The Spatial-Temporal Evolution of Population in the Yangtze River Delta, China: An Urban Hierarchy Perspective

: The reason for changes in ranking within urban systems is the subject of much debate. Employing the census data from 1990 to 2020, this paper investigates population dynamics across urban hierarchies and its inﬂuencing factors in the Yangtze River Delta. The results reveal an upward pattern of population dynamics and show that the advantages of high-ranking cities in population gathering are obvious, though they have declined recently. Based on a framework of urban amenity and the ridge regression model, the authors argue that concerns of residents in choosing cities in which to settle are gradually changing from economic opportunities to multidimensional amenities, ﬁnding that the inﬂuencing mechanisms vary across time. This is slightly different from Glaeser’s consumer cities; economic gains, as physiological needs, are always important for population growth. As higher-level needs, social and natural amenities, including Internet accessibility and urban green space, did not affect growth until the turn of the new millennium. In terms of negative factors, the ‘crowding-out effect’ of living costs and environmental pollution are not signiﬁcant, as theoretically expected, suggesting that residents tend to care more about development opportunities than the negative impacts of living in high-ranking cities. Finally, policies are proposed to promote population growth and the coordinated development of large, medium, and small cities in the Yangtze River Delta.


Introduction
As a marker of the economic health and vitality of cities and of places, population dynamics is a pressing issue of great concern to both academics and policy makers [1,2]. Particularly in an era with an aging population and a low fertility rate, the changes in population have a more prominent effect on the variation in city size than ever before [3]. Understanding the distribution of population and its growth across hierarchies takes on great importance for forecasting the evolution of the urban system and determining socioeconomic trends [4][5][6]. To date, two strands in the literature have been identified to uncover the pattern of population dynamics among cities: the upward pattern and the downward pattern. In the former strand, scholars found that populations moved from rural areas to nearby towns and then up the urban hierarchy to (larger) cities [7,8]. People tend to self-select upward mobility driven by rapid economic growth and higher prospects [9]. Higher-ranking cities are more likely to attract investments and firms from home and abroad, creating a large immigrant population [10]. For example, of the total population in the metro areas, more than 60% is concentrated in the 10 largest areas in Japan [11]. Approximately 21% of residents are concentrated in megacities in China [7,12]. In addition, others have argued that the generosity of the local welfare system may attract more population gathering in large cities [13]. For instance, scholars found that the population is more likely to be clustered in states with generous welfare systems in the United States [14,15]. In Europe, people gather in higher-ranking cities in search of welfare magnet effects [13]. In Germany, people tend to cluster in welfare states with equal opportunities and reduced income differences [16]. In summary, population dynamics in many countries tend to follow an upward pattern along the urban hierarchy.
Regarding the second strand, some studies identified a downward and decentralized tendency in developed countries or areas [6,17]. For instance, scholars found that most counties gained people from the nation's most populous cities in the United States [1,17,18]. That is, many of the major movements in the system of internal (or domestic) migration are flows down the urban hierarchy from central cities to adjacent suburbs which, in turn, sent migrants to exurban areas [18]. Similarly, a strengthening downward trend in the current migration pattern has also been identified in China in the 2020s [6]. With the outward transfer of industries and highly interlinked transportation, some people may move away from megacities to lower-ranking cities in search of better living conditions [6,19]. Micropolitan cities often occupy key positions at the interface of migration up and down the national urban hierarchy, such as the United Kingdom, Norway, and the United States [20,21].
Previous studies have found that the distribution of population in differently ranked cities is consistent with the process of urbanization. In the early stages of urbanization, the population gathers in small towns, which is mainly due to the development of factories and industries in these areas that attract a large number of rural surplus labor. In general, this happens in both developing countries and regions. For example, in 2012, 45% of the Asian population was concentrated in small cities under 500,000 [22], and 57% of the African population of Africa was clustered in small cities [23]. During the accelerated development period of urbanization, the population concentrated in medium and large cities due to economies of agglomeration [24,25]. Large cities can attract more domestic and foreign enterprises and investments, which provide more employment opportunities and higher wages, and thus promote further population agglomeration in large cities [10,26]. The research has also shown that social welfare increasingly has a role in people's residential choices [27,28]. However, when the ratio of population to urban agglomerates reaches a certain level, the dispersing effect created by rising costs and environmental pollution in large cities forces people with low skills or people seeking a high quality of life out to lower-ranking cities, which gives rise to a trend known as counter-urbanization [29]. Throughout much of the developed world, a new scenario of population movement is following the migratory steps of moving from large cities to nearby smaller cities, such as in the USA and Sweden [17,30]. In the period of re-urbanization, central locations of many cities have been transformed into areas that may be appealing to the population. These include not only the physical aspects of central districts, such as urban amenities and walkable streets, but also the cultural and social dimensions, such as a dynamic and diverse atmosphere [31,32]. This is exemplified in the work undertaken by Florida et al. and Glaeser et al. Cities with more restaurants and live performance theaters per capita have grown more quickly over the past 40 years in both the USA and France [33,34].
In general, studies have paid more attention to cities in developed countries, such as those in America and Europe. Few studies focused on urban cases in developing countries, such as China. The evolution of regional population distribution and the influencing factors calls for comparative research [35]. With respect to the case in transitional China, higher-ranking cities are more likely to attract investment from the central government and from abroad, due to the reform of decentralization since the early 1990s [36]. As a consequence, higher-ranking cities tend to have advantages in both economic opportunities and public service, and thereby cluster larger parts of the population. However, the state has, on several occasions, formulated a policy of controlling the size of large cities in a bid to alleviate the development pressure of large/megacities and balance the development of cities at different levels [7]. For instance, the maximum population in Beijing and Shanghai has been strictly limited by the urban master plans of the two megacities in 2016 and 2017, respectively. The academic community has not yet reached a consensus regarding the trend of population agglomerating dynamics.
The Yangtze River Delta was selected as a case study in this research for two reasons. First, the urban system in the YRD, on the one hand, is a typical example within the context of marketization and urbanization in China and, on the other, is representative of the changes in the world's urban system. Second, the YRD, as one of the six megalopolises in the world, is widely recognized as a polycentric region, making it an ideal case study of the attractiveness to people of different ranks of cities.
To better demonstrate the urbanization path in China, this article portrays the pattern of population dynamics across urban hierarchies in the Yangtze River Delta (YRD) with the help of the population census data from 1990, 2000, 2010, and 2020. More specifically, two research questions are addressed: (1) What are the changes in population distribution across urban hierarchies? (2) What matters for the growth of cities in hierarchical terms? In the following sections, we first provide a brief review of the study area, followed by a discussion of the data and methodology. We then begin to examine the population dynamics patterns and uneven distribution in the YRD. Thereafter, the determinants of the mentioned patterns are discussed. Finally, we conclude with major findings and policy implications.

Study Area and Data Collection
Located on the eastern coast of China, the YRD is one of the most urbanized regions in the country and has attracted a considerable number of migrants from outside the region. As Figure 1 shows, the study area includes Shanghai and three neighboring provinces (i.e., Jiangsu, Zhejiang, and Anhui), covering approximately 358,000 square kilometers with a total population of 235 million in 2020. The area is home to 15 percent of China's population and contributes roughly a quarter of the country's GDP. With a well-developed urban system, the YRD is an ideal area to investigate population dynamics and the growth of cities. Based on geographical locations and development levels, the authors further divide the YRD region into 9 sub-regions: Shanghai, Southern Jiangsu, Central Jiangsu, Northern Jiangsu, Northern Zhejiang, Southern Zhejiang, Southern Anhui, Northern Anhui, and Central Anhui.

Theoretical Framework
To shed further light on the driving impetus of population dynamics, we propose a conceptual framework in Figure 2 that is based on the theory of urban amenity [37,38]. We define urban amenities as location-specific marketed and nonmarketed attributes, such as income expectation, living costs, facilities and public services, environmental quality, and social atmosphere, which make people's living and working in a particular city more convenient. In general, residents tend to settle in cities based on an evaluation of mega metropolis (with at least 10 million dwellers), major metropolis (ranging from 5 to 10 million residents), large cities (from 1 to 5 million inhabitants, including type I and type II with 3 million as the threshold), medium cities (from 500,000 to 1 million dwellers), and small cities (less than 500,000 residents, including type I and type II with 200,000 as the threshold). To further explore the determinants of population dynamics, we also collected data on influencing factors from various statistical yearbooks based on the theoretical framework in the following section. Details of the data source are listed in Table 1.

Theoretical Framework
To shed further light on the driving impetus of population dynamics, we propose a conceptual framework in Figure 2 that is based on the theory of urban amenity [37,38]. We define urban amenities as location-specific marketed and nonmarketed attributes, such as income expectation, living costs, facilities and public services, environmental quality, and social atmosphere, which make people's living and working in a particular city more convenient. In general, residents tend to settle in cities based on an evaluation of both economic and other non-marketing amenities (including the natural and the social) [39]. It is widely recognized that big cities offer more job opportunities, higher income, better public services, and a welcoming social atmosphere with higher living costs and house prices, while small cities have a beautiful environment and lower living costs [40]. In other words, people choose to settle in cities of different ranks in order to meet their heterogeneous needs. Economically, people's primary need is to generate enough income to cover housing and living costs. According to Maslow's hierarchy of needs, when basic needs have been met, higher-level needs should be the focus, such as access to public services, an open-minded or a welcoming social atmosphere, and a better environment. These needs are related to social and natural amenities. house prices, while small cities have a beautiful environment and lower living costs [40]. In other words, people choose to settle in cities of different ranks in order to meet their heterogeneous needs. Economically, people's primary need is to generate enough income to cover housing and living costs. According to Maslow's hierarchy of needs, when basic needs have been met, higher-level needs should be the focus, such as access to public services, an open-minded or a welcoming social atmosphere, and a better environment. These needs are related to social and natural amenities.  First, availability of economic amenities has been widely viewed as a principal determinant of individual residential choice [30]. Residents gather in cities with a tradeoff between personal benefits and costs. On the one hand, high-ranking cities are more attractive to people due to better income expectations and job opportunities, because large cities can enjoy the external economy, such as economies of scale, saving transaction costs, and knowledge spillover [41]. On the other hand, the effects of income growth would be weakened by the 'crowding-out effect' caused by a rising cost of living and house prices due to population agglomeration in large cities [28]. Thus, economic development and income level are positive indices, but living costs and house prices are negative indices.
Second, public services and social atmosphere-as the key to social amenitiesarguably fulfill higher-level needs for residents once basic needs have been satisfied. According to the notion of voting with one's feet, public services are closely associated with residents' well-being and thus affect the distribution of the population across cities [2,42]. In advanced regions, cities become new areas of population growth by increasing the provision of high-quality facilities and public services [43]. In their developing counterparts, population growth tends to slow down due to congestion of public services and lack of infrastructure [44]. In addition, social atmosphere, referring to a climate of openness, forbearance, and possibility, would profoundly influence population gathering in cities as well. Residents are more likely to cluster in large cities with higher openness to the global market and information, as it is useful to decrease inequalities and increase social trust by providing more opportunities and possibilities [45]. In particular, within the context of globalization, openness to the world matters more for population agglomeration. Accessibility to information is also an important consideration for perceptions of social atmosphere. Information and communications technology (ICT) can, on the one hand, facilitate individuals' participation in economic activities [46], and on the other hand, help in reducing decision errors caused by incomplete information. For instance, both online learning and working from home during the COVID-19 pandemic depend on the Internet and ICT. Stemming from these, we propose the hypothesis that openness to the global market and the level of informatization of specific cities have a positive impact on population growth.
Third, natural amenities are widely considered as a positive driver of population gathering, due to their positive impact on human well-being, physical and mental alike [47]. Scholars have shown that urban green space plays an important role in attracting people in terms of its ecological, recreational, cultural, and educational function, which helps to reduce working pressure, eliminate negative mood, and promote psychological health [48]. By contrast, air pollution impedes population growth in big cities [49], which is conceptual- ized as the 'crowding-out effect'. The hypothesis is that green space has a positive impact on population in high-ranking cities but air pollution has a negative impact. On this basis, we constructed an indices system of urban amenities to examine the driving mechanism of population dynamics. As Table 1 shows, the gross domestic product (GDP) and number of employees (employ) indicate revenue prospects and employment opportunities, respectively. Per capita consumption expenditure of residents (livexp) and average house price (hp) show the impact of living costs. The annual value of PM2.5 (pm2.5) and area of green space (green) were employed to test environmental quality. With regard to public services, the number of hospital beds (bed) and expenditure on education (edu) were selected. Foreign direct invest (FDI) and Internet accessibility (inter) indicate the openness of the social atmosphere. In addition, we introduced urban hierarchy (rank) as a control variable.

Methodology
The authors utilized multiple regression models to empirically test the relationship between total population across urban hierarchy and urban amenity. In these models, the dependent variable is total population. The main explanatory variables of interest are economic amenities (i.e., GDP, employment, living expenditure, and house price), social amenities (i.e., number of beds in hospitals, education expenditure, FDI, and number of Internet users), and natural amenities (i.e., PM2.5 and public green space). The control variable is the rank of cities.
To shed further light on the detailed determinants of population dynamics, the authors employed OLS regression models to test the aforementioned hypothesis. First, we conducted collinearity analysis using the OLS model for three periods. The VIF of GDP and beds were greater than 10 and the tolerance was less than 0. Thus, we used the ridge regression model to overcome the presence of collinearity by adding a degree of bias to the regression estimation. To ensure comparability of the three periods, we chose k = 0.18 after viewing the ridge trace.

Temporal Evolution of Population across Hierarchies
As Figure 3 shows, the YRD has faced a strong tendency toward population agglomeration, namely population gathering within urban areas, such as high-ranking cities. In 1990, approximately 66% of the population dwelled in rural counties, with only 34% in cities at various levels. By 2020, the size of the population in rural counties decreased by 26%, becoming much smaller than urban counterparts, which increased by 74%, a situation that well echoes the unprecedented urbanization in transitional China. Compared with other ranking cities, megacities and major metropolises have witnessed the largest population growth of 5.2 million in the past three decades. Specifically, the pattern of population growth across hierarchies is reported as follows: 1990-2000: Rise in medium and small cities. With the upward migration of population, a total of 17 small cities achieved a rank jump in the last decade of the 20th century, including 5 growing into type II large cities and 12 into medium-sized cities ( Figure 4). Meanwhile, 37 rural counties developed into small cities. Consequently, medium and  1990-2000: Rise in medium and small cities. With the upward migration of population, a total of 17 small cities achieved a rank jump in the last decade of the 20th century, including 5 growing into type II large cities and 12 into medium-sized cities ( Figure 4). Meanwhile, 37 rural counties developed into small cities. Consequently, medium and small cities witnessed the largest population growth, accounting for 58% of the total growth in the YRD. By contrast, only 15% of the growth occurred in large cities. Shanghai, as the only major metropolis, developed into a mega metropolis with a total growth of 6.13 million. Notably, Yancheng experienced a population decline of approximately 50% due to the separation of Yandu County from its suburb, downgrading it from a large to a mediumsized city in 2010. Regarding potential reasons for the rise of small and medium-sized cities during this stage, scholars argue for the decentralization of administrative and fiscal authority in transitional China as well as household registration (hukou) control in large cities [6]. 1990-2000: Rise in medium and small cities. With the upward migration of population, a total of 17 small cities achieved a rank jump in the last decade of the 20th century, including 5 growing into type II large cities and 12 into medium-sized cities ( Figure 4). Meanwhile, 37 rural counties developed into small cities. Consequently, medium and small cities witnessed the largest population growth, accounting for 58% of the total growth in the YRD. By contrast, only 15% of the growth occurred in large cities. Shanghai, as the only major metropolis, developed into a mega metropolis with a total growth of 6.13 million. Notably, Yancheng experienced a population decline of approximately 50% due to the separation of Yandu County from its suburb, downgrading it from a large to a medium-sized city in 2010. Regarding potential reasons for the rise of small and mediumsized cities during this stage, scholars argue for the decentralization of administrative and fiscal authority in transitional China as well as household registration (hukou) control in large cities [6]. 2000-2010: Booming of large cities and emerging megacities. With the loosening of migration policy and hukou control, large cities witnessed the largest growth in the first decade of the new century. Specifically, more than half (54%) of the population growth in the YRD was concentrated in large cities of which the share of type I and type II large cities accounted for 19% and 35%, respectively ( Figure 5). The upgrading of small and medium cities to large was also pronounced. Three small cities and eight medium-sized cities grew into large cities. Another notable change is the upgrading of Nanjing and 2000-2010: Booming of large cities and emerging megacities. With the loosening of migration policy and hukou control, large cities witnessed the largest growth in the first decade of the new century. Specifically, more than half (54%) of the population growth in the YRD was concentrated in large cities of which the share of type I and type II large cities accounted for 19% and 35%, respectively ( Figure 5). The upgrading of small and medium cities to large was also pronounced. Three small cities and eight medium-sized cities grew into large cities. Another notable change is the upgrading of Nanjing and Hangzhou from large cities to major metropolises, which, coupled with the fact that Shanghai's population had skyrocketed by 7.96 million, suggests the popularity of megacities in this decade. In addition to the jump in city ranks, population growth within each rank (particularly small cities) was also worth noting. A total of 19 small cities grew from type I to type II, with their average size of population surpassing 400,000. Hangzhou from large cities to major metropolises, which, coupled with the fact that Shanghai's population had skyrocketed by 7.96 million, suggests the popularity of megacities in this decade. In addition to the jump in city ranks, population growth within each rank (particularly small cities) was also worth noting. A total of 19 small cities grew from type I to type II, with their average size of population surpassing 400,000. 2010-2020: Popularity of large cities and slowdowns in megacities. In the last 10 years, 82% of the population growth was witnessed in large cities, with only 18% in their small and medium-sized counterparts ( Figure 6). By the end of 2020, the number of large cities (both type I and II) in the YRD reached 27, accounting for 54% of the total number of cities. Compared with the previous decade, the annual rate of population growth in megacities decreased by 50% (from 10% to 5%), although three large cities (i.e., Suzhou, Hefei, and Ningbo) became new major cities. This may partially indicate the declining attractiveness of megacities to populations within the context of abrupt increases in living pressures. On the other hand, mobility toward large cities in the YRD is still the mainstream of population dynamics in this decade, though return migration from the coast has been appearing in inland China. Similar to the case of Yancheng in 2000-2010, Chaohu was downgraded from a medium-sized to a small city owing to administrative adjustment.  2010-2020: Popularity of large cities and slowdowns in megacities. In the last 10 years, 82% of the population growth was witnessed in large cities, with only 18% in their small and medium-sized counterparts ( Figure 6). By the end of 2020, the number of large cities (both type I and II) in the YRD reached 27, accounting for 54% of the total number of cities. Compared with the previous decade, the annual rate of population growth in megacities decreased by 50% (from 10% to 5%), although three large cities (i.e., Suzhou, Hefei, and Ningbo) became new major cities. This may partially indicate the declining attractiveness of megacities to populations within the context of abrupt increases in living pressures. On the other hand, mobility toward large cities in the YRD is still the mainstream of population dynamics in this decade, though return migration from the coast has been appearing in inland China. Similar to the case of Yancheng in 2000-2010, Chaohu was downgraded from a medium-sized to a small city owing to administrative adjustment.
Hangzhou from large cities to major metropolises, which, coupled with the fact that Shanghai's population had skyrocketed by 7.96 million, suggests the popularity of megacities in this decade. In addition to the jump in city ranks, population growth within each rank (particularly small cities) was also worth noting. A total of 19 small cities grew from type I to type II, with their average size of population surpassing 400,000. 2010-2020: Popularity of large cities and slowdowns in megacities. In the last 10 years, 82% of the population growth was witnessed in large cities, with only 18% in their small and medium-sized counterparts ( Figure 6). By the end of 2020, the number of large cities (both type I and II) in the YRD reached 27, accounting for 54% of the total number of cities. Compared with the previous decade, the annual rate of population growth in megacities decreased by 50% (from 10% to 5%), although three large cities (i.e., Suzhou, Hefei, and Ningbo) became new major cities. This may partially indicate the declining attractiveness of megacities to populations within the context of abrupt increases in living pressures. On the other hand, mobility toward large cities in the YRD is still the mainstream of population dynamics in this decade, though return migration from the coast has been appearing in inland China. Similar to the case of Yancheng in 2000-2010, Chaohu was downgraded from a medium-sized to a small city owing to administrative adjustment.

Spatial Evolution of Population
To shed further light on the patterns of population dynamics in the YRD, we charted the geographical distribution of population growth over the past three decades (Figure 7). Here, we highlight three arguments. First, a gradient growth pattern from peripheries to centers is demonstrated. In the first decade, growth was relatively scattered and evenly located in the YRD with only a few dark-colored growth centers. The advantages of large cities in terms of population agglomeration were not obvious, which was to some extent consistent with the aforementioned findings on the rise of medium and small cities in the 1990s. Entering the new century, counties/cities in the vast peripheries faced a rapid population decline with the growth of cities in southern Jiangsu Province and coastal Zhejiang Province, most of which were classified as large cities. In the last decade, areas of population increase and decrease were almost reversed compared to the 1990s. In summary, population movement can be considered as an upward agglomeration from rural counties to geographically close small and medium-sized cities and then to large cities and megacities in the southeast.

Spatial Evolution of Population
To shed further light on the patterns of population dynamics in the YRD, we charted the geographical distribution of population growth over the past three decades (Figure 7). Here, we highlight three arguments. First, a gradient growth pattern from peripheries to centers is demonstrated. In the first decade, growth was relatively scattered and evenly located in the YRD with only a few dark-colored growth centers. The advantages of large cities in terms of population agglomeration were not obvious, which was to some extent consistent with the aforementioned findings on the rise of medium and small cities in the 1990s. Entering the new century, counties/cities in the vast peripheries faced a rapid population decline with the growth of cities in southern Jiangsu Province and coastal Zhejiang Province, most of which were classified as large cities. In the last decade, areas of population increase and decrease were almost reversed compared to the 1990s. In summary, population movement can be considered as an upward agglomeration from rural counties to geographically close small and medium-sized cities and then to large cities and megacities in the southeast. Second, areas with population growth shrunk first and thereafter expanded, indicating a possible pattern of reversion in the YRD. That is, the population in large cities reaches a certain threshold after experiencing rapid growth and thereafter may leave opportunities for further development of the surrounding cities. This may be partly due to the spillovers and 'crowding-out effects' of megacities [50,51] but may also be because of the voluntary exurbanization of dwellers in megacities [52] or the sub-optimal selection of low-skilled immigrants who cannot afford the cost of living in megacities [53,54]. This suggests that the tide of population agglomeration to mega if not large cities may turn in the future.
Third, trends and the driving impetus of population dynamics may vary across regions/stages, though upward mobility tends to be the mainstream in the YRD and beyond. In the early stage (1990s), agglomeration to local or nearby cities was the mainstream of population dynamics; in the advanced stage (2010s), there might be a similar situation but for different reasons. For the former (e.g., the case of northern Anhui and Jiangsu in the 1990s), the ability of migrants matters; for the latter (e.g., the case of southern Zhejiang in the 2010s), migrating needs determine population growth. Only in the rapidly urbanizing era of the 2000s can long-distance movement from the peripheries to the core be witnessed.

Influencing Factors of Population Dynamics
After mapping the dynamic patterns of population growth, we confirmed the spatial associations between the rank of cities and the growth of population in the YRD. Table 2 shows the modeling results in detail. A positive and significant correlation exists between economic gains (i.e., GDP and employ) and population (both the total and growth size). Facilities and public services (i.e., bed and edu) are also positively related to the total Second, areas with population growth shrunk first and thereafter expanded, indicating a possible pattern of reversion in the YRD. That is, the population in large cities reaches a certain threshold after experiencing rapid growth and thereafter may leave opportunities for further development of the surrounding cities. This may be partly due to the spillovers and 'crowding-out effects' of megacities [50,51] but may also be because of the voluntary exurbanization of dwellers in megacities [52] or the sub-optimal selection of low-skilled immigrants who cannot afford the cost of living in megacities [53,54]. This suggests that the tide of population agglomeration to mega if not large cities may turn in the future.
Third, trends and the driving impetus of population dynamics may vary across regions/stages, though upward mobility tends to be the mainstream in the YRD and beyond. In the early stage (1990s), agglomeration to local or nearby cities was the mainstream of population dynamics; in the advanced stage (2010s), there might be a similar situation but for different reasons. For the former (e.g., the case of northern Anhui and Jiangsu in the 1990s), the ability of migrants matters; for the latter (e.g., the case of southern Zhejiang in the 2010s), migrating needs determine population growth. Only in the rapidly urbanizing era of the 2000s can long-distance movement from the peripheries to the core be witnessed.

Influencing Factors of Population Dynamics
After mapping the dynamic patterns of population growth, we confirmed the spatial associations between the rank of cities and the growth of population in the YRD. Table 2 shows the modeling results in detail. A positive and significant correlation exists between economic gains (i.e., GDP and employ) and population (both the total and growth size). Facilities and public services (i.e., bed and edu) are also positively related to the total population size. However, influences of other variables on total population and growth size vary across time, indicating a temporal heterogeneity of residents' concerns about urban amenities. Similar to Maslow's hierarchy of needs, economic gains can here be considered as physiological needs and are always important for population growth. Social and natural amenities including Internet accessibility and urban green space-as higher-level needsdid not matter for growth until the turn of the new millennium. For the negative factors, the 'crowding-out effect' of living costs and environmental pollution are not significant, as theoretically expected, suggesting that residents tend to care more about development opportunities than the negative impacts of living in high-ranking cities. In addition, the coefficient of cities' ranking in terms of population (both the total and growth size) vary across time as well. In the 1990s, the coefficient was insignificant, which indicates that the agglomeration of population was not necessarily in high-ranking cities and is in line with the rise of medium and small cities. In the recent two decades, the coefficients of rank for total population become significant, suggesting a positive relationship between population and urban hierarchy, well reflecting the booming and popularity of large cities. Notably, the coefficient of rank for population growth is significantly negative in the last decade. The result further demonstrates that although most population growth still occurred in large cities, the growth rate of population decreased.   Note: ***, **, * denote statistical significance (p value) of 1%, 5%, and 10%, respectively.

Economic Amenity
Economic gains play a positive role in both total population and growth of population, while the coefficients of cost variables are different. This is partly because cities with higher income and more job opportunities tend to be good for population growth. By 2010, the coefficient of GDP decreases with that of employ increasing. It implies that economic gains initially predominated but then gave way to non-marketing factors, when people focused more on quality of life. For the impact of living costs, the coefficient for total population size is significantly negative in 2000, suggesting that high costs can to some extent impede the growth of population. This well explains the rise of small and medium cities in the 1990s. Inconsistent with our expectation, the coefficients of house prices to total population size are significantly positive. This can be attributed to the small ratio of house purchases in big cities. Tenants do not have to pay down-payments and mortgages, which makes the 'crowding-out effect' of skyrocketing house prices insignificant. However, for the growth of population, the coefficient of living costs is significantly positive in 2010. It confirms the argument by Carlino and Saiz that economic gains rather than economic costs are the main determinant of residential choice [55].

Social Amenity
Facilities and public services can largely drive population to gather in large cities but have different impacts on total population and growth of population. In 2000, the coefficients of healthcare and education for population growth are insignificant, suggesting that public services had not become the main factors in people's choice of location. Although public services in large cities are attractive, most migrants are excluded from healthcare by the hukou system [56]. By 2010, the coefficient of facilities and public services for population growth became significantly positive, implying that residents were increasingly concerned about social welfare [16]. This can also be evidenced by the fact that people were attracted to larger cities with the agglomeration of public services. During 2000-2010, the total population in the YRD increases by approximately 37.92 million, including 36.09 million in large cities and mega/major cities, accounting for 95% of the population increase. Public services have the same trend in large cities: 87% of the increase in hospital beds in the YRD and more than half of new investment in education are concentrated in large cities. By 2020, the coefficient of public services for total population is stable, while for population growth, it decreases. The improvement of public services is becoming attractive for people gathering in large cities, but its influence on population growth has tended to decrease. That is partly because the inequality of public services across urban hierarchy narrows under the integration of the Yangtze River Delta, which promotes the sharing of inter-province and inter-city healthcare and education.
With respect to the impact of social atmosphere, the authors argue that a welcoming atmosphere does not necessarily lead to population growth. As Table 2 shows, the coefficient of openness to the global market for the total population is negative (p < 0.1), and the correlation between Internet accessibility and total population is insignificant in 2000. This may be related to the fact that China had not yet joined the World Trade Organization (WTO) [57]. By 2010, the two coefficients become significantly positive, indicating that cities with higher openness have larger population growth. By 2020, the positive impact of openness to the global market on the total population size diminishes, while the impact of Internet accessibility increases. This may be due to the adjustment of the international production structure and the rise in transaction costs in recent years; the impact of FDI on population growth becomes less significant. However, in the era of COVID-19, there is more contracting-out of tasks, more provision of services over a distance, and more sales to distant world markets. Therefore, the impact of the Internet on the total population has become more significant.

Natural Amenity
As shown in Table 2, green space has no significant relationship with total population or population growth in the 1990s, indicating that people cared less about the environment than economic opportunities in the first half of the urbanizing era. Since the turn of the new millennium, however, green space has become positively associated with population size in terms of both total amount and growth. This well echoes the finding by Shen et al. [47] that environmental facilities are nowadays important considerations for residents to choose locations in which to settle. For the coefficients of PM2.5, the hypothesis that the air population has a 'crowding out effect' on the total population fails to pass the test. Rather, the gathering of a population in cities with more opportunities generates a positive relationship between population size and air pollution (pm2.5). This can also be demonstrated by metropolises, such as London, Detroit, and Beijing, being the most popular cities in their corresponding countries, with no regard for their heavily polluted nature [58]. With regard to the impact on population growth, the coefficient of PM2.5 changes from positive in the 1990s to negative in the 2010s. The inhibitory effect of air pollution on population growth, coupled with the aforementioned impact of green space, indicates that people increasingly care about their physical health and then about natural amenities with the advancement of the society. As a sign of the awakening of citizens' environmental awareness, this can also be attributed to the widespread coverage of environmental pollution hazards in recent decades.

Discussion
Our findings have the following implications for the literature and for urban development strategies. First, urban amenities have gradually played a critical role in attracting people to live and work in cities. Such a finding is similar to the "consumer city" argument [33], where urban amenities rather than agglomeration economies attract people. Slightly differently, we find that economic gains are always important for population growth. Our finding suggests that the driving factors of population growth across urban hierarchy have gradually changed from economic factors to both economic and amenity factors. Second, our findings contribute to the fields of economic geography regarding polycentricity. This study explains the reasons for population growth in terms of the population's (consumers') choices of cities of different ranks. It contributes to the polycentric urban development literature, which traditionally attributes the benefits of polycentric urban development to the facilitation of agglomeration economies in terms of production [25].
To promote urban population growth, the above problems should be solved as an initial step. First, it is better to improve the natural amenities of the city. The authors find that environmental facilities are nowadays important considerations for residents when choosing locations in which to settle. For urban planners and governors, gradual reductions in air pollution and increased urban green space will be key to making a city more attractive to people. Second, megacities and major metropolises ought to gradually share public service resources with small and medium cities. The results demonstrate that facilities and public services can largely attract people to large cities, while public resources and favorable policies tend to polarize toward large cities in reality. In contrast, small and medium cities are in a disadvantageous position, with insufficient facilities and public services. Therefore, it is important to establish a cross-regional and urban sharing mechanism for public services. By this means, the attractiveness of small and medium cities could be effectively enhanced, where the population can enjoy the same facilities and public services. Third, urban amenities should meet the various needs of different groups. The findings suggest that low-income groups may care more about the city's economic affordability, while high-income groups seem more interested in the city's natural amenities and social atmosphere. For low-income groups, we should focus on providing adequate employment opportunities and public rental housing; for high-income groups and creative classes, we should pay more attention to providing a diverse and shared cultural environment and leisure space.

Conclusions
In this paper, we investigated population dynamics across urban hierarchies and its determinants in the Yangtze River Delta (YRD). The results imply that the YRD has witnessed an upward tendency of population dynamics, though the growth rate of populations in high-ranking cities declined recently. Specifically, the Yangtze River Delta witnessed a rise in medium and small cities in the 1990s, as the county-level cities had taken the lead in the transition from centrally planned economies to a market-driven economy. With the intensification of globalization and agglomeration of economic activities in large cities and emerging megacities, an unprecedented population explosion has occurred in the YRD since the turn of the new millennium. In the 2010s, the majority of population growth was still concentrated in large cities, while the growth rate in megacities decreased. Geographically, we find an emerging reversal from centripetal gathering (i.e., population declines in cities in the vast peripheries and increases in the core) to outward overflow (i.e., the geographic extent of cities with population growth shrinks first and thereafter expands) in the recent trend of population dynamics.
To shed further light on the impetus of population dynamics, the authors proposed a framework of urban amenity and found that i) concerns of residents in choosing cities in which to settle gradually changed from economic opportunities to multidimensional amenities, and ii) the influencing mechanisms vary across time. That is, slightly different from Glaeser's consumer cities, economic gains, as physiological needs, are always important for population growth. Social and natural amenities including Internet accessibility and urban green space, as higher-level needs, did not affect growth until the turn of the new millennium. In terms of negative factors, the 'crowding-out effect' of living costs is not significant, as theoretically expected, suggesting that residents tend to care more about development opportunities rather than the negative impacts of living in high-ranking cities. However, the negative coefficient of environmental pollution for growth in the new century, coupled with the positive influence of green space, indicates that people increasingly care about their physical health and then about natural amenities with the advancement of the society. In addition, the coefficients of public services and social atmosphere become significantly positive, suggesting that social amenities matter for the development of the population.
Finally, this study could be improved in the future by more fully taking into account the floating population. As the natural population growth drops, the floating population is a supplement to the increase in the total population of high-ranking cities. Moreover, we have not considered the impact of policy and strategy, such as urban development policy, transport infrastructure development, and talent introduction policy. Taking the political factors into consideration may potentially further improve our understanding of the impetus underlying population dynamics.

Conflicts of Interest:
The authors declare no conflict of interest.