflow of middle and high-end talents. In addition, improving social network facilities and forming a safe cyberspace help cities develop.

4) The spatial pattern is the geographical basis of city development. The natural conditions and topographic features of our country lead to uneven distribution of population. Improving city transportation conditions, especially the external transportation construction of cities whose geographical location leads to obstructed communication with the outside world, improves transportation accessibility, reduces the spatial distance of cities, allows wider access to resources between cities, and thus promotes the development of cities with relatively weak economy.

Generally speaking, the samples in this paper were selected by setting thresholds based on the existing criteria for classifying city scale, however, different thresholds, as well as statistical, calibers can cause differences in the research results of city scale. In the future, we need to pay great attention to the problem of city sample selection and use multiple samples for comparative analysis as much as possible. In addition, attention should be paid to the changes in the division of the administrative areas of individual cities. Lastly, data sources should be expanded and more big data analysis tools should be used to conduct a more sophisticated study of the evolution of city scale.

The authors declare no conflicts of interest regarding the publication of this paper.

Zhang, M. and Jia, Z. (2021) Analysis of the Characteristics of City Scale Distribution and Evolutionary Trends in China. Open Journal of Statistics, 11, 443-462. https://doi.org/10.4236/ojs.2021.113028