# Research on Urban Expansion and Population Density Change of an Urban Agglomeration in the Central-Southern Region of Liaoning Province, China

Authors: Min Guo; Shijun Wang
Journal: Complexity
 (2022)

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## Abstract

The relationship between urban expansion and population density changes is complex and plays a fundamental role in urban sustainable development research. This relationship has been studied in multiple large cities. However, there is no report of the relationship of the two factors mentioned above in urban agglomeration in a particular region of China. Ten cities located in the central-southern region of Liaoning province are selected as research samples in this study. The spatial growth rate and urban compactness index of the sample cities were calculated using the land use and population data of these cities in three time phases: 1995, 2005, and 2015. Then, the geographical growth features, the population density changes, and the link between these two in the sample cities were investigated at these three periods. Our results revealed that the studied cities of central-southern Liaoning province expanded at the three time phases under the driver of positive population density growth, but the effects of urban population change on urbanization growth modes across time were uneven across different periods. Our study showed a trend that active transition of different urbanization growth modes was associated with decreased population density.


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## Body

## 1. Introduction

Urban expansion is a popular area of human geography study. Evolution characteristics of urban construction land’s temporal and spatial patterns are evaluated by assessing gravity center shifts and intensity expansion through time and space [1, 2]. To date, most of the research on urban expansion focuses on analyzing its temporal and spatial evolution characteristics, such as the magnitude, elements, structures, and manners of urban spatial growth [3]. Primary studies have also discussed the mode, mechanism, and measurement method of urban spatial growth [4–7] and analyzed the urban growth process through constructing indicators, such as the degree of freedom, compactness, and sprawl of urban expansion [8, 9].Urban population density is an important feature that is used to characterize the development of a city [10, 11]. With respect to urban population density, previous research has mainly focused on the following two aspects: (1) the spatial distribution patterns of urban population density, including the spatial distribution patterns and model research of urban population density at the national and provincial levels [12–14]; (2) temporal and spatial changes in urban population density, mainly from a global perspective and the perspective of urban districts to study population density trends and influencing factors [15–17]. Beyond these aspects, population density changes can affect and determine environment and urban development [18–20].Over the past four decades, China has experienced the world’s fastest urbanization process [21]. With a continuous increase in urban population across the whole country and an ongoing outward expansion of urban land, urban area expansion has developed at a quicker pace than urban population growth, resulting in a drop in urban population density over time [22, 23]. The feature of quick urban expansion is closely related to many urban factors and can be used to measure the development of a city [24, 25]. When there is an imbalance between land urbanization and population density, the reduction in urban population density due to quick urban expansion will result in low-density and fragmented city growth [18]. Eventually, this imbalance will lead to the destruction of city growth. In the context of rapid urbanization in China, it is crucial to comprehensively study the characteristics and mechanisms of urban population density fluctuations on urban expansion because this type of assessment can help guide the coordinated growth of urban land and population and thus establish a healthy form of urbanization development [19].The central-southern region of Liaoning province is one of the earliest formed urban agglomerations in China [26, 27]. Some researchers believe that this area is the fourth-largest urban agglomeration after the Yangtze River Delta, the Pearl River Delta, and the Beijing Tianjin Hebei region [28]. The cities in this region provide the most significant sources of growth for Liaoning province and northeastern China [29, 30]. In 2010, China issued the “National Major Function Zone Plan,” the first national land and spatial development plan [31]. The urban agglomeration in the central-southern area of Liaoning province was designated as an optimized development zone at the national level in this plan [31]. During the last decades, the development of the cities in this particular urban agglomeration was relatively slower than that of the other cities in China but still in process [32, 33]. In line with the urbanization of these cities, more and more countryside people have emerged in cities and settled down as citizens in these cities [34, 35]. To meet the growing need of these newcomers for living and production, urban land in urban agglomerations shows a trend toward continuous expansion [36, 37].Although scholars have conducted a significant amount of research on urban expansion and population density [10, 14, 38, 39], the relationship between urban expansion rates and changes in population density within the urban agglomeration in the central-southern region of Liaoning has not yet been studied. The following questions guided our research on the relationship that has emerged between urban expansion rates and population density changes in this particular region: (1) “Will the increased population in this region promote city expansion of the urban agglomeration in the central-southern part of Liaoning province?” (2) “Can the theories of preexisting studies about the relationship between urban expansion rates and population density changes be applied to this urban agglomeration?”In this study, the urban agglomeration in central-southern Liaoning province was selected as the study region. In total, ten cities were taken as research samples. We studied urban land density based on the cities’ land use data from 1995, 2005, and 2015. The urban spatial growth rate at each period was calculated based on fitted parameters using the inverse sigmoid function (Section 2.3.2) to fit the relationship between urban land density and population density change. Based on the fitted parameters, the relationship between urban expansion and population density was assessed, and a compactness index that characterizes urban expansion was created. The study holds the potential of serving as the basis of sustainable urban development research and a valuable reference for future urban planning decisions and land policy formulations.


## 2. Data and Methods

### 2.1. Overview of the Research Area

Ten cities in the urban agglomeration located within the central-southern region of Liaoning province were taken as research samples (Figure1). The urban agglomeration is located in the hinterland of Liao He Plain, one of the three major plains in northeast China. The city cluster is centered on two sub-provincial cities, which are Shenyang and Dalian. Besides the two centers, the urban agglomeration contains other eight prefecture-level cities (Anshan, Fushun, Benxi, Dandong, Liaoyang, Yingkou, Panjin, and Tie Ting) and 12 county-level cities, as well as 18 counties. At the end of 2015, the total population of the central-southern Liaoning urban agglomeration was 31.266 million, accounting for 73.69% of Liaoning province’s total population. The total land area of this region is 96,690 km2 with a built-up area of 1,666 km2. The total urban land use development intensity reached 85.3% in 2015.Figure 1
Schematic diagram of the study area location.


### 2.2. Data Sources

The research data consisted of regional land use data and population data that were collected in 1995, 2005, and 2015. The land use data comes from Landsat remote sensing images with a spatial resolution of 30 m. The land use types in this region were divided into six categories (construction land, waterbody, cultivated land, forest land, grassland, and unused land) based on the interpretation of remote sensing data. Urban population data comes from the census data of each city as is presented on the China Demographics Bureau’s website (https://www.stats.gov.cn/).


### 2.3. Research Methods

#### 2.3.1. Circle Analysis Method

Circle analysis refers to the establishment of a series of equidistant buffer zones with the city center as the center of the circle. Each circle was used as the basic unit for three separate purposes: (1) to describe the spatial differentiation of urban expansion, (2) to calculate relevant spatial indicators, and (3) to analyze the urbanization process to discover the spatial characteristics of different periods [39, 40].We then analyzed the buffer zone of the urban land expansion process of each city. A buffer zone with a width of 1 km was established with the geometric center of the main urban area of each city in 1995 as the center and gradually expanding the outermost layer contained the main urban area of each city. Outer ring roads of the studied cities and contiguous built-up regions were used to determine the scope of the urban area (the scope determination of Shenyang city was selected as an example and illustrated in Figure2). Based on the formed circle layer structure, the construction land density was calculated in each circle layer (i.e., the ratio of the construction land area in each circle layer to the total land area minus the nonconstructible land [water body]) [41]. The calculation formula for construction land density is as follows:(1)Density=SconstructionSland−swater.Figure 2
The buffer area and urban land area at three time points in Shenyang.In the formula,Sconstruction is the construction land area of each circle in the buffer zone, Sland is the total land area of each circle in the buffer zone, and Swater is the water area of each circle in the buffer zone.


#### 2.3.2. Inverse Sigmoid Method of Characterizing Urban Expansion

Jiao analyzed the decreasing law of impervious surface density with distance from the city center using three time phases of remote sensing photos from 28 major Chinese cities as the research sample and developed an inverse sigmoid function to fit the distribution of impervious surface density [42]. Using the inverse sigmoid function is helpful in modeling city expansion. Here, we took the function as a reference and used it to perform a fitting analysis on the land circle density distribution of ten sample cities, and the urban morphology of each city was determined based on the fitting results. The inverse sigmoid function is as follows:(2)fr=1−c1+eα2r/D−1+c.In the formula,f(r) indicates the density of the city; r represents the distance to the city center; e is Euler number; and α, c, and D are parameters for this investigation. The α value is a parameter that controls the slope of the inverse sigmoid function curve, the c value represents the background value of the urban hinterland construction land density, and the D value represents the fitted estimated value of the radius of the main urban area.The growth rate of city radiusD value is used to characterize urban spatial growth rate (V) in the following formula:(3)V=DtDon−1.In the formula,Dt is the city radius at the end of the study, D0 is the city radius at the beginning of the study, and n is the study period.The compactness of each research point is calculated according to the parameters of the inverse sigmoid function fitting formula (2). The compactness value is the ratio of the inner urban area to the urban radius given by the function fitting. The compactness Kp value and the parameter α are inversely proportional to each other. If the Kp value at a later point in time decreases relative to the previous point in time, it indicates that the development of city urbanization followed a compact direction during the study period. The calculation formula for compactness (Kp) is as follows [42]:(4)Kp=r2−r1D=1.316957α.In the formula,r2 – r1 represents the inner-city area, D is taken as the city radius, and α is the parameter that is used to control the slope of the inverse sigmoid function curve. The parameter D obtained by inverse sigmoid function fitting is the estimated value of the main urban area radius. By investigating the parameter D value change, the growth rates of each city space can be compared.


#### 2.3.3. Method of Calculating the Relationship between City Expansion and Urban Population Density

The urban population density for each corresponding city is calculated by counting the population within the defined urban land area. Based on population density, population density changes are calculated during different research periods (1995–2005, 2005–2015, and 1995–2015). City expansion rates are obtained from the output result of (3). The correlation value of these two values with p value is calculated based on R statistics programming.The relationship between city compactness and population density is studied separately with three different city growth modes, “compact,” “maintenance,” and “spread,” characterized based on city compactness valueKp from (4). Generally, when the Kp value of a city increased from the previous point in time, the urban spatial growth model was defined as a “spread” mode. When the Kp value decreased, the urban spatial growth mode was defined as “compact.” If the difference in Kp values between two periods was less than 0.01, the type of city growth mode is regarded as “maintenance.”


## 2.1. Overview of the Research Area

Ten cities in the urban agglomeration located within the central-southern region of Liaoning province were taken as research samples (Figure1). The urban agglomeration is located in the hinterland of Liao He Plain, one of the three major plains in northeast China. The city cluster is centered on two sub-provincial cities, which are Shenyang and Dalian. Besides the two centers, the urban agglomeration contains other eight prefecture-level cities (Anshan, Fushun, Benxi, Dandong, Liaoyang, Yingkou, Panjin, and Tie Ting) and 12 county-level cities, as well as 18 counties. At the end of 2015, the total population of the central-southern Liaoning urban agglomeration was 31.266 million, accounting for 73.69% of Liaoning province’s total population. The total land area of this region is 96,690 km2 with a built-up area of 1,666 km2. The total urban land use development intensity reached 85.3% in 2015.Figure 1
Schematic diagram of the study area location.


## 2.2. Data Sources

The research data consisted of regional land use data and population data that were collected in 1995, 2005, and 2015. The land use data comes from Landsat remote sensing images with a spatial resolution of 30 m. The land use types in this region were divided into six categories (construction land, waterbody, cultivated land, forest land, grassland, and unused land) based on the interpretation of remote sensing data. Urban population data comes from the census data of each city as is presented on the China Demographics Bureau’s website (https://www.stats.gov.cn/).


## 2.3. Research Methods

### 2.3.1. Circle Analysis Method

Circle analysis refers to the establishment of a series of equidistant buffer zones with the city center as the center of the circle. Each circle was used as the basic unit for three separate purposes: (1) to describe the spatial differentiation of urban expansion, (2) to calculate relevant spatial indicators, and (3) to analyze the urbanization process to discover the spatial characteristics of different periods [39, 40].We then analyzed the buffer zone of the urban land expansion process of each city. A buffer zone with a width of 1 km was established with the geometric center of the main urban area of each city in 1995 as the center and gradually expanding the outermost layer contained the main urban area of each city. Outer ring roads of the studied cities and contiguous built-up regions were used to determine the scope of the urban area (the scope determination of Shenyang city was selected as an example and illustrated in Figure2). Based on the formed circle layer structure, the construction land density was calculated in each circle layer (i.e., the ratio of the construction land area in each circle layer to the total land area minus the nonconstructible land [water body]) [41]. The calculation formula for construction land density is as follows:(1)Density=SconstructionSland−swater.Figure 2
The buffer area and urban land area at three time points in Shenyang.In the formula,Sconstruction is the construction land area of each circle in the buffer zone, Sland is the total land area of each circle in the buffer zone, and Swater is the water area of each circle in the buffer zone.


### 2.3.2. Inverse Sigmoid Method of Characterizing Urban Expansion

Jiao analyzed the decreasing law of impervious surface density with distance from the city center using three time phases of remote sensing photos from 28 major Chinese cities as the research sample and developed an inverse sigmoid function to fit the distribution of impervious surface density [42]. Using the inverse sigmoid function is helpful in modeling city expansion. Here, we took the function as a reference and used it to perform a fitting analysis on the land circle density distribution of ten sample cities, and the urban morphology of each city was determined based on the fitting results. The inverse sigmoid function is as follows:(2)fr=1−c1+eα2r/D−1+c.In the formula,f(r) indicates the density of the city; r represents the distance to the city center; e is Euler number; and α, c, and D are parameters for this investigation. The α value is a parameter that controls the slope of the inverse sigmoid function curve, the c value represents the background value of the urban hinterland construction land density, and the D value represents the fitted estimated value of the radius of the main urban area.The growth rate of city radiusD value is used to characterize urban spatial growth rate (V) in the following formula:(3)V=DtDon−1.In the formula,Dt is the city radius at the end of the study, D0 is the city radius at the beginning of the study, and n is the study period.The compactness of each research point is calculated according to the parameters of the inverse sigmoid function fitting formula (2). The compactness value is the ratio of the inner urban area to the urban radius given by the function fitting. The compactness Kp value and the parameter α are inversely proportional to each other. If the Kp value at a later point in time decreases relative to the previous point in time, it indicates that the development of city urbanization followed a compact direction during the study period. The calculation formula for compactness (Kp) is as follows [42]:(4)Kp=r2−r1D=1.316957α.In the formula,r2 – r1 represents the inner-city area, D is taken as the city radius, and α is the parameter that is used to control the slope of the inverse sigmoid function curve. The parameter D obtained by inverse sigmoid function fitting is the estimated value of the main urban area radius. By investigating the parameter D value change, the growth rates of each city space can be compared.


### 2.3.3. Method of Calculating the Relationship between City Expansion and Urban Population Density

The urban population density for each corresponding city is calculated by counting the population within the defined urban land area. Based on population density, population density changes are calculated during different research periods (1995–2005, 2005–2015, and 1995–2015). City expansion rates are obtained from the output result of (3). The correlation value of these two values with p value is calculated based on R statistics programming.The relationship between city compactness and population density is studied separately with three different city growth modes, “compact,” “maintenance,” and “spread,” characterized based on city compactness valueKp from (4). Generally, when the Kp value of a city increased from the previous point in time, the urban spatial growth model was defined as a “spread” mode. When the Kp value decreased, the urban spatial growth mode was defined as “compact.” If the difference in Kp values between two periods was less than 0.01, the type of city growth mode is regarded as “maintenance.”


## 2.3.1. Circle Analysis Method

Circle analysis refers to the establishment of a series of equidistant buffer zones with the city center as the center of the circle. Each circle was used as the basic unit for three separate purposes: (1) to describe the spatial differentiation of urban expansion, (2) to calculate relevant spatial indicators, and (3) to analyze the urbanization process to discover the spatial characteristics of different periods [39, 40].We then analyzed the buffer zone of the urban land expansion process of each city. A buffer zone with a width of 1 km was established with the geometric center of the main urban area of each city in 1995 as the center and gradually expanding the outermost layer contained the main urban area of each city. Outer ring roads of the studied cities and contiguous built-up regions were used to determine the scope of the urban area (the scope determination of Shenyang city was selected as an example and illustrated in Figure2). Based on the formed circle layer structure, the construction land density was calculated in each circle layer (i.e., the ratio of the construction land area in each circle layer to the total land area minus the nonconstructible land [water body]) [41]. The calculation formula for construction land density is as follows:(1)Density=SconstructionSland−swater.Figure 2
The buffer area and urban land area at three time points in Shenyang.In the formula,Sconstruction is the construction land area of each circle in the buffer zone, Sland is the total land area of each circle in the buffer zone, and Swater is the water area of each circle in the buffer zone.


## 2.3.2. Inverse Sigmoid Method of Characterizing Urban Expansion

Jiao analyzed the decreasing law of impervious surface density with distance from the city center using three time phases of remote sensing photos from 28 major Chinese cities as the research sample and developed an inverse sigmoid function to fit the distribution of impervious surface density [42]. Using the inverse sigmoid function is helpful in modeling city expansion. Here, we took the function as a reference and used it to perform a fitting analysis on the land circle density distribution of ten sample cities, and the urban morphology of each city was determined based on the fitting results. The inverse sigmoid function is as follows:(2)fr=1−c1+eα2r/D−1+c.In the formula,f(r) indicates the density of the city; r represents the distance to the city center; e is Euler number; and α, c, and D are parameters for this investigation. The α value is a parameter that controls the slope of the inverse sigmoid function curve, the c value represents the background value of the urban hinterland construction land density, and the D value represents the fitted estimated value of the radius of the main urban area.The growth rate of city radiusD value is used to characterize urban spatial growth rate (V) in the following formula:(3)V=DtDon−1.In the formula,Dt is the city radius at the end of the study, D0 is the city radius at the beginning of the study, and n is the study period.The compactness of each research point is calculated according to the parameters of the inverse sigmoid function fitting formula (2). The compactness value is the ratio of the inner urban area to the urban radius given by the function fitting. The compactness Kp value and the parameter α are inversely proportional to each other. If the Kp value at a later point in time decreases relative to the previous point in time, it indicates that the development of city urbanization followed a compact direction during the study period. The calculation formula for compactness (Kp) is as follows [42]:(4)Kp=r2−r1D=1.316957α.In the formula,r2 – r1 represents the inner-city area, D is taken as the city radius, and α is the parameter that is used to control the slope of the inverse sigmoid function curve. The parameter D obtained by inverse sigmoid function fitting is the estimated value of the main urban area radius. By investigating the parameter D value change, the growth rates of each city space can be compared.


## 2.3.3. Method of Calculating the Relationship between City Expansion and Urban Population Density

The urban population density for each corresponding city is calculated by counting the population within the defined urban land area. Based on population density, population density changes are calculated during different research periods (1995–2005, 2005–2015, and 1995–2015). City expansion rates are obtained from the output result of (3). The correlation value of these two values with p value is calculated based on R statistics programming.The relationship between city compactness and population density is studied separately with three different city growth modes, “compact,” “maintenance,” and “spread,” characterized based on city compactness valueKp from (4). Generally, when the Kp value of a city increased from the previous point in time, the urban spatial growth model was defined as a “spread” mode. When the Kp value decreased, the urban spatial growth mode was defined as “compact.” If the difference in Kp values between two periods was less than 0.01, the type of city growth mode is regarded as “maintenance.”


## 3. Results

### 3.1. Population Density Change

In this study, we investigated urbanization by studying the urban expansion effects of urban population density. The urban population density was based on the census data from the government annual release of each city and is calculated as the ratio of urban permanent population to the built-up area (Supplementary Table1). Figure 3 shows the change of overall population density between the three research time points (i.e., 1995, 2005, and 2015) in each city of the studied area. Comparing the population densities of different periods showed that the population density of the studied area in 2015 was lower than that in 1995 and 2005 (Figure 3(a)). The average population density of the studied area in 2015 was 12.42 people/hm2, while the average population density in 1995 and 2005 was 13.901 people/hm2 and 13.813 people/hm2, respectively.Figure 3
The population density of the sampled cities. The box plot (a) shows the average population of the studied cities during the three studied periods. The bar plot (b) represents the population density of the cities in the studied area in 1995, 2005, and 2015. The heatmap plot (c) depicts the population changes of each city between the three studied periods.
(a)(b)(c)A comparison of the population density of each sample city as is depicted in Figures3(b) and 3(c) reveals that three city types can be distinguished according to population density changes in the three different research periods (1995–2005, 2005–2015, and 1995–2015). The first type was characterized by a yearly increase in population. The second type consisted of cities whose population has increased and then declined. The third type included cities with annual population decline. The population densities of the studied cities Dalian, Shenyang, Panjin, and Yingkou increased during the studied periods. The population density increase rate of these four cities was 0.67%, 0.65%, 1.21%, and 1.72%. The population density of Benxi, Anshan, and Liaoyang increased between 1995 and 2005, while it decreased between 2005 and 2015, with a decline rate of 1.81%, 2.02%, and 4.23%, respectively. The population density of the other cities (Fushun, Dandong, and Tieling) showed a downward annual trend. Among these three cities, the population density of Fushun declined the most from 2005 to 2015, with a decline rate of 6.52%.


### 3.2. Urban Sprawl

Nonlinear least square method was used in the R software [43] to fit the land density of the ten cities by calculating the land density value of the corresponding circle layer of each city according to (2) in Section 2.3.2. Fitting parameter results of the inverse sigmoid function of the urban land density distribution are shown in Table 1, and the raw land density of the corresponding circle layer of each city is provided in Supplementary Table 2.Table 1
Parameters of fitted inverseS-shaped functions in ten sample cities.
Cities199520052015acDpacDpacDpDandong2.3140.0477.9320.0042.3640.0487.9770.0042.3020.0508.0790.004Dalian1.3190.03917.8850.0431.6660.03722.2710.0201.7980.04422.5810.012Fushun2.9020.1398.957<0.0013.0210.1499.087<0.0013.0530.1599.062<0.001Benxi3.3810.0407.386<0.0013.3890.0417.374<0.0013.4460.0547.285<0.001Shenyang4.6040.09517.779<0.0014.1490.10019.383<0.0013.4860.09822.829<0.001Panjin3.0660.1786.310<0.0013.7770.1816.967<0.0013.2920.1778.318<0.001Yingkou2.6380.09116.209<0.0012.5430.08217.958<0.0012.8020.13719.235<0.001Liaoyang7.1980.1637.8040.0027.0460.1647.8320.0025.6850.1718.0220.003Tieling5.8970.0496.3060.0015.6150.0656.354<0.0015.9420.1056.292<0.001Anshan1.7700.05011.8110.0092.0080.05112.8050.0101.9200.04413.9690.056Thep value represents the significance of function fitting.As depicted in Table1, the fitting function effect is excellent with less than 0.01 of p values, indicating that the parameters from the fitted functions can accurately reflect city expansion. Generally, the parameters were summarized as follows. The α value reflects the compactness of the city form (the larger the α value, the more compact the city). The α values were taken at three time points in the sample cities with a value range of 1.319–7.198. The value of c is the land density value of the urban fringe hinterland, and the value range of c in the sample city was from 0.037 to 0.181. For most of the cities included in this study, the c value was less than 0.1. Some cities had a relatively large value, such as Panjin, which reached 0.181, suggesting that cities with this characteristic are almost always connected with the surrounding cities. The D value represents the city radius, and the city radius of each city changes with time. These fitting values increased with time, which suggests that the radiuses of these cities gradually increased during the periods analyzed in this study, but the growth rates were different. In 1995, the cities with the smallest and largest urban radiuses were Tieling and Dalian. In 2015, the cities with the smallest and largest urban radiuses were Tieling and Shenyang.The spatial attenuation mode and fitting curve of the land density function of the ten cities are plotted and presented in Figure4. The curve shape is used to reflect city expansion based on the following definition. (1) The curve of a compact city is relatively flat near the city center. (2) The curve of a maintenance city has a rapid decline from a steep shape on the middle part. (3) The curve of a rapidly expanding city shifts back to the right by a large margin. Overall, most of the sample cities were relatively compact in 1995, especially Dandong, Benxi, Fushun, and Shenyang. A few cities were relatively loose, such as Dalian and Anshan. The curves of these cities shifted backward to the right, which indicates that these cities were in a looser state. After 2005, some sample cities began to expand rapidly, and the extent of the expansion in the second period was greater than it was in the first one. For example, Shenyang and Yingkou experienced more significant expansions during the two studied periods. Compared with the cities that were in a status of significant expansions, the compactness degrees in Dandong, Fushun, Benxi, and Liaoyang has not changed significantly since 1995.Figure 4
Spatial variation of urban land density in different circles with the distance to the city center and the curve fitted by inverse sigmoid function.


### 3.3. The Relationship between Urban Expansion and Population Density

#### 3.3.1. The Relationship between Urban Expansion Rates and Population Density Change

The estimated value of the city radiusD was obtained based on the inverse sigmoid function fitting, and city radius change was used to characterize the change in the urban spatial growth rate. The urban spatial growth rate of each city in three periods was calculated using (4) (Supplementary Table 3 and Figure 5(a)), and a correlation analysis was performed in accordance with the speed of population density change that was recorded during the same period (Figure 5(b)).Figure 5
An overall observation of spatial growth rates and population density changes in the sample cities. The line plot (a) shows the spatial growth rate of sample cities in different periods. The point plot (b) shows the relationship between the urban expansion rate and the population density change rate.
(a)(b)From 1995 to 2015, the spatial growth rates of the sample cities were between 0.00 and 0.015. Spatial growth rates of cities such as Dalian, Panjin, and Shenyang were higher than 0.01, while lower values (less than 0.01) were observed for the cities of Yingkou, Anshan, Liaoyang, and Dandong. The urban spatial growth rate decreased in five cities from 2005 to 2015, including Dalian, Fushun, Benxi, and Yingkou. However, the urban spatial growth rate of Dandong, Shenyang, Panjin, Liaoyang, Tieling, and Anshan increased during this same period. This means that the sampled cities are all expanding at different growth rates and that the changes in spatial growth rates are inconsistent. The correlation coefficient was calculated to study the correlation between the urban spatial growth rate and the population density change rate. The overall correlation coefficient was 0.613 with ap value of less than 0.01. A positive correlation between these two values indicated that the population growth might be one of the driving forces of urban expansion in the sampled cities.


#### 3.3.2. The Relationship between City Compactness and Population Density Change

City expansion rate is one important attribute characterizing city expansion while city compactness determines urban sustainable development and growth [44]. City compactness is highly related to rising urban populations [45, 46]. To characterize the relationship between city expansion compactness and population density changes in the areas of this study, the value Kp was used to characterize the urban form at a certain time across an entire city radius and calculated as (4). The smaller the Kp value, the more compact the urban city forms and vice versa. The Kp values at two time points can be used to describe urban compactness change that occurs during two studied periods. In this article, if the Kp value of a city increased from the previous point in time, the urban spatial growth model was defined as a spread mode. If the Kp value decreased, the urban spatial growth mode was defined as compact. If the Kp values remained unchanged between the two periods (i.e., the difference in Kp values at each time point was less than 0.01), the urban spatial growth model was regarded as a maintenance type. Xu et al. also used this standard to classify city explanation in different periods [47] and showed robust results in studying population effects on city explanation. Based on this method, we calculated the compactness values Kp of the ten sample cities at three time points (Figures 6(a)–6(c)) and then characterized urban spatial growth mode changes between the periods of 1990–2005 and 2005–2015 according to the difference in the compactness Kp values of the two time points (Supplementary Table 4 and Figure 6(d)).Figure 6
Land growth mode of each city. The point plots ((a)–(c)) show the comparison of theKp values of cities between the periods of 1995–2005, 2005–2015, and 1995–2015. The schematic plot (d) represents the land growth modes of the sampled cities during each period.
(a)(b)(c)(d)The geometric growth rates of urban population density were calculated in relation to three different urban spatial growth modes of varying periods (Figure7). Based on the analysis mentioned above, the relationship between the two was studied. Almost all the sample cities grew in a compact manner during the first period (Figure 6(d)), and the population density change rates of the cities in a compact mode had no significant changes (Figure 7). On the contrary, the cities in a spread mode (i.e., Shenyang, Yingkou, and Tieling) showed population density increase (Figures 6(d) and 7). In the second period, most of the sampled cities spread outward as they grew (Figure 6(d)), and their population density decline rates increased (Figure 7). This observation is consistent with Chinese development. During the period from 2005 to 2015, China was experiencing rapid urbanization, and cities expanded in a sprawling spatial growth mode, which led to an increase in the rate of population density decline. These findings suggest that a comparative analysis of sample cities at different development stages can serve as a valuable reference point for individuals who are making urban development decisions in rapidly urbanizing areas.Figure 7
The population density variation rate of sample cities with different growth modes in each research period is depicted in a box plot.Our analysis also indicated that population density’s influence on urban expansion was complex and manifested itself in different ways throughout the study periods. In the first period (1995–2005), the population density rate of sustaining and sprawling cities showed an upward trend. The increase in population promoted the growth of urban space to a certain extent, which suggests that population growth is the driving force of urban expansion. This result fits with the previous research [48]. However, in the second period (2005–2015), the population density of compact cities increased significantly compared with sprawling cities. At this time, it seems that an increase in population density was no longer the main factor of urban expansion, and economic development may have driven urban expansion [49]. In the longer period (1995–2015), both contraction and expansion cities had high growth rates, indicating the superposition of the different effects of urban population density change on urban expansion in the first two periods. In contrast, the maintenance-oriented cities show a downward trend, suggesting that the long-term reduction in urban population change will slow the rate of urban expansion.Next, the urban spatial growth modes were analyzed in combination with the rate of population density change in each studied city in detail (Figure8). In the two periods of 1995–2005 and 2005–2015, different types of transitions between cities were more likely to be manifested as a decline in urban population density, which suggests that the decline in population density promoted a shift in city type from spread to maintenance and then to compact, or vice versa. For example, in Fushun, the decrease in population density has caused the city to transform from the original spread type to the maintenance type. Population density decrease in Dandong and Anshan encouraged them to shift from being spread-type cities to becoming compact-type cities. Moreover, population density decrease brought on a transition change between urban types. The population density decrease that took place in Tieling between 2005 and 2015 was smaller than it was between 1995 and 2005, which suggests that population density decrease promoted the transformation of urban types from compact to spread types. In summary, the types of urban expansion in the selected area of this study have changed significantly, except for Shenyang, Benxi, and Dalian, whose expansion types have not changed during the two periods. These three cities remained spread, maintenance, and compacted cities, respectively.Figure 8
The relationship between the expansion type of the sampled cities and the rate of population density change is depicted in a bar plot.


## 3.1. Population Density Change

In this study, we investigated urbanization by studying the urban expansion effects of urban population density. The urban population density was based on the census data from the government annual release of each city and is calculated as the ratio of urban permanent population to the built-up area (Supplementary Table1). Figure 3 shows the change of overall population density between the three research time points (i.e., 1995, 2005, and 2015) in each city of the studied area. Comparing the population densities of different periods showed that the population density of the studied area in 2015 was lower than that in 1995 and 2005 (Figure 3(a)). The average population density of the studied area in 2015 was 12.42 people/hm2, while the average population density in 1995 and 2005 was 13.901 people/hm2 and 13.813 people/hm2, respectively.Figure 3
The population density of the sampled cities. The box plot (a) shows the average population of the studied cities during the three studied periods. The bar plot (b) represents the population density of the cities in the studied area in 1995, 2005, and 2015. The heatmap plot (c) depicts the population changes of each city between the three studied periods.
(a)(b)(c)A comparison of the population density of each sample city as is depicted in Figures3(b) and 3(c) reveals that three city types can be distinguished according to population density changes in the three different research periods (1995–2005, 2005–2015, and 1995–2015). The first type was characterized by a yearly increase in population. The second type consisted of cities whose population has increased and then declined. The third type included cities with annual population decline. The population densities of the studied cities Dalian, Shenyang, Panjin, and Yingkou increased during the studied periods. The population density increase rate of these four cities was 0.67%, 0.65%, 1.21%, and 1.72%. The population density of Benxi, Anshan, and Liaoyang increased between 1995 and 2005, while it decreased between 2005 and 2015, with a decline rate of 1.81%, 2.02%, and 4.23%, respectively. The population density of the other cities (Fushun, Dandong, and Tieling) showed a downward annual trend. Among these three cities, the population density of Fushun declined the most from 2005 to 2015, with a decline rate of 6.52%.


## 3.2. Urban Sprawl

Nonlinear least square method was used in the R software [43] to fit the land density of the ten cities by calculating the land density value of the corresponding circle layer of each city according to (2) in Section 2.3.2. Fitting parameter results of the inverse sigmoid function of the urban land density distribution are shown in Table 1, and the raw land density of the corresponding circle layer of each city is provided in Supplementary Table 2.Table 1
Parameters of fitted inverseS-shaped functions in ten sample cities.
Cities199520052015acDpacDpacDpDandong2.3140.0477.9320.0042.3640.0487.9770.0042.3020.0508.0790.004Dalian1.3190.03917.8850.0431.6660.03722.2710.0201.7980.04422.5810.012Fushun2.9020.1398.957<0.0013.0210.1499.087<0.0013.0530.1599.062<0.001Benxi3.3810.0407.386<0.0013.3890.0417.374<0.0013.4460.0547.285<0.001Shenyang4.6040.09517.779<0.0014.1490.10019.383<0.0013.4860.09822.829<0.001Panjin3.0660.1786.310<0.0013.7770.1816.967<0.0013.2920.1778.318<0.001Yingkou2.6380.09116.209<0.0012.5430.08217.958<0.0012.8020.13719.235<0.001Liaoyang7.1980.1637.8040.0027.0460.1647.8320.0025.6850.1718.0220.003Tieling5.8970.0496.3060.0015.6150.0656.354<0.0015.9420.1056.292<0.001Anshan1.7700.05011.8110.0092.0080.05112.8050.0101.9200.04413.9690.056Thep value represents the significance of function fitting.As depicted in Table1, the fitting function effect is excellent with less than 0.01 of p values, indicating that the parameters from the fitted functions can accurately reflect city expansion. Generally, the parameters were summarized as follows. The α value reflects the compactness of the city form (the larger the α value, the more compact the city). The α values were taken at three time points in the sample cities with a value range of 1.319–7.198. The value of c is the land density value of the urban fringe hinterland, and the value range of c in the sample city was from 0.037 to 0.181. For most of the cities included in this study, the c value was less than 0.1. Some cities had a relatively large value, such as Panjin, which reached 0.181, suggesting that cities with this characteristic are almost always connected with the surrounding cities. The D value represents the city radius, and the city radius of each city changes with time. These fitting values increased with time, which suggests that the radiuses of these cities gradually increased during the periods analyzed in this study, but the growth rates were different. In 1995, the cities with the smallest and largest urban radiuses were Tieling and Dalian. In 2015, the cities with the smallest and largest urban radiuses were Tieling and Shenyang.The spatial attenuation mode and fitting curve of the land density function of the ten cities are plotted and presented in Figure4. The curve shape is used to reflect city expansion based on the following definition. (1) The curve of a compact city is relatively flat near the city center. (2) The curve of a maintenance city has a rapid decline from a steep shape on the middle part. (3) The curve of a rapidly expanding city shifts back to the right by a large margin. Overall, most of the sample cities were relatively compact in 1995, especially Dandong, Benxi, Fushun, and Shenyang. A few cities were relatively loose, such as Dalian and Anshan. The curves of these cities shifted backward to the right, which indicates that these cities were in a looser state. After 2005, some sample cities began to expand rapidly, and the extent of the expansion in the second period was greater than it was in the first one. For example, Shenyang and Yingkou experienced more significant expansions during the two studied periods. Compared with the cities that were in a status of significant expansions, the compactness degrees in Dandong, Fushun, Benxi, and Liaoyang has not changed significantly since 1995.Figure 4
Spatial variation of urban land density in different circles with the distance to the city center and the curve fitted by inverse sigmoid function.


## 3.3. The Relationship between Urban Expansion and Population Density

### 3.3.1. The Relationship between Urban Expansion Rates and Population Density Change

The estimated value of the city radiusD was obtained based on the inverse sigmoid function fitting, and city radius change was used to characterize the change in the urban spatial growth rate. The urban spatial growth rate of each city in three periods was calculated using (4) (Supplementary Table 3 and Figure 5(a)), and a correlation analysis was performed in accordance with the speed of population density change that was recorded during the same period (Figure 5(b)).Figure 5
An overall observation of spatial growth rates and population density changes in the sample cities. The line plot (a) shows the spatial growth rate of sample cities in different periods. The point plot (b) shows the relationship between the urban expansion rate and the population density change rate.
(a)(b)From 1995 to 2015, the spatial growth rates of the sample cities were between 0.00 and 0.015. Spatial growth rates of cities such as Dalian, Panjin, and Shenyang were higher than 0.01, while lower values (less than 0.01) were observed for the cities of Yingkou, Anshan, Liaoyang, and Dandong. The urban spatial growth rate decreased in five cities from 2005 to 2015, including Dalian, Fushun, Benxi, and Yingkou. However, the urban spatial growth rate of Dandong, Shenyang, Panjin, Liaoyang, Tieling, and Anshan increased during this same period. This means that the sampled cities are all expanding at different growth rates and that the changes in spatial growth rates are inconsistent. The correlation coefficient was calculated to study the correlation between the urban spatial growth rate and the population density change rate. The overall correlation coefficient was 0.613 with ap value of less than 0.01. A positive correlation between these two values indicated that the population growth might be one of the driving forces of urban expansion in the sampled cities.


### 3.3.2. The Relationship between City Compactness and Population Density Change

City expansion rate is one important attribute characterizing city expansion while city compactness determines urban sustainable development and growth [44]. City compactness is highly related to rising urban populations [45, 46]. To characterize the relationship between city expansion compactness and population density changes in the areas of this study, the value Kp was used to characterize the urban form at a certain time across an entire city radius and calculated as (4). The smaller the Kp value, the more compact the urban city forms and vice versa. The Kp values at two time points can be used to describe urban compactness change that occurs during two studied periods. In this article, if the Kp value of a city increased from the previous point in time, the urban spatial growth model was defined as a spread mode. If the Kp value decreased, the urban spatial growth mode was defined as compact. If the Kp values remained unchanged between the two periods (i.e., the difference in Kp values at each time point was less than 0.01), the urban spatial growth model was regarded as a maintenance type. Xu et al. also used this standard to classify city explanation in different periods [47] and showed robust results in studying population effects on city explanation. Based on this method, we calculated the compactness values Kp of the ten sample cities at three time points (Figures 6(a)–6(c)) and then characterized urban spatial growth mode changes between the periods of 1990–2005 and 2005–2015 according to the difference in the compactness Kp values of the two time points (Supplementary Table 4 and Figure 6(d)).Figure 6
Land growth mode of each city. The point plots ((a)–(c)) show the comparison of theKp values of cities between the periods of 1995–2005, 2005–2015, and 1995–2015. The schematic plot (d) represents the land growth modes of the sampled cities during each period.
(a)(b)(c)(d)The geometric growth rates of urban population density were calculated in relation to three different urban spatial growth modes of varying periods (Figure7). Based on the analysis mentioned above, the relationship between the two was studied. Almost all the sample cities grew in a compact manner during the first period (Figure 6(d)), and the population density change rates of the cities in a compact mode had no significant changes (Figure 7). On the contrary, the cities in a spread mode (i.e., Shenyang, Yingkou, and Tieling) showed population density increase (Figures 6(d) and 7). In the second period, most of the sampled cities spread outward as they grew (Figure 6(d)), and their population density decline rates increased (Figure 7). This observation is consistent with Chinese development. During the period from 2005 to 2015, China was experiencing rapid urbanization, and cities expanded in a sprawling spatial growth mode, which led to an increase in the rate of population density decline. These findings suggest that a comparative analysis of sample cities at different development stages can serve as a valuable reference point for individuals who are making urban development decisions in rapidly urbanizing areas.Figure 7
The population density variation rate of sample cities with different growth modes in each research period is depicted in a box plot.Our analysis also indicated that population density’s influence on urban expansion was complex and manifested itself in different ways throughout the study periods. In the first period (1995–2005), the population density rate of sustaining and sprawling cities showed an upward trend. The increase in population promoted the growth of urban space to a certain extent, which suggests that population growth is the driving force of urban expansion. This result fits with the previous research [48]. However, in the second period (2005–2015), the population density of compact cities increased significantly compared with sprawling cities. At this time, it seems that an increase in population density was no longer the main factor of urban expansion, and economic development may have driven urban expansion [49]. In the longer period (1995–2015), both contraction and expansion cities had high growth rates, indicating the superposition of the different effects of urban population density change on urban expansion in the first two periods. In contrast, the maintenance-oriented cities show a downward trend, suggesting that the long-term reduction in urban population change will slow the rate of urban expansion.Next, the urban spatial growth modes were analyzed in combination with the rate of population density change in each studied city in detail (Figure8). In the two periods of 1995–2005 and 2005–2015, different types of transitions between cities were more likely to be manifested as a decline in urban population density, which suggests that the decline in population density promoted a shift in city type from spread to maintenance and then to compact, or vice versa. For example, in Fushun, the decrease in population density has caused the city to transform from the original spread type to the maintenance type. Population density decrease in Dandong and Anshan encouraged them to shift from being spread-type cities to becoming compact-type cities. Moreover, population density decrease brought on a transition change between urban types. The population density decrease that took place in Tieling between 2005 and 2015 was smaller than it was between 1995 and 2005, which suggests that population density decrease promoted the transformation of urban types from compact to spread types. In summary, the types of urban expansion in the selected area of this study have changed significantly, except for Shenyang, Benxi, and Dalian, whose expansion types have not changed during the two periods. These three cities remained spread, maintenance, and compacted cities, respectively.Figure 8
The relationship between the expansion type of the sampled cities and the rate of population density change is depicted in a bar plot.


## 3.3.1. The Relationship between Urban Expansion Rates and Population Density Change

The estimated value of the city radiusD was obtained based on the inverse sigmoid function fitting, and city radius change was used to characterize the change in the urban spatial growth rate. The urban spatial growth rate of each city in three periods was calculated using (4) (Supplementary Table 3 and Figure 5(a)), and a correlation analysis was performed in accordance with the speed of population density change that was recorded during the same period (Figure 5(b)).Figure 5
An overall observation of spatial growth rates and population density changes in the sample cities. The line plot (a) shows the spatial growth rate of sample cities in different periods. The point plot (b) shows the relationship between the urban expansion rate and the population density change rate.
(a)(b)From 1995 to 2015, the spatial growth rates of the sample cities were between 0.00 and 0.015. Spatial growth rates of cities such as Dalian, Panjin, and Shenyang were higher than 0.01, while lower values (less than 0.01) were observed for the cities of Yingkou, Anshan, Liaoyang, and Dandong. The urban spatial growth rate decreased in five cities from 2005 to 2015, including Dalian, Fushun, Benxi, and Yingkou. However, the urban spatial growth rate of Dandong, Shenyang, Panjin, Liaoyang, Tieling, and Anshan increased during this same period. This means that the sampled cities are all expanding at different growth rates and that the changes in spatial growth rates are inconsistent. The correlation coefficient was calculated to study the correlation between the urban spatial growth rate and the population density change rate. The overall correlation coefficient was 0.613 with ap value of less than 0.01. A positive correlation between these two values indicated that the population growth might be one of the driving forces of urban expansion in the sampled cities.


## 3.3.2. The Relationship between City Compactness and Population Density Change

City expansion rate is one important attribute characterizing city expansion while city compactness determines urban sustainable development and growth [44]. City compactness is highly related to rising urban populations [45, 46]. To characterize the relationship between city expansion compactness and population density changes in the areas of this study, the value Kp was used to characterize the urban form at a certain time across an entire city radius and calculated as (4). The smaller the Kp value, the more compact the urban city forms and vice versa. The Kp values at two time points can be used to describe urban compactness change that occurs during two studied periods. In this article, if the Kp value of a city increased from the previous point in time, the urban spatial growth model was defined as a spread mode. If the Kp value decreased, the urban spatial growth mode was defined as compact. If the Kp values remained unchanged between the two periods (i.e., the difference in Kp values at each time point was less than 0.01), the urban spatial growth model was regarded as a maintenance type. Xu et al. also used this standard to classify city explanation in different periods [47] and showed robust results in studying population effects on city explanation. Based on this method, we calculated the compactness values Kp of the ten sample cities at three time points (Figures 6(a)–6(c)) and then characterized urban spatial growth mode changes between the periods of 1990–2005 and 2005–2015 according to the difference in the compactness Kp values of the two time points (Supplementary Table 4 and Figure 6(d)).Figure 6
Land growth mode of each city. The point plots ((a)–(c)) show the comparison of theKp values of cities between the periods of 1995–2005, 2005–2015, and 1995–2015. The schematic plot (d) represents the land growth modes of the sampled cities during each period.
(a)(b)(c)(d)The geometric growth rates of urban population density were calculated in relation to three different urban spatial growth modes of varying periods (Figure7). Based on the analysis mentioned above, the relationship between the two was studied. Almost all the sample cities grew in a compact manner during the first period (Figure 6(d)), and the population density change rates of the cities in a compact mode had no significant changes (Figure 7). On the contrary, the cities in a spread mode (i.e., Shenyang, Yingkou, and Tieling) showed population density increase (Figures 6(d) and 7). In the second period, most of the sampled cities spread outward as they grew (Figure 6(d)), and their population density decline rates increased (Figure 7). This observation is consistent with Chinese development. During the period from 2005 to 2015, China was experiencing rapid urbanization, and cities expanded in a sprawling spatial growth mode, which led to an increase in the rate of population density decline. These findings suggest that a comparative analysis of sample cities at different development stages can serve as a valuable reference point for individuals who are making urban development decisions in rapidly urbanizing areas.Figure 7
The population density variation rate of sample cities with different growth modes in each research period is depicted in a box plot.Our analysis also indicated that population density’s influence on urban expansion was complex and manifested itself in different ways throughout the study periods. In the first period (1995–2005), the population density rate of sustaining and sprawling cities showed an upward trend. The increase in population promoted the growth of urban space to a certain extent, which suggests that population growth is the driving force of urban expansion. This result fits with the previous research [48]. However, in the second period (2005–2015), the population density of compact cities increased significantly compared with sprawling cities. At this time, it seems that an increase in population density was no longer the main factor of urban expansion, and economic development may have driven urban expansion [49]. In the longer period (1995–2015), both contraction and expansion cities had high growth rates, indicating the superposition of the different effects of urban population density change on urban expansion in the first two periods. In contrast, the maintenance-oriented cities show a downward trend, suggesting that the long-term reduction in urban population change will slow the rate of urban expansion.Next, the urban spatial growth modes were analyzed in combination with the rate of population density change in each studied city in detail (Figure8). In the two periods of 1995–2005 and 2005–2015, different types of transitions between cities were more likely to be manifested as a decline in urban population density, which suggests that the decline in population density promoted a shift in city type from spread to maintenance and then to compact, or vice versa. For example, in Fushun, the decrease in population density has caused the city to transform from the original spread type to the maintenance type. Population density decrease in Dandong and Anshan encouraged them to shift from being spread-type cities to becoming compact-type cities. Moreover, population density decrease brought on a transition change between urban types. The population density decrease that took place in Tieling between 2005 and 2015 was smaller than it was between 1995 and 2005, which suggests that population density decrease promoted the transformation of urban types from compact to spread types. In summary, the types of urban expansion in the selected area of this study have changed significantly, except for Shenyang, Benxi, and Dalian, whose expansion types have not changed during the two periods. These three cities remained spread, maintenance, and compacted cities, respectively.Figure 8
The relationship between the expansion type of the sampled cities and the rate of population density change is depicted in a bar plot.


## 4. Conclusion

Ten cities located in the urban agglomeration of the central-southern region of Liaoning province were selected as research objects in this study. The studied area took around 73.69% of Liaoning province’s total population, suggesting that population density plays important roles in this studied area. Our result showed that populations of some cities (e.g., Dalian, Shenyang, Panjin, and Yingkou) in this studied area increased while the population of others decreased. The population study provided a foundation for this study in understanding the effects of population on urban land use. The urban land density was studied through circle analysis, which is a method of analyzing the expansion of urban land use based on calculating construction land use on each circle from the city center [50, 51]. Based on the urban land growth analysis on each circle through fitting to inverse sigmoid function, we found that all the studied cities expand in construction area across the three studied periods. The fitting to inverse sigmoid function can not only provide the size of urban area but also be used to calculate compactness, which tells the quality or density of city expansion, and to reflect city expansion modes [38, 39, 42]. The calculation of compactness showed that the city expansion modes changed during different periods of this study in the study area of the urban agglomeration in Liaoning province.We integrated population density changes and urban land use information by systematically analyzing the relationships between these two factors. Integrating the urban expansion rate and urban population density data showed that the urban population density was positively correlated with the urban expansion rate, suggesting that urban population density growth was a driving force for urban expansion of the cities in the research area of this study. Although we observed that low population density and a decline in moderate population density were prevalent in the area of this study, the population increase was strongly associated with significant city expansion in relatively large cities (e.g., Shenyang and Dalian), strongly proving that population increase was a driver of city expansion.Furthermore, the relationship between population density and city compactness was different in the two studied periods (i.e., 1995–2005 and 2005–2015). Our results showed that urban population density drives the cities to a “compact” development mode during the period from 1995 to 2005. On the contrary, the increase in urban population density from 2005 to 2015 is related to the “spread” development mode. These results clarified that the effects of urban population on urban expansion changes were inconsistent in different periods and highlighted the flexible development of urban growth in the study region. More interestingly, detailed analysis showed that the decrease in population density had a positive effect on the conversion of urban types, suggesting that population density is a determinant factor in controlling city expansion modes.


## 5. Discussion

This study took the urban agglomeration in the central-southern area of Liaoning province as a research region. The cities in this area are representative and comparable to other city clusters in northeastern China because the region is more early developed and is one of the economic centers of the northeastern region of China [26, 37]. Our results showed that the urban population density of some cities (such as Benxi, Anshan, Liaoyang, Fushun, Dandong, and Tieling) in the central-southern area of Liaoning province followed a downward trend while the population increased in some other cities (i.e., Dalian, Shenyang, Panjin, and Yingkou). Generally, the population in northeast China decreases dramatically [52]. However, this study showed that the population of the relatively larger cities (e.g., Shenyang and Dalian, which are the sub-provincial cities of the studied area) increased during the two studied periods while the population in the small cities showed a decreasing trend. This is possible due to population movement during urbanization from countryside to city and from small cities to large cities [53, 54]. The further gathering of the population data in countryside and small cities can help in figuring out population movement and understanding urban population density change.We revealed that the urban expansion rate was positively correlated with population density changes. This finding is different from the negative correlation of the relationship in another study that focused on large cities in Europe and China [38]. One possibility is that the urban expansion rates of medium-sized cities in this study are different from those of large cities. The results of this study thus fill several gaps that exist in research on urban expansion and population density changes in medium-sized cities. This finding suggests further interesting research on the comparison of the relationship between population density changes and urban expansion in cities of different sizes.On the other hand, the relationship between population density and city compactness was different in the two studied periods (1995–2005 and 2005–2015), which suggests that population density changes show significant temporal characteristics for urban expansion in different years. This is probably due to other determination factors in urbanization, such as population loss during the studied periods and the urbanization policy of China during recent years (2010–2020) [55]. We suggest further research should consider the combined effects of these factors with population density due to the complicated relationship between population density changes and urban expansion. Based on the fact that the severe population loss observed in the studied region in recent years (2010–2020) will gradually become significant [55], it is possible that the relationship between population density changes and urban expansion in the region will become more complicated in the future.This study specifically focused on the relationship between urban expansion and changes in urban population density in ten cities of the central-southern area of Liaoning province. However, urban expansion is a complex process that is influenced by the joint action of multiple variables [56, 57]. Because of limitations in data availability, this paper only discussed the difference between urban spatial growth and population density changes that have taken place since 1995 in the urban agglomeration located in the central-southern region of Liaoning province. Horizontally, future research is needed to compare the various urban agglomerations in China, examine the differences and similarities between typical urban agglomerations in different countries, and explore the development differences between different urban agglomerations. A comprehensive analysis of the relationship between urban growth and population density changes in these different urban agglomerations can be used to compare and analyze the impact of regional characteristics on city types and urban expansion. Vertically, it is necessary to go deep into the interior of the city and explore the association between spatial growth and population density changes on a smaller scale, such as polycentric urban structures of large cities. We did not consider polycentric urban structures of the studied cities due to the lack of population density datasets at that scale even though one of the studied cities (Shenyang) has been proved with three subcenters [58]. Further study should be carried out to understand the relationship of population density and city expansion at polycentric urban structures. Moreover, the relationship at the county or town level is worth studying if population dataset in this level is available. In future, with the continuous emergence of massive amounts of data [59], combining multisource data to perceive the density changes of different population types will help broaden our understanding of the micro mechanisms of urban spatial growth and urban population density changes.



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*Source: 5327023-2022-03-30.xml*