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Journal of Geographical Sciences >

2019 , Vol. 29 >Issue 3: 363 - 376

DOI: https://doi.org/10.1007/s11442-019-1603-4

Research Articles

Comprehensive evaluation of regional resources and environmental carrying capacity using a PS-DR-DP theoretical model

  • WANG Liang , 1, 2, 3, 4 ,
  • LIU Hui , 1, 2, 3, *
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  • 1. Key Laboratory of Regional Sustainable Development Modeling, CAS, Beijing 100101, China
  • 2. Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China
  • 3. College of Resource and Environment, University of Chinese Academy of Sciences, Beijing 100049, China
  • 4. Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China
*Corresponding author: Liu Hui, Professor, E-mail:

Author: Wang Liang (1989-), PhD, specialized in regional sustainable development. E-mail:

Received date: 2018-05-21

  Accepted date: 2018-07-15

  Online published: 2019-03-20

Supported by

The Specific Project of National Key Research and Development Program of China, No.2016YFC0503506

Strategy Priority Research Program of Chinese Academy of Sciences, No.XDA20010103

Copyright

Journal of Geographical Sciences, All Rights Reserved
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Abstract

The concepts of regional resources and environmental carrying capacity are important aspects of both academic inquiry and government policy. Although notable results have been achieved in terms of evaluating both these variables, most researchers have utilized a traditional analytical method that incorporates the “pressure-state-response” model. A new approach is proposed in this study for the comprehensive evaluation of regional resources and environmental carrying capacity; applying a “pressure-support”, “destructiveness-resilience”, and “degradation-promotion” (“PS-DR-DP”) hexagon interaction theoretical model, we divided carrying capacity into these three pairs of interactive forces which correspond with resource supporting ability, environmental capacity, and risk-disaster resisting ability, respectively. Negative carrying capacity load in this context was defined to include pressure, destructiveness, and degradation, while support, resilience, and promotion comprised positive attributes. The status of regional carrying capacity was then determined via the ratio between positive and negative contribution values, expressed in terms of changes in both hexagonal shape and area that result from interactive forces. In order to test our “PS-DR-DP” theory-based model, we carried out a further empirical study on Beijing over the period between 2010 and 2015. Analytical results also revealed that the city is now close to attaining a perfect state for both resources and environmental carrying capacity; the latter state in Beijing increased from 1.0143 to 1.1411 between 2010 and 2015, an improved carrying capacity despite the fact that population increased by two million. The average contribution value also reached 0.7025 in 2015, indicating that the city approached an optimal loading threshold at this time but still had space for additional carrying capacity. The findings of our analysis provide theoretical support to enable the city of Beijing to control population levels below 23 million by 2020.

Key words： resources and environmental carrying capacity; “pressure-support”; “destructiveness-resilience” and “degradation-promotion” model;; evaluation; Beijing

Cite this article

WANG Liang , LIU Hui . Comprehensive evaluation of regional resources and environmental carrying capacity using a PS-DR-DP theoretical model[J]. Journal of Geographical Sciences, 2019 , 29(3) : 363 -376 . DOI: 10.1007/s11442-019-1603-4

1 Introduction

Carrying capacity was first defined in the field of ecology as “a limit on the number of a biological population and individuals under specific conditions” (Park et al., 1920). The Club of Rome later published “the limits to growth” in which they defined the joint concepts of resources and environmental carrying capacity for the first time. It is clear that “food shortages and environmental destruction will make the Earth’s population reach the limit at a certain period along with rapid industrialization, population explosion, private ownership of grain, non-renewable resources depletion and ecological deterioration” (Meadows et al., 1972). A series of related definitions, methods, and lots of evaluation index system have all been more recently developed in this field to support research on carrying capacity.
Western scholars prioritized both theory and methods in early research in this area. In one example, however, although the agro-ecological zone project method (FAO, 1996) is widely available, this approach tests carrying capacity by selecting just natural agricultural indexes and so reaches incomplete conclusions. Another approach, system dynamics (Karnopp et al., 1990), has also proved popular in forewarning studies that address carrying capacity; this method establishes a dynamic model to explain causality through internal system structure and places particular emphasis on environmental issues. The ecological footprint approach similarly provides a method to calculate the Earth’s carrying capacity, the balance between supply and demand that results from human economic activity, and to measure the extent of sustainable development (Rees, 1992; Rees et al., 1994). This approach can also be used to perform regional comparisons but cannot fully illustrate the impact of socioeconomic activities on ecological carrying capacity. One further approach, energy analysis, therefore aims to develop an integrated energy value index system by converting different variables into uniform standard values. This method is useful because it can be used to assess the ecological capacity of the Earth on the basis of energy values (Odum, 1996); although this approach is of considerable significance, high parameter demands mean that practical applications have lagged behind theory in this case (Feng et al., 2017). Researchers in developed countries have turned their attention to micro-level studies in recent years, including coastal protection and aquaculture (Chadenas et al., 2008; Guyondet et al., 2015; Reghunathan et al., 2016), while some scholars in developing regions have addressed sustainable development (Patil et al., 2008; Sarma et al., 2016; Irankhahi et al., 2017). It is the case that international researchers have tended to be more focused on assessing the micro-carrying capacity of resources and the environment, paying less attention in recent years to comprehensive regional studies.
Carrying capacity studies within China were initiated with quantitative research on climate and potential grain production (Zhu, 1964). The Environmental Research Institute of Beijing Normal University initially proposed stipulating a norm concept of “environmental carrying capacity” (Zeng et al., 1991), while the Xinjiang Water Resources Research Group of the Chinese Academy of Sciences (CAS) proposed the concept of “water resources carrying capacity” (Shi et al., 1992). At the same time, scholars proposed a series of methods to calculate regional carrying capacity; the resources and demand differences method (Wang et al., 1999) seems both appropriate and simple in this context but cannot be used to express socioeconomic situations and the living standards of people. The comprehensive evaluation (Gao, 1999) is flexible but requires a huge amount of information while calculation difficulties are inherent to the state space approach (Mao et al., 2001). Numerous researchers within China have emphasized land resources to reveal differences in regional population carrying capacities (Shi, 1992; Feng, 1994; Liao, 1998; Chen et al., 2002; Feng et al., 2008; Yu et al., 2015). A number of studies in this area have also emerged on single elements, including the water environment and resources as well as the atmosphere and soil environment (Cui, 1998; Feng et al., 2003; Luo et al., 2011; Pan, 2016). These studies have all underestimated regional carrying capacities, however; thus, scholars in recent decades have tended to study regional comprehensive carrying capacity in light of functional area (Mao et al., 2001; Fan, 2007) and regional planning studies (Fan, 2009). A consensus of researchers is therefore interested in developing forewarning applications (Gao et al., 2010; Fang et al., 2011; Feng et al., 2016).
Numerous researchers have more-or-less ignored both the openness and dynamic nature of systems without incorporating the stability of the human-Earth relationship system. These approaches have therefore led to underestimates for the actual capacity of specific regions. In an attempt to remedy this issue, the Institute of Geographic Sciences and Natural Resources Research Team at the CAS initially developed a comprehensive evaluation system and theoretical framework for monitoring and forewarning about resources and environmental carrying capacity at the national level based on the dual concepts of “short board” and “growth limit” (Fan et al., 2015; Fan et al., 2017). Although this led to the development of a technological process that was issued by the National Development and Reform Commission and is now being implemented domestically, practical issues remain because this system does not include a specific critical threshold value or an early warning index standard for overloading.
The aim of this study is to develop a novel method to comprehensively evaluate regional resources and environmental carrying capacity. We therefore initially created a “pressure-support”, “destructiveness-resilience”, and “degradation-promotion” “PS-DR-DP” hexagonal interaction theoretical model based on the concept of “growth limit” and the human-earth relationship stability system. We then developed a comprehensive evaluation index system and standard on the basis of this theoretical model and then applied it to determine its validity and practicability to empirical studies in Beijing. This approach has enabled us to develop a series of new results that are informative with regard to the carrying capacity of this city.

2 Methodology

2.1 Theoretical model

It is clear that the dual concepts of “growth limit” and “short board” can be used to define stability in the context of the human-earth system as a research prerequisite. Thus, utilizing mechanics-bearing and “growth limit” ecological principles, we define regional resources and environmental carrying capacity as the point at which “the regional population will reach its limit in a specific condition when the resource use is ‘fulfilling’ and ‘most efficiency’ under a stable human-earth relationship system”. Carrying capacity in this context includes resource support, environmental capacity, and risk-disaster resistance. The first of these refers to the largest population supported by total available resources depending on current technology and economy, while environmental capacity refers to the ability of water, soil, and atmosphere to accommodate pollutants generated by humans. This concept reveals the largest population a region can accommodate when regional water, soil, or atmospheric quality meet the minimum standards for agricultural production and human health. The concept of risk resistance refers to the ability to protect the largest number of people when a given region suffers from a major natural disaster. It is clear that the concepts of both resources and environmental carrying capacity comprise open and hierarchical systems; thus, different regional ranks will encompass basic carrying capacities and load limit ranges. Regional carrying capacity is therefore dynamic and related to both technological advances and economic development.
The “pressure-state-response” and “driving force-pressure-state-impact-response” models have both become a mainstream in regional carrying capacity studies. Although the former can be used to adequately characterize causal relationships, it nevertheless depends on subjective judgments and empirical models for index development. This approach cannot therefore be used to grasp the structure and decision-making processes of the system and does not work well in the context of complex feedback systems (Li et al., 2012). Indeed, the latter can be utilized to improve the former via comprehensive human-earth relationships, emphasizes the “limit of growth”, and just expresses a traditional “responsive” environmental protection concept (Cao, 2005). It is clear that both these approaches do not encapsulate urgently needed early warning-oriented evaluation processes.
We therefore advance a new hexagonal interaction force model in this study to remedy these shortcomings that is founded on “pressure-support”, “destructiveness-resilience”, and “degradation-promotion” (“PS-DR-DP”). This model is founded on the original carrying capacity concept and incorporates both the “limit of growth” and “structural stability” of the human-earth system. We utilize a hexagonal filling degree to simulate dynamic changes in resources and environmental carrying capacity in order to create an “early warning-oriented” evaluation system (Figure 1).
Figure 1 The warning model used in this analysis, comprising a fully loaded resource state and environmental carrying capacity
Pressure in this “PS-DR-DP” model refers to total resource consumption, while support denotes the entirety of potential resources available given current technology. The resultant force of these variables therefore characterizes resource use status, while destructiveness refers to the habitat damage caused by human activities, including environmental pollution, epidemics, and major natural disasters. Resilience therefore refers to the abilities of humans to mitigate environmental pollution as well as the power to predict, resist, and repair major natural disasters, while the concepts of destructive force and resilience together characterize ability to mitigate risk. Degradation refers to the degenerative state of resources and ecology while promotion denotes the ability to use advanced technologies, to improve resource use, or to delay or repair degradation. Taken together, pressure, destructiveness, and degradation therefore encapsulate negative resource load and environmental carrying capacity; in this context, positive load includes support, resilience, and promotion such that the ideal regional resource state and environmental carrying capacity requires that the limit is avoided and the system is held stable (Figure 2).
Figure 2 The perfect state model used in this analysis encompassing resources and environmental carrying capacity

2.2 Research methods

2.2.1 Reliability index analysis
We performed a reliability analysis in order to completely avoid (where possible) and mitigate reductions in subjective influence when selecting indicators for inclusion in our index system. Reliability in this context refers to the degree of consistency of results when this index system is used as a measurement tool. We therefore used the Cronbach Alpha coefficient to test the internal consistency of our standardized index system (Mangi et al., 2007); this approach reveals high reliability if a coefficient is not less than 0.9, while a value between 0.9 and 0.7 is also acceptable. However, if the coefficient falls to between 0.7 and 0.5 then certain items are in need of revision, and some might need to be abandoned entirely if the value is lower than 0.5. The equations used for this calculation are as follows:
$\alpha =\left( {n}/{n-1}\; \right)\left( 1-\sum{{s_{i}^{2}}/{s_{t}^{2}}\;} \right)$ (1)
$\sum{s_{i}^{2}=\sum{{{\left( k_{i}^{m}-{{k}_{m}} \right)}^{2}}}}$ (2)
where α is the reliability coefficient and n denotes the number of variables, while $\sum{s_{i}^{2}}$ is equal to the sum of subentry variances, $s_{t}^{2}$ is the total variances, $k_{i}^{m}$ stands for the variable values of the m index system, and km is the mean value of the variables in this system.
2.2.2 Contribution of carrying capacity
We revised the entire-array-polygon method as proposed by Wu et al. (2005) to render our mathematical expression more exact (equation 3). This approach supposes the presence of N standardization indexes, sets the zero point as the origin, and takes one (the largest standardized value) as the radius to form a central N polygon. This means that each variable value is distributed between the zero point and vertex such that value points link up and form an irregular N polygon. Thus, N indexes can generate (N-1)!/2 irregular N polygons according to the multiplication principle of classified arrangement, and the ratio between the irregular N polygonal average area and the central N polygonal area is the contribution value of each component of carrying capacity.
As influencing factors interact with one another in a complex fashion, the “short board” principle cannot be the sole criterion applied. Thus, in order to supplement this feature, we defined carrying capacity status is the ratio between positive and negative contribution values (equation 4). This means that if the ratio is bigger than one, a region is in good condition, while a larger overall number denotes enhanced carrying capacity. Other values can be used as warnings of danger; thus:
$C=\frac{\sum\limits_{i<j}^{i,j}{\left( k_{i}^{m}+1 \right)\left( k_{j}^{m}+1 \right)}}{N\left( N-1 \right)}$ (3)
$S=\frac{\sum\limits_{i=1}^{i}{C_{i}^{p}}}{\sum\limits_{j=1}^{j}{C_{j}^{n}}}$ (4)
where C is the carrying capacity contribution value of the subentry, N is the index number, $k_{i}^{m}$. and$k_{i}^{m}$. stand for the i and the j variable value in the m index system, respectively, S is the state of the carrying capacity, $C_{i}^{p}$ is the i positive contribution value, and $C_{j}^{n}$ is its negative counterpart.
2.2.3 Carrying capacity status classification
Although resources and environmental carrying capacity are limited by natural factors, both economic growth and technological progress exert significant influence. At the same time, the urbanization process provides the fundamental impetus for changes in regional carrying capacity; a generally higher urbanization level is therefore reflected in a stronger carrying capacity. If the urbanization level is too high, however, to exert negative impacts on regional carrying capacity, changes in the latter will impede the former. We therefore refer to the “threshold value of three stage urbanization” developed in the China Modernization Report (2013): Urban Modernization Study (He, 2014) while also taking the turning point of counter urbanization in developed countries into account. These stages enabled us to finally determine resources and environmental carrying capacity rating standard (Table 1).
Table 1 Classification of resources and environmental carrying capacity
Rank Mean contribution value Carrying capacity state
Ⅰ ≤ 0.30 Balance load at lower level with an approximate stable state
Ⅱ 0.30-0.70 Unstable state developing at high speed
Ⅲ 0.70-0.85 An ideal carrying capacity close to the stable state
Ⅳ ≥ 0.85 A fully loaded state with the system collapsing

Note: Mean contribution value denotes the average subentry contribution sum.

3 Evaluation index system

An index system provides the key to judge whether, or not, an evaluation result is credible because resources and environmental carrying capacity are comprehensive, uncertain, open, and dynamic. The hugely variable and complex indicators in different regions also make it hard to build a unified quantitative index system. Existing research suggests that land (pressure index) and water resources (usage amount), as well as the environment (exceeding pollutants) and ecology (eco-health) should be the primary contents of such an index (Fan et al., 2015, 2017). Thus, by applying the “PS-DR-DP” theoretical model and literature, we present a scientific and workable evaluation index system that is based on three pairs of interaction forces. The consumption and stock of water, soil and energy comprise the “fulfilling” state, while ‘energy consumption per unit of gross domestic product (GDP)’ and ‘whole-society productivity’ comprise the degree of “efficiency” (Table 2). Indexes presented in Tables 3 and 4 were used to assess whether, or not, regional ecology and the environment were stable.
Table 2 The evaluation index system for pressure and support used in this analysis
Force Influencing factor Index No.
Pressure

 Water Average water consumption (m3)
Total water consumption (108 m3)		 K11
K12
Land Requisition of cultivated area (km2)
Requisition of industrial and mining land (km2)		 K13
K14
Energy Coal consumption (108 ton)
Oil consumption (104 ton)
Gas consumption (108 m3)
Electricity consumption (108 kw·h)
Energy consumption per unit of GDP (ton of standard coal/104 yuan)		 K15
K16
K17
K18
K19
Population Population density (person/km2)
Total population at year-end (104)
Population growth rate (‰)
Urban unemployment rate (%)
GDP (104 yuan)		 K110
K111
K112
K113
K114
Support
 Resources Water resource per capita (m3/per capita)
Total water resources (108 m3)
Total land area (km2)
Cultivated land increments of a year (km2)
Cultivated land area (km2)
Per capita food production (kg)
Hydropower generation (108 kw·h)
Coal reserves (108 ton)
Crude oil production (104 ton)
Gas production (108 m3)
Electrical energy production (108 kw·h)		 K115
K116
K117
K118
K119
K120
K121
K122
K123
K124
K125
Socioeconomy Whole-society productivity (104 yuan/per capita)
Disposable income per capita for urban citizens (104 yuan)
Rural per capita net income (104 yuan)		 K126
K127
K128

Note: $k_{i}^{1}$ is the pressure and support variable in this evaluation index system.

Table 3 The evaluation index system for destructiveness and resilience used in this analysis
Force Influencing factor Index No.
Destructiveness


 Atmospheric environment Sulfur dioxide emission (104 ton)
Flue dust emission (ton)		 K21
K22
Water environment Wastewater discharge (104 ton)
Chemical oxygen demand (104 ton)		 K23
K24
Soil environment Dangerous industrial solid waste output (104 ton)
General industrial solid waste output (104 ton)		 K25
K26
Major disaster Fatality rate of class A and class B infectious diseases (1/105)
Number of geological disasters
Number of sudden environmental accidents		 K27
K28
K29
Resilience


 Pollutant treatment Proportion of environmental pollution control costs in GDP (%)
Amount of industrial sulfur dioxide removal (104 ton)
Disposal of general industrial solid waste (104 ton)
Disposal of dangerous industrial solid waste (104 ton)
City sewage treatment rate (%)		 K210
K211
K212
K213
K214
Disaster prevention Number of disease control centers
Number of automatic meteorological stations
Number of seismological stations
Number of emergency shelters		 K215
K216
K217
K218

Note: $k_{i}^{2}$ is the destructiveness and resilience variable in this evaluation index system.

Table 4 The evaluation index system for degradation and promotion used in this analysis
Force Influencing factor Index No.
Degradation Desertification Desertification land area (hm2) K31
Forest degradation Area of plantation forestry (hm2)
Forest disease and insect pest and rodent disaster area (hm2)		 K32
K33
Water and soil erosion Increased area of water and soil erosion (hm2)
Scope of responsibility for soil erosion control (hm2)		 K34
K35
Promotion Protection and
governance		 Forest area (hm2)
Wetland area (hm2)
Afforestation area (hm2)		 K36
K37
K38
Small watershed management area (hm2)
Control rate of forest disease and insect pest and rodent disaster (%)
Control area of water and soil erosion (hm2)
Natural reserve area (hm2)		 K39
K310
K311
K312

Note: $k_{i}^{3}$ is the degradation and promotion variable in this evaluation index system.

4 An empirical study in Beijing

4.1 Data

The data used in this analysis were mostly extracted from the China Statistical Yearbook, the China Statistics Yearbook of Environment, the China Statistical Yearbook of Land & Resources, the China Rural Statistical Yearbook, the China Forestry Statistical Year book, and the Bulletin of Soil and Water Conservation in China, and encompass the period between 2008 and 2016. A component of the data used here were also extracted from the Beijing Statistical Yearbook (2008-2016), as well as various public information and annual reports released by concerned departments of Beijing Municipal Government.

4.2 Reliability analysis

We selected original data encompassing the period between 2008 and 2010 for Beijing and standardized records using the min-max method (Table 5). We then used the software SPSS to analyze data reliability; our results (Table 6) show that all three index systems are credible because their coefficients are all greater than 0.9.
Table 5 Evaluation index standardization values for Beijing between 2008 and 2010
Index 2008 2009 2010 Index 2008 2009 2010 Index 2008 2009 2010
K11
K12
K13
K14
K15
K16
K17
K18
K19
K110
K111
K112
K113
K114
K115
K116
K117
K118
K119		 1.0000
0.1665
0.0527
0.2323
0.0130
0.0530
0.2877
0.3272
0.0031
0.0376
0.0840
0.0162
0.0863
0.0527
0.9749
0.1622
0.0778
0.0094 0.0110		 1.0000
0.1725
0.1440
0.4116
0.0129
0.0565
0.3372
0.3592
0.0029
0.0369
0.0904
0.0170
0.0680
0.0591
0.6152
0.1059
0.0797
0.0096
0.0113		 0.8629
0.1604
0.0679
1.0000
0.0120
0.0509
0.3407
0.3690
0.0026
0.0544
0.0894
0.0140
0.0638
0.0643
0.5658
0.1052
0.0748
0.0090
0.0106		 K120
K121
K122
K123
K124
K125
K126
K127
K128
K21
K22
K23
K24
K25
K26
K27
K28
K29
K210		 0.3577
0.0002
0.3173
0.0000
0.0000
0.1172
0.0548
0.0124
0.0051
0.0661
0.0190
0.6089
0.0543
0.0645
0.0622
0.1115
0.0860
0.1989
0.0785		 0.3513
0.0002
0.3401
0.0000
0.0000
0.1200
0.0597
0.0137
0.0057
0.0538
0.0165
0.6372
0.0448
0.0507
0.0562
0.0500
0.0543
0.1403
0.0778		 0.2838
0.0020
0.1727
0.0000
0.0000
0.1230
0.0634
0.0140
0.0060
0.0542
0.0181
0.5308
0.0434
0.0538
0.0599
0.0725
0.0519
0.1415
0.0774		 K211
K212
K213
K214
K215
K216
K217
K218
K31
K32
K33
K34
K35
K36
K37
K38
K39
K310
K311
K312		 0.0605
0.0402
0.0366
0.4243
0.1667
1.0000
0.5591
0.1774
0.1202
0.5959
0.0858
0.0706
0.0098
0.0198
0.8336
0.0757
0.0610
0.0219
1.0000
0.2991		 0.0511
0.0341
0.0258
0.3633
0.1403
1.0000
0.4570
0.1493
0.1049
0.6849
0.0754
0.1105
0.0142
0.0346
1.0000
0.0661
0.0164
0.0191
0.9833
0.2611		 0.0613
0.0368
0.0307
0.3873
0.1462
1.0000
0.4387
0.1557
0.0965
0.6568
0.0730
0.0571
0.0276
0.0258
0.9589
0.0634
0.0146
0.0183
1.0000
0.2504
Table 6 Reliability index analysis results
Evaluation index system Cronbachs Alpha Sample size Elimination
Pressure and support 0.949 28 0
Destructiveness and resilience 0.998 18 0
Degradation and promotion 0.999 12 0

4.3 Results and analysis

Researchers from across various fields have shown a great deal of interest since the turn of the 21st century in predicting the likely upper population limit for Beijing. Indeed, most workers have argued that both the resources and environmental carrying capacity of this city are already overloaded (Fan et al., 2005; Feng et al., 2005; Qiang et al., 2007; Tong, 2010; Tong et al., 2011); one early study even suggested that the population of Beijing should not exceed 18 million (Wang et al., 2005), and the Beijing Urban Master Plan (2016-2035) (Beijing Municipal Planning and Land Resources Management Commission, 2017) states that the resident population should be less than 23 million by 2020. It is therefore important to evaluate the loadable population of this city by calculating the overall carrying capacity state. Incorporating China’s national five-year plans, we selected 2010 and 2015 as dates for a comparative analysis and to explore the carrying capacity status of Beijing; results are presented in Figure 3 as well as in Table 7.
Figure 3 The resources and environmental carrying capacity state of Beijing in 2010 (a) and 2015 (b)
Table 7 The carrying capacity of Beijing between 2010 and 2015
Contribution value Pressure Support Destructiveness Resilience Degeneration Promotion Carrying state Mean
contribution
2010 0.7468 0.6065 0.6191 0.7874 0.6917 0.6931 1.0143 0.6908
2015 0.7428 0.6627 0.5827 0.7443 0.6432 0.8394 1.1411 0.7025

Note: The internal data holds to four decimal places based on the original data.

According to the classification standards of resources and environmental carrying capacity applied in this paper (Table 1) and our results, it is clear that the city of Beijing did not overload in either 2010 or 2015. In the first of these two years, the carrying capacity state reached 1.0143 and the mean contribution value was 0.6908; these values are both indicative of a good state and an ideal development trend. Indeed, both values were larger in 2015 than their counterparts in 2010, which shows that the city actually had a better carrying capacity in the later year than the earlier one. Secondly, data show that negative forces had weakened and positive ones had strengthened in 2015 compared to 2010; we show that two sets of forces were characteristic that if the negative one increased (or reduced) and its corresponding positive counterpart also trended in the same direction, with the exception of pressure and support. Third, data show that both destructiveness and degradation declined sharply between 2010 and 2015; this result means that environmental management and ecological protection are well controlled within the city and its ability to resist risks has enhanced. The contribution value of degradation also decreased while promotion increased between 2010 and 2015; this result suggests that humans have transitioned from a passive model of “driving force-pressure-state-response” and have developed a positive attitude towards warning and prevention. In contrast to the widespread belief that the carrying pressure of Beijing is increasing, our research results show instead that pressure on the city actually decreased in 2015 compared to 2010, even though population increased by 2.09 million and GDP increased by 890.1 billion yuan.
It is clear that local natural resources within the city are scarce and thus Beijing is subject to a high level of external dependence (Table 8); at the same time, however, the concept of regional carrying capacity will reveal the largest population that can be supported under such global and regional conditions. This ability also embodies the openness of regional carrying capacity; obviously, Beijing could support a much smaller population than is the current case if just local resources were employed. Although pressure on the city is greater than support at present, we can nevertheless look forward to a better carrying potential given the emergence and progress of new technologies.
Table 8 The degree to which the energy and resources of Beijing were externally dependent between 2010 and 2015
Net input Crude oil (104 tons) Gas (108 m3) Water resource (108 m3)
2010 1,116.29 74.79 12.1
2015 1,165.18 130 11.4
External dependence in 2010 (%) 100 100 34.375
External dependence in 2015 (%) 100 88.51 29.84

Note: External dependence is equal to the ratio of net input to total consumption in a given year.

One previous study in this area utilized the possible-satisfaction method to predict the carrying capacity of Beijing; this research estimated that a total level between 22.5 million people and 25 million people would be acceptable, a size around 23.5 million would be optimal, and that a level of 25 million people would be problematic (Wang et al., 2016). Our data reveal an average 2015 contribution value within Beijing of 0.7025, compared with an upper value of 0.85; this result indicates that there is still room for a larger population even though almost 22 million people currently live within this agglomeration. Indeed, given the level of human satisfaction within Beijing, our result is actually consistent with that of Wang et al. (2016). The problematic nature of previous research is also illustrated by the most commonly cited paper in this field in the context of resource capacity research (Xia et al., 2006) which suggested that water resources are the most critical limiting factor influencing the future development of Beijing. This study used Tongzhou District as an example and concluded that the population of this area can only rise to 1.119 million people by 2020 yet 1.184 million were living in this zone in 2010. A further study in this area also predicted that the population of Haidian District would be 3.0733 million by 2020 (Zhang et al., 2008) yet some 3.2 million people were living in this region in 2010. Several researchers have addressed these discrepancies by arguing that the actual population of Beijing has consistently been larger than its corresponding capacity since at least 1995 (Wang et al., 2005); we note that previous researchers have only focused on local resources and have ignored the extrinsic capacities of this region to acquire resources. Earlier predictions have thus been underestimated and therefore have limited practical application.
We argue in this study that natural resources represent both absolute variables for development and are important restrictions. It is clear that as regional carrying capacity will change along with economic development, the city of Beijing will be able to maintain a perfect level of the former by enhancing comprehensive carrying capacity and controlling population size.

5 Discussion and conclusions

The concepts of resources and environmental carrying capacity from the point of “growth limit” and the stable structure of the human-earth system are defined in this study. This enabled us to determine “PS-DR-DP” hexagonal interaction theoretical model and divide carrying capacity into three pairs of interacting forces, “pressure-support”, “destructiveness-resilience”, and “degradation-promotion”, corresponding to resource supporting ability, environmental capacity, and risk-disaster resisting ability, respectively. The carrying capacity state can therefore be calculated via the value length between the origin and the vertex of an equilateral-hexagon; differences in hexagon shape can therefore also be used to simulate dynamic changes in carrying capacity.
In order to apply our “PS-DR-DP” theoretical model, we built a comprehensive evaluation index system that was certified via Cronbachs Alpha reliability analysis. We modified the entire-array-polygon method as a classified-array polygonal approach in order to avoid the influence of subjective assignment on results. This new method is easier to visualize and use as it reduces complicated calculations and avoid the impacts of imprecise weighting.
Our results reveal that the city of Beijing has attained to close to perfect carrying capacity state. Indeed, the state value of carrying capacity increased from 1.0143 to 1.1411 over the period between 2010 and 2015; the city has therefore more recently attained enhanced resource and environmental carrying capacity status levels. As the average contribution value reached 0.7025 in 2015, Beijing attained an optimal loading threshold while maintaining additional space for further carrying. This result differs from previous research in this area that has converged on the opinion that Beijing is overloaded and that population should restricted to less than 23 million people by 2020. Despite this significant result, we nevertheless cannot ignore competition in land resource between ecological protection and urban construction going forward.
We show that the “PS-DR-DP” model represents a marked improvement on traditional approaches for the study of regional resources and environmental carrying capacity. However, as the key issue faced by research in this area is to determine the underlying mechanisms controlling the factors influencing resources, environmental carrying capacity, and population limits under specific conditions, our model is able to only test the relative status of these two variables. It will be necessary to continue with research in this area to determine methods that can be applied to calculate approximately optimal solution given maximum population levels or those of optimal size.
Previous researchers have argued that increases in population will mean a concomitant pressure on regional resources. Our results show, however, that this pressure on Beijing was actually reduced as population expanded. We hypothesize that perhaps technical progress has enhanced both regional resources and environmental carrying capacity. A number of questions remain to be addressed, including how to adequately express this offset effect between technological progress and negative forces. In addition, can this pressure continue to decline under the premise of technological progress? Will this mean more room for a larger population? How can this threshold be determined? These issues are all key areas for future research.

The authors have declared that no competing interests exist.

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Publishing order | Descend order by publishing year | Descend order by cited within
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Mao H Y, Yu D L, 2001. Regional carrying capacity in Bohai Rim.Acta Geographica Sinica, 56(3): 363-371. (in Chinese)http://en.cnki.com.cn/article_en/cjfdtotal-dlxb200103012.htmBohai Rim, one of the developed and urbanized regions in China, plays an important role in the new century development. Now the load on the regional resource and environment has been over carried which has been one of the main restrictive factors for the future socioeconomic development in this region. After retrospection of the previous research methods on regional carrying capacity at home and abroad, this paper takes the state space as a basic method to measure regional carrying capacity on account of implementing regional sustainable development strategy. It does quantitative evaluation of regional carrying capacity by building an index system. The conclusions are as follows. The carrying status of resource and environment was over loaded from 1994 to 1998 in this region. Seriously inadequate per capita possession of water resource and utilizable water decreasing caused by pollution are main restrictive factors. Furthermore serious shortage of water resource has close relationship with furious speed extensive economic development pattern. In view of the above mentioned conclusions, this paper simulates and forecasts the regional carrying capacity and status by the agency of system dynamics. The general trend is briefed below. The over loaded tendency remains as before, but the carrying status of each time is evolving toward better. It is forecasted that the carrying status will approach the carrying capacity in the year 2015 which shows this region will develop from weaker to stronger sustainable direction. According to this forecast, the authors raise four countermeasures as follows: (1) economic countermeasure: seeking continuous, moderate and coordinated economic growth and adjusting the industrial structure and location; (2) resource countermeasure: adopting the principle of increasing income and decreasing expenditure for shortage resources and building the regulation of utilizing resource upon consideration; (3) environmental countermeasure: strictly executing the total emission control of pollutant, adopting the resource consumption into national economic accounting system progressively and increasing the input to improve eco environmental quality; and (4) population countermeasure: strictly controlling the quantity and improving the quality.

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[35]
Qiang Z, Qi Y B, Bai X M, 2007. Study on population carrying capacity of cultivated land in big city: Taking Beijing City as a case.Resource Development & Market, 23(2): 147-148. (in Chinese)http://en.cnki.com.cn/Article_en/CJFDTotal-ZTKB200702015.htmDuring the national urbanization and industrialization period,the scale of cultivated land and food production in some big cities such as Beijing was fallen year after year.Population food demand scale depended on other areas more and more,the city food ensurence was depressed at the same time.Based on demonstrated data,this study analyzed the food security and village labour force allocation in Beijing,and put forward some suggestions for cultivated land protection.

[36]
Rees W E, 1992. Ecological footprints and appropriated carrying capacity: What urban economics leaves out.Focus, 6(2): 121-130.

[37]
Rees W E, Wackernagel Mathis, 1994. Ecological footprints and appropriated carrying capacity: Measuring the natural capital requirements of the human economy.Focus, 6(2): 121-130.http://eric.ed.gov/?id=EJ548060Ecological footprints and appropriated carrying capacity: what urban economics leaves out uses the concepts of human carrying capacity and natural capital to develop a framework to evaluate each city's "ecological footprint". It also argues that prevailing economic assumptions regarding urbanization and the sustainability of cities must be revised in light of global ecological change.

DOI

[38]
Reghunathan V M, Joseph S, Warrier C Uet al., 2016. Factors affecting the environmental carrying capacity of a freshwater tropical lake system.Environmental Monitoring & Assessment, 188(11): 615.http://europepmc.org/abstract/med/27738895Abstract Environmental carrying capacity is a measure of competence of a lake to accommodate pollution inputs without degrading water quality. In the research reported here, we identified the factors influencing the environmental carrying capacity of Vellayani Lake or VL (a typical tropical freshwater lake), Thiruvananthapuram, Kerala State, India. R-mode factor analysis is used to identify the factors controlling the carrying capacity of the lake, whereas hierarchical cluster analysis (HCA) helped to classify the lake. The carrying capacity of the lake is low with respect to alkalinity, due to ion deficiency, and is potentially reactive to sudden changes in pH. Eutrophic condition exists in the entire lake system. Acidic factor, mineralization factor, fertilizer factor (P & K), evaporation factor and organic pollution factor are the controllers of VL water quality during the pre-monsoon period. The same factors (but not evaporation factor) and an additional runoff factor control the water quality during monsoon. In the post-monsoon, the aforesaid factors (other than runoff, alkalinity) and soil erosion factor influence the water quality. Hence, managers of the lake system need to also focus on combating acidic factor during pre- and post-monsoons and runoff during monsoon. Smaller areal extent and shallow depth of VL, reduced outflow from it, less rainfall, presence of lateritic rock and soil and absence of limestone strata in the catchment are the chief elements affecting the acidic factor of Vellayani Lake.

DOI PMID

[39]
Sarma A K, Sarma B, Das S, 2016. Estimating Sustainable Carrying Capacity of Flood Prone Hilly Urban Areas. Urban Hydrology, Watershed Management and Socio-Economic Aspects. Springer International Publishing.http://link.springer.com/content/pdf/10.1007/978-3-319-40195-9_23.pdfThe carrying capacity of an area is the maximum number of people that can be supported by the environment in an eco-friendly manner utilizing the available resources. Cities of the developing countrie

DOI

[40]
Shi Y F, Qu Y G, 1992. The Carrying Capacity of Water Resources and Its Reasonable Use of Urumqi River. Beijing: Science Press. (in Chinese)

[41]
Shi Y L, 1992. Research of Population Carrying Capacity of Chinese Land Resource. Beijing: Science and Technology of China Press. (in Chinese)

[42]
Tong Y F, 2010. Dynamic simulation and analysis to population carrying capacity of Beijing.China Population Resources and Environment, 20(9): 42-47. (in Chinese)http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZGRZ201009010.htmWater resource is a kind of the most important and necessary one for the development of population and economy of any city,and it is very difficult for its amount to be changed in a short time.So it was often seen as a "the shortest piece of a wood barrel" in research of population carrying capacity.Beijing,as a city in shortage of water resource,is confronted with the serious contradiction between rapid population growth,economic development and water shortage.This paper analyzed the population carrying capacity in future with system dynamics method.Some supplying factors such as surface water,groundwater,regenerated water and the water from south-to-north water diversion and some water using factors such as industrial and agricultural water use,ecological water use and domestic water use,as well as the impacts of those factors on the carrying capacity and their interactions were considered in the model.The various change trends of those factors in the future were simulated.The results showed: first,the carrying capacity of Beijing would decline if current water supply and use standard and structure were unchangeable.Second,the water from south-to-north water diversion could increase the capacity,but it could only resolved the problem temporarily.Third,to change the structure of water use and raise the efficiency of water use simultaneously would have a very important effects for raising the population carrying capacity of Beijing.

DOI

[43]
Tong Y F, Liu G J, 2011. Research on urban population carrying capacity based on potential-satisfaction degree method: A case study of Beijing.Jilin University Journal Social Sciences Edition, 51(1): 152-157. (in Chinese)

[44]
Wang S T, Guo H C, Wang L J, 2005. An analysis of relative loading capacity of resources in Beijing City.Journal of Safety and Environment, 5(5): 90-94. (in Chinese)http://en.cnki.com.cn/Article_en/CJFDTOTAL-AQHJ200505023.htmThe present paper intends to introduce the method of analyzing the relative capacity of the resources in Beijing in reference to the whole country as well as to its co-equivalent city—Shanghai.It is a new method to estimate the regional loading capacity of the resources by comparing the relative loading capacities of the natural resources.So far,the method has been studied broadly both at home and abroad.Our analysis indicates that the relative loading capacity of the resources in Beijing is in a comparatively overloaded state in recent years,and the deteriorating tendency is getting more and more apparent.Actually,the essential reason lies in its over-consuming natural resources—the new economic development mode that is caused by the irrational industrisl structure.Thus,it is very important to optimize the industrial structure and adjust the economic development mode,sequentially,enhance the relative capacity of the resources in Beijing so as to realize the sustainable development of population,resources and environment of Beijing.

[45]
Wang Z G, Xia J, 1999. Quantitative analysis on bearing capacity of ecological environment.Journal of Changjiang Vocational University, 16(4): 9-12. (in Chinese)http://en.cnki.com.cn/Article_en/CJFDTotal-CJZG199904003.htmAccording to the theory of bearing capacity of environment,the new quantitative analysis method of bearing capacity of ecological environment is put forward.Case study indicates the method is simple and feasible,and can be applied to analyse and forecast the bearing capacity of ecological environment.

[46]
Wang Z S, Yuan K K, Lyu C Yet al., 2016. Research of population carrying capacity of Beijing based on the resources & environment constraints.China Population, Resources and Environment, 26(5): 351-354. (in Chinese)

[47]
Wu Q, Wang R S, Li H Qet al., 2005. The indices and the evaluation method of eco-city.Acta Ecologica Sinica, 25(8): 2090-2095. (in Chinese)http://en.cnki.com.cn/Article_en/CJFDTotal-STXB200508036.htmEco-city is a social-economic-natural harmonization development system according with the ecology principle. Now the research of eco-city theory is mainly focused on the planning, designing, and management of city. The assessment of eco-city is the basis for the planners to evaluate the effect of their eco-city planning. This paper reviewed the history and the connotation of eco-city theory, and designed the indices system of the Yangzhou eco-city planning based on the expert consultation to evaluate the eco-city's development ability. The indices system includes social, economic and natural factors, and the coupling status of these three subsystems. The entire-array-polygon evaluation method was offered to evaluate the Yangzhou eco-city planning using the designed indices system. And the results show that the synthesis index of Yangzhou Eco-city will be 0.44 in 2005, and the development ability will belong to class III and will be general. It will be 0.64 in 2010, and the ability will belong to class II and will be better. It will reach to 0.85 in 2020, and the ability will belong to class I and will be excellent. The process of evaluation shows that the indices system and the evaluation method are very simple and easily applied, and the entire-array-polygon method is capable of validating the system integrating theory that synthesis is bigger or smaller than the sum of elements.

[48]
Xia J, Zhang Y Y, Wang Z G, 2006. Water carrying capacity of urbanized area.Journal of Hydraulic Engineering, 37(12): 1482-1488. (in Chinese)http://en.cnki.com.cn/Article_en/CJFDTotal-SLXB200612013.htmThe connotation and characteristics of water resources carrying capacity were discussed by analyzing the effect of urbanization on water cycle,social economy,ecology and environment.Based on the concept of natural-social water cycle and following the sustainable development principle,a water resources carrying capacity model for the urbanized area was developed by adopting a comprehensive analysis and applying the multi-level gray relative analysis method.This model was applied to analyze the water resources in Tongzhou District,Beijing.The result showed that the model is feasible for solving the resources and eco-environmental problems happened to the urbanized area and provided a theoretical basis for water resources deployment and the implementation of sustainable development strategy.

[49]
Yu G H, Sun C Z, 2015. Land carrying capacity spatiotemporal differentiation in the Bohai Sea coastal areas.Acta Ecologica Sinica, 35(14): 4860-4870. (in Chinese)

[50]
Zeng W H, Wang H D, Xue J Xet al., 1991. Environmental carrying capacity: A key to the coordination of the development of population, resources and environment.China Population, Resources and Environment, 1(2): 33-37. (in Chinese)

[51]
Zhang L H, Chen G, Xu X Xet al., 2008. A theoretical and empirical study of urban population carrying capacity: taking Haidian of Beijing as an example. Management Review, 20(5): 28-32. (in Chinese)

[52]
Zhu K Z, 1964. Some characteristic features of Chinese climate and their effects on crop production.Acta Geographica Sinica, 30(1): 1-13. (in Chinese)http://en.cnki.com.cn/article_en/cjfdtotal-dlxb196401000.htmIn China, from the time immemorial, climate has always been considered as capable of exerting an inordinate influence on the production of agricultural crops. Among the various climatic factors, total amount of insolation, temperature and rainfall are deemed to be the most important. 1. Total amount of insolation Basing on the data obtained at 26 solar radiation stations by direct observation at earth's surface in various parts of China during the period 1957?960, and 136 other points calculated by interpolation, maps of annual and monthly total radiation, as well as annual and monthly radiation balance of whole China were drawn by Mr. T. K. Zuo etal, of Institute of Geography, Academia Sinica, in terms of kilogram calories per square centimeter per minute (for annual distribution of total solar radiation see Fig. 1). In the annual chart, the striking thing appears to be the fact that the lines of equal insolation do not go parallell with the latitudes, but in the eastern part of the country, they form in concentric circles with the Red basin of Sze-chuan province as the nadir point, with 90 kilogram calories, and the amount increases outward, more rapidly toward W. and less so toward E. This is largely due to the increasing cloudiness toward that province, owing to the SE. monsoon and the mountainous topography. Another interesting feature is the fact that in North China the annual insolation increases landward due to the de- crease of cloudiness and the increase of altitude. Maximum insolation occurs in Southern Tibet, but even in Northern Sinkiang the amount of annual insolation still exceeds any place south of the Yangtze River. The distribution of total radiation explains at least partly, why the yield of paddy rice in Tientsin district is 30% or so higher than that of Shanghai district per unit area, and why the record of highest yield of spring wheat, over 500 kilogram per mu (1/6 of an acre) is held by the agricultural experimental sta- tion at Delinha, about 240 kilometers W. of lake Kukunor, at the altitude of about 2500 meters. Compared with the chart of annual total radiation of the whole world as construc- ted by Dr. M. E. Bydiko, Director of the Central Geophysical observatory at Lenin- grad, USSR, it is obvious that besides the Sahara, Arabia, and Mediterranean regions, Tibet and NW. China, including Sinkiang and Tsaidam Basin, rank very high in the amount of solar energy received every year among large land areas in the N. Hemi- sphere. Even in E. China the amount of solar energy received annually exceeds that of Japan or W. Europe where the rice and wheat crops give the highest yield per unit area in the world. 2. Temperature The lowland of E. China, where most of the grain crops are produced in the coun- try, is located in monsoon region. The monsoon climate distinguishes itself by firstly, a regime of maximum summer rainfall and a long dry season in winter; and secondly, by its excessive heat in summer and inordinate cold climate in winter, compared with re- gions on the same latitude. Thus monsoon climate is extremely favorable for the grow- ing of paddy rice, which gives very high yield per unit area when compared with other grain crops such as wheat, barley or rye. It is, therefore, not an incidental fact that 90 % of the rice crop in the world in the past were produced in SE. Asia where mon- soon climate prevails. According to meticulous investigations made by Japanese meteorologists on the cor- relation coefficients between different climatic factors, such as duration of sunshine, tem- perature and rainfall on the one hand, and amount of yield of rice crops on the other, it was apparent that temperature exerted an outstanding influence on the rice harvest in Japan, especially the monthly mean temperature for July and August. The higher the temperature for July and August, the higher the rice yield. This is true not only in Hokkaida in N. Japan, but also valid in Kyoto districts in Honshu. Whenever

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