MEASUREMENT OF POPULATION CARRYING CAPACITY BASED ON A P-S MODEL: A CASE STUDY OF ZHEJIANG PROVINCE

The implementation of the “second child policy” and the influx of large numbers of people have led to an increase in the population of Zhejiang Province in China, placing pressure on the environment, health care, and education. In this context, this study intends to use the possibility-satisfaction (P-S) model to predict the population carrying capacity of Zhejiang Province from 2020 to 2025. This prediction system comprises economic, social, resource, and environmental systems. The following conclusions are drawn: the maximum population carrying capacity of Zhejiang in 2025 is 62 million. According to the current population development trend, the population of Zhejiang Province in 2025 will still be within the carrying capacity range. The population carrying capacity of the social system is the weakest.


Introduction
Zhejiang Province has the second largest floating population in China, with its net people inflow ranking second in the country. Since the implementation of the "two-child policy" in 2015, the birth rate has reached its highest level in 20 years. In recent years, increases in the net population inflow and birth rate have led to a sustained population growth. Population is the driving force of economic development, but overpopulation creates pressure on the economy, society, the environment, and resources, leading to social problems such as difficulties in school enrolment, shortage of hospital beds, traffic congestion, high house prices, environmental deterioration, and so on. In this context, this paper intends to estimate the population carrying capacity of Zhejiang Province.
There are currently numerous definitions of population carrying capacity in international organizations and academia. Although most definitions have different expressions, they have some basic commonalities. According to the International Society of Ecology, population carrying capacity refers to the number of people who can obtain long-term and stable support from various resources without destroying the biosphere or consuming unreasonable non-renewable resources. The United Nations Educational, Scientific, and Cultural Organization (UNESCO) suggests that population carrying capacity refers to the number of people that the country or region can maintain in a predictable time, using local energy, resources, information, technology, and other conditions to ensure that material living conditions are met. Based on the above definition, this paper defines the carrying capacity of population as the population scale that the ecological environment, resources of a region can support under certain living conditions. According to the above definition, this paper views Zhejiang Province as the research object and then do the next steps. First, it constructs four sub-systems (including 30 indicators) of economy, resources, environment, and society. Second, the P-S approach is used to estimate the population carrying capacity of economic, resource, environmental, and social sub-systems in Zhejiang Province from 2020 to 2025 under different satisfaction levels. Next, it calculates the overall population carrying capacity of Zhejiang Province. Finally, based empirical conclusions, it summarizes the research findings.

Literature review
There has been extensive research on regional population carrying capacity according to different ecological and resource categories. Brown and Kane (1995) examined the impact of food fluctuations on population carrying capacity. Daily and Ehrlich (1992) investigated the impact of agriculture, water, renewable, ecological, soil, forest, and other resources on population carrying capacity. Cohen (1995) estimated the impact of the economy, environment, and culture on population. Seidl and Tisdell (1999) mainly focused on estimating the capacity of culture to limit population. A series of studies have been conducted on the relationship between land, water, urban power supply, urban greening, housing prices, economic level, marine fishery resources, and population carrying capacity (Ali, 2018;Dorini, Cecconello and Dorini, 2016;Peters et al., 2016;Diachenko and Zubrow, 2015;Ma et al., 2017). Based on a review of the aforementioned literature, we find that the restrictive conditions of population carrying capacity mainly include economy, natural resources, ecological environment, and social resources. Therefore, in the empirical

Measurement of Population Carrying Capacity based on a P-S Model: A Case Study of Zhejiang Province
analysis, this research will calculate the population carrying capacity of Zhejiang Province based on these aspects.
Quantification of a region's population carrying capacity has always been the focus of academic attention. The calculation methods include the Logistic model, resource supply balancing model, index system, and system model approaches. The Logistic model (Korobenko and Braverman, 2012;Dushoff, 2000;Scarano, 2012) is simple and easy to implement but does not consider the restrictive factors of population as it only sets a Logistic regression model based on sample data. As a result, it is commonly used to forecast population, but not a region's population carrying capacity. The resource supply balancing approach includes land resource carrying capacity (Ye, Xie and Tan, 2017), ecological footprint (Wackernagel et al., 1999;Gossling et al., 2002;Ester, 1999;Wackernagel et al., 2004), and the energy value analysis methods (Songsore and Buzzelli, 2017;Sliogeriene et al., 2009). These approaches are more inclined to consider the regional population capacity based on the ecological carrying capacity, do not involve the social and economic carrying capacity, and cannot comprehensively measure the population carrying capacity; they therefore have certain limitations. Since the 1970s, the index system approach (Gong and Jin, 2009;Zubrow, 1971;Ma et al., 2017) has been used with greater frequency. However, the complexity of the index system leads to incomplete data and high correlation between the indicators, affecting the accuracy of the study. It is therefore necessary to maintain independence between the indicators when constructing the index system. The system model approach considers research areas as a system and deduces the population carrying capacity through system optimization. This type of approach includes multi-objective decisions, scenario analysis, and system dynamics. The multi-objective decision approach (Carrion et al., 2008) first designs the development goals of the research area and calculates the population carrying capacity from the perspective of such development goals. Scenario analysis (Stewart and Scott, 1995;Brook et al., 1997;Peters et al., 2016) can essentially be viewed as a multi-objective decision approach because these two methods utilize the same processes to estimate the carrying capacity. That is, this approach builds an objective utility function (or effect function) and analyzes it using multi-level analysis. Systemic dynamics (Holt and McPeek, 1996;McCann and Yodzis, 1994;Klee and Allen, 2016;Robra and Heikkurinen, 2019) were first used by the Club of Rome to evaluate the relationship between resources (including land, water, food, minerals, etc.) and people. Domestic and foreign scholars applied the systemic dynamics approach to the study of population carrying capacity. This approach uses a differential equation system with time delay, which can conveniently deal with non-linear and time-varying phenomena, and can be used for long-term, dynamic, and strategic simulation analysis.
The aforementioned methods lay the foundation for the current study. However, most of the traditional methods of population carrying capacity analysis are based on single factors such as land resources, grain production, environmental resources, and so on. In fact, the factors affecting urban population carrying capacity are more complex. Natural resources, urban infrastructure construction, social public service system, urban ecological environment, and other factors will all become constraints of urban population development. Therefore, the population carrying capacity determined by single factor analysis has some limitations. In contrast the possibility-satisfaction (P-S) approach can incorporate many factors related to population carrying capacity through the index system design and can comprehensively consider the population carrying capacity of the region from the perspectives of possibility and satisfaction. Assuming that an event has a probability curve P(r) for one attribute R and a satisfaction curve Q(s) for another attributes S. R, S and another attribute A satisfy a certain relationship, that is, f (r, s, a) =0. Then P(r) and Q(s) can be merged into a possiblesatisfaction curve of attribute A through certain rules, which quantitatively describes the degree of both possibility and satisfaction, and is recorded as w [0, 1]. When w=1, the thing is completely possible and satisfactory; when w=0, it is either entirely impossible or entirely unsatisfactory.
In practical application, according to the definition of possibility and satisfaction, we can express possibility and satisfaction by using the mathematical form of curves such as threefold curve and S curve. For example, for the description of possibility degree P, we use three-fold curve follows: In addition to the three-fold curve, there are also S curves. This is a curve often be used. This paper mainly uses this kind of curve in the study of population capacity. Equation is described as follows: The mathematical form of the satisfaction curve Q(s) is similar to that of the above probability curve. With functional expressions of , and , possibility degree and satisfaction degree can be combined to possibility-satisfaction curve: 1. When the restriction conditions are: as r  , r  , R s  , the three-fold curves of and can be solved as follows:

Measurement of Population Carrying Capacity based on a P-S Model: A Case Study of Zhejiang Province Amfiteatru Economic
The S curves is: 3. When the restriction conditions are: , r  , R s  , the three-fold curves of and can be solved as follows: After figuring out several possibility-satisfaction curves, some of them should be combined when making decisions. There are many combination algorithms. Here we mainly consider three types.
Assume that there are two possibility-satisfaction curves 1 w , 2 w , several combination algorithms can be used for them: 1. Weak combination.

Empirical analysis and results
There are four steps in calculating population carrying capacity using the P-S model: construction of an index system, estimation of extreme values corresponding to possibility and satisfaction, calculation of population carrying capacity of sub-systems, and calculation of total population carrying capacity.

Construction of the index system
This paper selects four sub-systems to construct the index system: economy, society, resources, and environment.
In the economic sub-system (figure no.1), we use GDP, local financial revenue, and total retail sales of consumer goods to measure the scale of regional economic development from three aspects: the degree of regional economic development, the vitality of regional economic development, and the degree of regional economic prosperity. The output value of tertiary industry can well reflect the regional economic structure, and the number of employees can reflect the scale of employment, which is also a symbol of regional economic development. The corresponding per capita indexes reflect the relationship between population and economic systems.

Population and economic system
Number of employees

Proportion of employed people
Total retail sales of consumer goods Per capita total retail sales of consumer goods Output value of the tertiary industry Per capita output value of the tertiary industry Gross regional domestic product Per capita gross regional domestic product Local financial revenue Per capita local financial revenue

Figure no. 1: Population and economic index sub-system
In the social sub-system (figure no. 2), miles of highway reflects the level of infrastructure construction, the number of beds and staff in health institutions reflect the level of development of social medical and health services, and the number of students enrolled and faculties reflects the scale and level of development of educational resources in the region. Correspondingly, the per capita indexes are used to reflect the correlation between population and social resources.

Estimation of extreme values corresponding to possibility and satisfaction
First, we construct corresponding linear or non-linear models based on historical data of each index and also ensure that the model regression parameter passes the examination with significance of . Second, we use the model to estimate the value of this index from 2020 to 2025. We then calculate the variance and standard error of sample distribution and obtain the prediction interval of each index with confidence coefficients of 95%. Finally, we consider the critical value of the prediction interval as the peak value of the index and estimate the corresponding P-S. Due to space limitations, table no. 1 only presents the calculation data for 2025.
In the economic sub-system, Zhejiang's GDP in 2025 is most likely to reach 7.238 trillion yuan. The satisfaction degree is highest when per capita gross regional product reaches 135,100 yuan, but is the lowest when per capita gross regional product is 91,500 yuan. Similarly, the possibility and satisfaction degrees of other indexes can be calculated with coefficients of 95%. The results are presented in table no. 1.

Calculation of population carrying capacity of sub-systems
According to equation (4), the following curve (figure no. 5) is obtained by substituting the interval values of GDP and per capita GDP.

Figure no. 5: P-S curve of gross regional domestic product Amfiteatru Economic
The P-S curves of local financial revenue, total retail sales of consumer goods, output value of tertiary industry, the number of employees can be obtained using similar methods. Therefore, the P-S degree curve of population and economic system (figure no. 6) is obtained according to equation (9).
According to figure no. 6, when the population is less than 64 million, the P-S degree starts to decline rapidly. Thus, given the relationship between population and economy, the population of Zhejiang Province should be kept below 64 million.   According to figure no. 7 and table no. 2, we find that the carrying capacity of different sub-systems is different. Generally speaking, the carrying capacity of economy and resources is greater while the capacity of society and environment is weaker. When the P-S value is high (P-S > 0.8), the main factors restricting population growth are social and environmental factors. As the P-S values gradually decrease (0.6 < P-S < 0.8), the main factors restricting population growth are environmental factors. This is also in line with the reality. Economic development requires the support of the population. Economic system has the strongest demand in terms of population and the strongest carrying capacity. Zhejiang Province is rich in water resources. In addition, as an economically developed province, it has abundant power resources and strong resource carrying capacity. Population has the most significant impact on social system, which represents the carrying capacity of education, medical treatment, and transportation. The population has surged in a short period of time and the corresponding support facilities of education, medical treatment, and transportation have not kept up, which has resulted in the social system having the weakest carrying capacity. The environmental system represents the carrying capacity of garbage disposal and environmental protection. With the development of the economy and the high concentration in cities, the disposal capacity of garbage is improving but the production of domestic garbage is also increasing. As the satisfaction value has continued to fall, the environment has gradually become an important factor restricting population growth.

Calculation of total population carrying capacity
According to equation (9), the weight of each system was set as 0.25 and is used to calculate all P-S values. The total population P-S curve is presented in figure no. 8. According to Chart 8, when the population is larger than 62 million, it will exceed the population carrying capacity of Zhejiang Province. When the population is between 59 million and 62 million (0.6 < P-S < 0.7), which is still acceptable. When the population is between 55 million and 59 million (0.7 < P-S < 0.8), the status is better. As the population decreases, the status is getting better. When the population is less than 49 million (P-S >0.9), which is optimal.