Abstract

A unified co-evolutionary model was developed to study the adaptability conditions of regional water security systems, which is important for the coordinated development of these systems. In this work, the main factors that affect the adaptability of regional water security systems, the contribution of each sub-problem domain to the development of the problem domain, and the fitness values of regional water security systems were analyzed based on the model. Taking Jiansanjiang as an example, the results showed that in 2002–2011, the water resources system had strong adaptability and contributed greatly to improve the adaptability of the water security system; the socioeconomic system had poor adaptability to environmental changes and contributed little to the adaptability of the water security system; and the eco-environmental system was barely able to adapt to the changing environment and contributed less to the adaptability of the water security system. Due to the influence of the socioeconomic and eco-environmental systems, the adaptability of the water security system was relatively weak. Therefore, strengthening the sustainable utilization of water resources, promoting the coordinated development of the social economy, and improving the quality of the ecological environment are effective strategies to improve the adaptability of water security systems.

INTRODUCTION

In recent years, due to fluctuations in the natural water cycle and the destruction of the water balance, regional water security is becoming increasingly serious; water security refers to a region (or country) under certain socioeconomic conditions and includes the ability to withstand water disasters and the sustainable use of water resources to ensure sustainable economic, social, and ecological development (Petersen-Perlman et al. 2012; Anand et al. 2013; Fu et al. 2013). Water security systems are complex systems including water resources, socioeconomic and eco-environmental subsystems, which must be individually examined to comprehensively and systematically analyze and study the regional water security situation. Additionally, water resource systems are the basis for the development of subsystems in water security systems; socioeconomic systems aim to maximize the benefits of the subsystems. In the context of sustainable development, eco-environmental systems provide an environment for the good functioning of water security systems. Thus, water security systems are highly integrated with complex adaptive characteristics (Giacomoni et al. 2013; Cheng et al. 2015).

This paper introduces a cooperative evolutionary algorithm to study the operational mechanisms and development of water security systems. Co-evolution refers to the combined evolution of both organisms and the environment under long-term mutual adaptation, whereas evolution corresponds to the individual development of organisms and the environment (Ehrlich & Raven 1964). The co-evolutionary algorithm is an evolutionary computational method that was first proposed in the 1990s to simulate the co-evolution phenomenon in ecological evolution (Hillis 1990; Panait 2010). The method calculates the fitness of individuals according to the collaborative relationship between individuals. Compared with the genetic algorithm, the co-evolutionary algorithm can simulate ecological evolution more effectively, and the algorithm is more adaptive and can overcome the premature convergence of the genetic algorithm. Therefore, some researchers have introduced cooperative evolutionary computations in research on optimization problems; for example, an innovative variation of the co-evolutionary genetic algorithm (CGA) was proposed by Baek & Yoon (2002) to determine adaptive scheduling strategies in a complex multi-machine system. The CGA effectively suppressed premature convergence and produced dispatching rules for spatial adaptation that outperformed other heuristic methods. In a study of the optimal allocation of water resources, a CGA was proposed by Wang et al. (2014) to improve the utilization of water resources. A hybrid CGA was proposed by Korayem et al. (2016) to determine the optimal moving paths of concentrated nanoparticles in a complex environment. Infeasible initial paths significantly reduced the efficacy of the path planning algorithm, especially in large and complex environments. Tian & Gong (2014) proposed a new CGA that uses two types of alternating co-evolution to generate test data for path coverage. This proposed method displayed the highest success rate, lowest requirement for human evaluation, and lowest time consumption.

Based on an individual competitive relationship or partnership, co-evolutionary algorithms can be divided into competitive co-evolutionary algorithms (CCEAs) and cooperative co-evolutionary algorithms (Chandra et al. 2011; Nogueira Collazo et al. 2014). The fitness of individuals in competitive co-evolution algorithms depends on the ability of the individual to defeat an opponent in a competition, and the progress of either party in the competition will endanger the survival of the other party. This method has been used by some researchers to solve various problems. A simple, non-problem-specific framework was proposed by Sato & Arita (2009) to extend the range of CCEAs and avoid local optima by utilizing the loss of gradient. A competitive co-evolutionary multi-objective genetic algorithm (cc-MOGA) was used to approximate a Pareto front of efficient silvicultural regimes of Eucalyptus fastigiata based on maintaining a maximum growth rate for as long as possible for any one rotation (Chikumbo & Straka 2012). The fitness of individuals in a CCEA depends on the cooperation of individuals, and in a competition, there is a beneficial impact on the individual associated with cooperation. The progress of any party involved in cooperation is beneficial to both sides. The cooperative co-evolutionary algorithm has been widely used in various studies. A cooperative evolutionary approach was proposed for the solution of the instance selection problem, and the experimental results showed that the proposed method was robust and could effectively solve the problem using large data sets (García-Pedrajas et al. 2009). A new cooperative co-evolutionary algorithm for solving structural configuration and parameter optimization issues based on adaptive platform product customization (PPC) was proposed by Li et al. (2008). However, the method is slow to converge at the beginning of the evolutionary process. This initial slow convergence property improves its searching capability and ensures a high-quality solution. Moreover, cooperative co-evolutionary algorithms have been used to study the dynamic optimization problems of random migration and evolution strategy. The experimental results show that the method is effective in locating and tracking the optimal solution and more scalable than the evolution strategy in a dynamic environment (Au & Leung 2014). In addition, the competitive and cooperative co-evolutionary algorithms were applied to the design of a multi-objective particle swarm optimization algorithm, and the simulation results showed that the proposed algorithm was superior to other methods of competition and co-evolution (Goh et al. 2010). However, the fitness values of these two algorithms change for different cooperative individuals, which increases the computational time.

To solve this problem, a uniform co-evolutionary algorithm involving absolute fitness and relative fitness is adopted. The absolute fitness depends on an individual, while the relative fitness is determined by the coordination between individuals. The adaptability of individuals and their interactions based on the external environment determines the ability of the entire system to adapt to environmental change. The absolute fitness value reflects the ability of individuals to adapt to environmental change, the relative fitness value reflects the adaptability of each element in the problem domain, and the comprehensive fitness value is the comprehensive adaptability of each element based on the absolute fitness and relative fitness.

STUDY AREA AND RESEARCH METHODS

Study area

Jiansanjiang is located on the northeastern Sanjiang Plain. It belongs to the humid monsoon climate zone (cold temperate) and is home to the largest agro-ecological park in China. Its geographical coordinates are 132°31′–134°32′E longitude and 46°49′–48°12′N latitude. The annual average temperature over the entire area is 1.0 °C to 2.0 °C, the region covers an area of 1.24 × 104 km2, the population is 2.3 × 105, and the per capita cultivated land area is 3.33 km2. The region contains 15 large and medium-sized state-owned farms, and there are three major rivers in the region, including the Songhua River, Heilongjiang River, and Wusu River (see Figure 1). The water area is wide and the water quality is good. The total amount of surface water resources in this area is 2.85 × 1011 m3; the surface water transit capacity is 2.74 × 1011 m3, including 2.14 × 1011 m3 in the Heilongjiang River and 5.99 × 1010 m3 in the Wusu River. The exploitable amount of groundwater resources in this area is 14.84 × 108 m3/a, and its utilization is 13.35 × 108 m3/a, indicating that the region is rich in water resources and has great potential for development and utilization. However, because the region is largely populated with domestic housing, industrial water consumption is relatively small and the utilization of surface water resources is low. The rapid development of rice planting has led to a large concentration of groundwater resources in recent years, resulting in an imbalance in the supply and demand of water resources, which has seriously affected the ability of the water security system to adapt to environmental changes (Liu 2013).

Figure 1

Regional map of Jiansanjiang.

Figure 1

Regional map of Jiansanjiang.

Research methods

Grey relational analysis and a cooperative algorithm for regional water security systems

The grey system theory was proposed by Deng in 1982 (Morán et al. 2006). This theory can effectively address incomplete information and unclear problems. In the grey system, black represents the lack of system information, and white represents the complete information. A system containing incomplete and unclear information is called a grey system (Morán et al. 2006; Vinoth Kumar & Pradeep Kumar 2014). Grey correlation analysis uses the similarity degree of sequence curve geometry to determine the degree of correlation of a grey process development scenario. It is a quantitative method for analyzing the correlation degree of each factor in a grey system. The internal information in a water security system is incomplete, and the grey correlation degree uses the existing white information to reduce the associated error when evaluating the system (Lin & Lin 2002; Hasani et al. 2012). In this paper, the measured values of regional water security systems are used as comparative sequences, their ideal values are treated as reference sequences, and the grey correlation degree of each index is used as the adaptive measure value (absolute fitness).

Ehrlich and Raven proposed the concept of co-evolution in ecology in 1964 (Hillis 1990). This concept refers to the ability of several related populations to interact with each other, adapt to environmental changes and promote their ability to adapt to these changes. The co-evolutionary algorithm is a global optimization algorithm that was inspired by the co-evolution phenomena associated with the interactions between individuals in nature (Nogueira Collazo et al. 2014). According to the principle of constructing the problem domain of the co-evolutionary algorithm (Zhang et al. 2010), the adaptability of water security systems is studied based on the entire problem domain and several sub-problem domains. The factors that affect the adaptability of water security systems are considered the elements of the problem domain, and the relative fitness between individuals is calculated using the improved co-evolutionary algorithm.

The division of the problem domain

In this paper, the adaptability of the water security systems in the study area is considered the research domain, and it is divided into water resource system adaptability, socioeconomic system adaptability, and eco-environmental system adaptability. The adaptability of water resources systems is based on the water resource content, water use efficiency, and human control. The influence of regional, social, and economic development on the sustainable development of water security systems is the concentrated embodiment of the adaptability of socioeconomic systems. The adaptability of eco-environment systems reflects the adaptability of water security systems to changes in environmental conditions related to water and soil resources, natural disasters, man-made factors caused by climate change, and the destruction of the water and soil environment. The evaluation elements of each sub-problem domain are selected according to the ‘International water management standards for the promotion of sustainable use of freshwater’ issued by the Global Water Management Partnership (GWP), the ‘World environmental assessment report’ issued by the United Nations Environment Program (UNEP), the ‘Annual report on water resources management’ issued by the Water Resources Department of Ministry of Water Resources in China, and the principles of being objective, systematic, dynamic, data-focused, and attentive to regional characteristics (see Table 1).

Table 1

Evaluation index system of the adaptability of water security systems

Problem domain Sub-problem domain Element (Index) Index type 
Water security system adaptability Water resources system adaptability Total water resources (X1) (1 × 108m3
Stream runoff volume (X2) (1 × 108m3
Surface water resources (X3) (1 × 108m3
Groundwater resources (X4) (1 × 108m3
Volume of groundwater exploitation (X5) (1 × 108m3
Comprehensive supply of groundwater (X6) (1 × 108m3
Total annual precipitation (X7) (mm) 
Water environment and public facilities (X8) (1 × 104t·d−1
Industrial water recycling rate (X9) (%) 
The processing capacity of wastewater treatment facilities (X10
Urban sewage concentrated treatment rate (X11) (%) 
Drainage and irrigation stations (X12) (PCS) 
Tap water penetration rate (X13) (%) 
Wastewater treatment facilities operating costs (X14) (1 × 108yuan
Socioeconomic system adaptability Total population (X15
Natural population growth rate (X16) (%) 
GDPPC (X17) (RMB yuan
Water use amount per ten thousand Yuan of GDP (X18) (m3/104 RMB yuan
The proportion of investment in environmental protection accounted for by GDP (X19) (%) 
Grain yield per unit area (X20) (hm2
Regional agricultural production density (X21) (%) 
Eco-environmental system adaptability Food crop planting area (X22) (hm2
Effective irrigation area (X23) (hm2
Actual irrigation area (X24) (hm2
Land area (X25) (hm2
Agricultural acreage (X26) (hm2
Drought disaster proportion (X27) (%) 
Flood disaster proportion (X28) (%) 
Vegetation coverage rate (X29) (%) 
Pesticide application amount (X30) (t
Fertilizer application amount (X31) (t
Livestock fence amount (X32) (PCS) 
Forested area (X33) (hm2
Problem domain Sub-problem domain Element (Index) Index type 
Water security system adaptability Water resources system adaptability Total water resources (X1) (1 × 108m3
Stream runoff volume (X2) (1 × 108m3
Surface water resources (X3) (1 × 108m3
Groundwater resources (X4) (1 × 108m3
Volume of groundwater exploitation (X5) (1 × 108m3
Comprehensive supply of groundwater (X6) (1 × 108m3
Total annual precipitation (X7) (mm) 
Water environment and public facilities (X8) (1 × 104t·d−1
Industrial water recycling rate (X9) (%) 
The processing capacity of wastewater treatment facilities (X10
Urban sewage concentrated treatment rate (X11) (%) 
Drainage and irrigation stations (X12) (PCS) 
Tap water penetration rate (X13) (%) 
Wastewater treatment facilities operating costs (X14) (1 × 108yuan
Socioeconomic system adaptability Total population (X15
Natural population growth rate (X16) (%) 
GDPPC (X17) (RMB yuan
Water use amount per ten thousand Yuan of GDP (X18) (m3/104 RMB yuan
The proportion of investment in environmental protection accounted for by GDP (X19) (%) 
Grain yield per unit area (X20) (hm2
Regional agricultural production density (X21) (%) 
Eco-environmental system adaptability Food crop planting area (X22) (hm2
Effective irrigation area (X23) (hm2
Actual irrigation area (X24) (hm2
Land area (X25) (hm2
Agricultural acreage (X26) (hm2
Drought disaster proportion (X27) (%) 
Flood disaster proportion (X28) (%) 
Vegetation coverage rate (X29) (%) 
Pesticide application amount (X30) (t
Fertilizer application amount (X31) (t
Livestock fence amount (X32) (PCS) 
Forested area (X33) (hm2

‘P’ represents a positive index based on a ‘larger is better’ index value. ‘N’ represents a negative index based on a ‘smaller is better’ index value.

A unified co-evolution model of water security systems

The weight of each element (index) is determined using the improved entropy weight method. The absolute fitness of each index is determined using improved Euclidean grey weighted correlation analysis, and the relative fitness of each element is obtained using the improved co-evolutionary algorithm. According to the absolute fitness and relative fitness of each element (index), a unified co-evolution model is constructed, and the comprehensive fitness of each index is obtained. Simultaneously, the influence of the sub-problem domain on the overall problem domain is analyzed based on the comprehensive fitness and coordination index of each sub-problem domain. Then, the fitness of the entire problem domain is determined according to the projected weight value of the comprehensive fitness of each index. According to an assessment of urban water security systems, the ability of regional water security systems to adapt to environmental change is analyzed. The specific process is shown in Figure 2, and the model operation procedure is as follows.

Figure 2

Flow chart of the co-evolution model of regional water security systems.

Figure 2

Flow chart of the co-evolution model of regional water security systems.

Step 1: Numerical normalization processing of evaluation indexes

Assume that the sample matrix of the evaluation indexes is , where denotes the index of the sample, and m and n denote the number of indexes and sample size, respectively. The specific process of the index is shown in Equation (1):  
formula
(1)
where and indicate the maxima and minima of , respectively, of the index of the sample.

Step 2: Determine the weight of the evaluation index in the sub-problem domain

The weight of each index is determined using the improved entropy weight method. This method overcomes the shortcoming that the index weight is affected by the difference coefficient and prevents an index weight of 0 from being assigned. Additionally, this approach fully considers the influence of the interactions between the indexes.

Assume that is the entropy value of the evaluation index, and n is the number of evaluation objects. The entropy information of the evaluation index can be calculated as follows:  
formula
(2)
where  
formula
Assume that is the entropy weight value of the evaluation index, and m is the number of indexes. Additionally, . The standard deviation of the sample is introduced to preserve the objectivity of the traditional entropy method, and the computational formula for is as follows:  
formula
(3)
where  
formula

Step 3: Calculate the absolute fitness of the index in the sample information matrix using the improved Euclidean grey weighted average correlation method

Set as the initialization decision matrix, and select as the reference sequence based on the index attributes and as a comparison sequence. The decision matrix is obtained by the dimensionless processing of the grey correlation factor matrix: (for positive indicators), (for negative indicators). The correlation coefficient between the comparison sequence and the reference sequence at each point is as follows:  
formula
(4)
where denotes the resolution coefficient, which is generally equal to 0.5. The average grey correlation degree is as follows:  
formula
Let indicate that is related to , namely, . For any pair , close to each other, the following expression reflects the grey Euclid closeness:  
formula
indicates that has the greatest correlation with . Therefore, taking the closeness of and as the correlation between and yields the following expression:  
formula
(5)
Assume that the fluctuation in the comparison series and the reference sequence at each point can be reflected by the correlation coefficient relative to the weighted average value of . Thus, , and can be denoted as follows:  
formula
(6)
The improved Euclidean grey weighted average correlation can be calculated using Equations (7) and (8), and it is used as the absolute fitness of each sub-problem domain for water security systems:  
formula
(7)

Step 4: Calculate the relative fitness of each index using the improved co-evolutionary algorithm, and the comprehensive fitness is obtained by combining the relative fitness and absolute fitness

The relative fitness of indexes in the system depends on their Hamming distance and average Hamming distance. Considering the importance of the indexes in the system, the weight is added to the calculation of the relative fitness. Additionally, the comprehensive fitness is related to the adaptive ability of the index itself and affected by other indexes that are related to the synergy. The associated computational formula is as follows:  
formula
(8)
where denotes the comprehensive fitness of index i at t time, denotes the difference in the absolute fitness between index j and index i at t time, denotes the relative fitness of index i affected by other indexes at t time, denotes the weighted Hamming distance of elements i and j in the problem domain, AHD denotes the weighted average Hamming distance of all elements, and 0.5 denotes the smoothing factor, which is used to avoid severe effects on the system associated with small AHD values.

Step 5: Calculate the adaptability of each sub-problem domain, and analyze the importance of each sub-problem domain to the problem domain based on the coordination index

Assume that is the adaptability of each sub-problem domain and that is the coordination index of each sub-problem domain. The computational formula is as follows:  
formula
(9)
where .

Step 6: Calculate the adaptability of the entire problem domain

Assume that the comprehensive fitness projection value of each element is . The adaptability of the entire problem domain can be obtained by the weighted summation of the weight of each element. The specific calculation formula is as follows:  
formula
(10)

Adaptive grade threshold division of water security systems

Based on the Chinese city water security system indexes and grading standards (Liu 2011; Shao et al. 2013), project survey statistics, the relevant literature regarding index classification methods (Xiang 2011), and the regional characteristics of the study area (Li & Ma 2015), the adaptability is divided into four levels. The grade threshold of each element is shown in Table 2. According to the threshold of each element of water security systems, the adaptability criterion is obtained by the unified co-evolution model (see Table 3).

Table 2

Element level thresholds of water security systems

Element (Index) Level threshold
 
Element (Index) Level threshold
 
UA BA VA UA BA VA 
X1 18 30 46 54 X18 1,050 650 480 210 
X2 2,400 3,500 4,580 5,100 X19 0.35 0.72 1.2 1.8 
X3 15 20 X20 2,035 3,265 4,576 6,630 
X4 1.2 7.5 12 16 X21 10.5 20 38.5 65 
X5 18 14 9.2 5.2 X22 125,000 320,000 550,000 750,000 
X6 2.5 7.6 12.8 16.5 X23 12.5 20 45 70 
X7 150 385 575 750 X24 9.5 18.6 42 68 
X8 650 2,120 4,500 6,500 X25 350,000 855,000 1,250,000 1,460,000 
X9 50 70 80 90 X26 800,000 630,000 450,000 180,000 
X10 0.0089 0.02 0.08 0.15 X27 0.15 0.095 0.055 0.01 
X11 20 35 65 90 X28 0.152 0.105 0.075 0.008 
X12 3.5 10 15 20 X29 10 15 30 50 
X13 70 80 90 98 X30 5,000 4,500 3,800 2,050 
X14 1.2 3.5 5.5 8.5 X31 90,000 70,000 45,000 10,000 
X15 305,000 253,500 152,500 95,000 X32 255,000 420,000 600,000 720,000 
X16 10 1.76 X33 500 1,250 3,850 4,730 
X17 6,500 12,600 18,700 28,000           
Element (Index) Level threshold
 
Element (Index) Level threshold
 
UA BA VA UA BA VA 
X1 18 30 46 54 X18 1,050 650 480 210 
X2 2,400 3,500 4,580 5,100 X19 0.35 0.72 1.2 1.8 
X3 15 20 X20 2,035 3,265 4,576 6,630 
X4 1.2 7.5 12 16 X21 10.5 20 38.5 65 
X5 18 14 9.2 5.2 X22 125,000 320,000 550,000 750,000 
X6 2.5 7.6 12.8 16.5 X23 12.5 20 45 70 
X7 150 385 575 750 X24 9.5 18.6 42 68 
X8 650 2,120 4,500 6,500 X25 350,000 855,000 1,250,000 1,460,000 
X9 50 70 80 90 X26 800,000 630,000 450,000 180,000 
X10 0.0089 0.02 0.08 0.15 X27 0.15 0.095 0.055 0.01 
X11 20 35 65 90 X28 0.152 0.105 0.075 0.008 
X12 3.5 10 15 20 X29 10 15 30 50 
X13 70 80 90 98 X30 5,000 4,500 3,800 2,050 
X14 1.2 3.5 5.5 8.5 X31 90,000 70,000 45,000 10,000 
X15 305,000 253,500 152,500 95,000 X32 255,000 420,000 600,000 720,000 
X16 10 1.76 X33 500 1,250 3,850 4,730 
X17 6,500 12,600 18,700 28,000           

UA, under adaptation; BA, basic adaptation; A, adaptable; VA very adaptable.

Table 3

Adaptability criterion of water security systems

Adaptation degree Under adaptation (I) Basic adaptation (II) Adaptation (III) Very adaptable (IV) 
Discriminate criterion <0.528 0.528–0.661 0.661–0.862 0.862–1 
Adaptation degree Under adaptation (I) Basic adaptation (II) Adaptation (III) Very adaptable (IV) 
Discriminate criterion <0.528 0.528–0.661 0.661–0.862 0.862–1 

Data source

The evaluation index system for water security systems was established based on the index values between 2002 and 2011 in the study area (see Table 4). Our research data were primarily obtained from the ‘Jiansanjiang Statistical Yearbook (2002–2011)’, the ‘Heilongjiang Reclamation Area Statistical Yearbook (2002–2011)’, and a field study conducted during this research project.

Table 4

The original data of evaluation index of the study area's water security system

Year 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 
X1 46.575 47.543 47.993 43.626 39.598 39.564 51.332 37.113 40.0566 41.616 
X2 50,139 50,106 50,668 49,077 47,486 47,486 47,486 47,156 47,148 47,051 
X3 16.02 13.09 15.08 11.1 10.38 10.74 15.06 10.74 10.39 10.9 
X4 14.81 15.19 12.08 14.23 14.23 13.43 15.21 11.41 12.83 13.39 
X5 6.489 7.603 8.498 9.448 9.642 9.800 10.770 9.494 11.080 11.672 
X6 11.145 15.563 15.333 15.296 14.988 15.394 15.562 14.963 14.837 15.336 
X7 450 460.5 467.3 487.4 487.2 491.1 580.5 572.7 503.1 405.9 
X8 1,996 2,430 2,819 5,844 6,522 5,684 5,585 6,014 5,480 7,065 
X9 27.23 28.1 28.1 27.84 21.07 20.68 47.8 46.88 28.74 44.5 
X10 0.02 0.02 0.02 0.02 0.09 0.1 0.19 0.19 0.19 0.19 
X11 49.75 50.62 54.21 52.69 50.53 49.87 50 51.18 57.4 57.4 
X12 11 12 12 13 14 14 14 14 14 21 
X13 55.3 77.5 96.8 96.8 97.3 98.1 98.1 98.5 98.9 100 
X14 3.5 3.5 3.5 3.5 8.3 8.3 8.3 8.3 
X15 190,795 194,873 198,997 200,135 200,319 203,819 206,600 207,695 209,692 240,604 
X16 3.86 2.68 2.2 2.28 2.44 2.23 1.54 0.84 1.07 1.14 
X17 11,017 14,244 18,340 16,382 26,419 30,386 37,478 50,880 64,282 79,390 
X18 297 290.04 302.63 1,100 241.43 242 242 1,100 1,050 1,050 
X19 64 71 72 104 104 104 104 100 100 125 
X20 4,065 4,589 5,640 6,534 6,649 7,702 7,586 7,559 8,311 8,661 
X21 0.321 0.315 0.315 0.432 0.432 0.441 0.545 0.575 0.590 0.597 
X22 369,147 345,411 369,291 385,051 511,675 530,225 614,290 707,098 726,908 736,633 
X23 22.24 20.62 27.85 30.85 39.84 49.37 45.34 49.94 64.41 69.97 
X24 20.41 20.6 23.71 24.83 35.76 43.8 44.92 49.22 57.64 63.34 
X25 1,237,514 1,237,514 1,237,514 1,237,514 1,237,514 1,237,514 1,237,514 1,234,694 1,234,694 1,238,164 
X26 396,955 390,053 389,553 534,666 535,069 545,393 674,150 710,244 728,710 738,922 
X27 0.018 0.508 0.110 0.035 0.012 0.119 0.043 0.028 0.003 0.001 
X28 0.040 0.029 0.082 0.037 0.052 0.050 0.007 0.152 0.049 0.008 
X29 15.2 15.3 15.6 16.6 16.7 16.9 17 17.1 17.2 17.2 
X30 1,283 1,330 1,404 1,320 1,841 2,139 2,917 3,303 3,851 4,309 
X31 48,695 49,097 53,190 57,311 72,600 88,600 99,661 11,562 12,388 10,815 
X32 485,010 483,907 624,312 655,375 640,189 715,149 721,147 676,944 581,774 552,398 
X33 3,704 3,581.5 3,459 1,749 989 809 1,465 3,309 2,184 1,178 
Year 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 
X1 46.575 47.543 47.993 43.626 39.598 39.564 51.332 37.113 40.0566 41.616 
X2 50,139 50,106 50,668 49,077 47,486 47,486 47,486 47,156 47,148 47,051 
X3 16.02 13.09 15.08 11.1 10.38 10.74 15.06 10.74 10.39 10.9 
X4 14.81 15.19 12.08 14.23 14.23 13.43 15.21 11.41 12.83 13.39 
X5 6.489 7.603 8.498 9.448 9.642 9.800 10.770 9.494 11.080 11.672 
X6 11.145 15.563 15.333 15.296 14.988 15.394 15.562 14.963 14.837 15.336 
X7 450 460.5 467.3 487.4 487.2 491.1 580.5 572.7 503.1 405.9 
X8 1,996 2,430 2,819 5,844 6,522 5,684 5,585 6,014 5,480 7,065 
X9 27.23 28.1 28.1 27.84 21.07 20.68 47.8 46.88 28.74 44.5 
X10 0.02 0.02 0.02 0.02 0.09 0.1 0.19 0.19 0.19 0.19 
X11 49.75 50.62 54.21 52.69 50.53 49.87 50 51.18 57.4 57.4 
X12 11 12 12 13 14 14 14 14 14 21 
X13 55.3 77.5 96.8 96.8 97.3 98.1 98.1 98.5 98.9 100 
X14 3.5 3.5 3.5 3.5 8.3 8.3 8.3 8.3 
X15 190,795 194,873 198,997 200,135 200,319 203,819 206,600 207,695 209,692 240,604 
X16 3.86 2.68 2.2 2.28 2.44 2.23 1.54 0.84 1.07 1.14 
X17 11,017 14,244 18,340 16,382 26,419 30,386 37,478 50,880 64,282 79,390 
X18 297 290.04 302.63 1,100 241.43 242 242 1,100 1,050 1,050 
X19 64 71 72 104 104 104 104 100 100 125 
X20 4,065 4,589 5,640 6,534 6,649 7,702 7,586 7,559 8,311 8,661 
X21 0.321 0.315 0.315 0.432 0.432 0.441 0.545 0.575 0.590 0.597 
X22 369,147 345,411 369,291 385,051 511,675 530,225 614,290 707,098 726,908 736,633 
X23 22.24 20.62 27.85 30.85 39.84 49.37 45.34 49.94 64.41 69.97 
X24 20.41 20.6 23.71 24.83 35.76 43.8 44.92 49.22 57.64 63.34 
X25 1,237,514 1,237,514 1,237,514 1,237,514 1,237,514 1,237,514 1,237,514 1,234,694 1,234,694 1,238,164 
X26 396,955 390,053 389,553 534,666 535,069 545,393 674,150 710,244 728,710 738,922 
X27 0.018 0.508 0.110 0.035 0.012 0.119 0.043 0.028 0.003 0.001 
X28 0.040 0.029 0.082 0.037 0.052 0.050 0.007 0.152 0.049 0.008 
X29 15.2 15.3 15.6 16.6 16.7 16.9 17 17.1 17.2 17.2 
X30 1,283 1,330 1,404 1,320 1,841 2,139 2,917 3,303 3,851 4,309 
X31 48,695 49,097 53,190 57,311 72,600 88,600 99,661 11,562 12,388 10,815 
X32 485,010 483,907 624,312 655,375 640,189 715,149 721,147 676,944 581,774 552,398 
X33 3,704 3,581.5 3,459 1,749 989 809 1,465 3,309 2,184 1,178 

RESULTS AND DISCUSSION

Model verification

In this paper, based on the data of the water security system evaluation index for the period 2002–2011 and using Matlab2012a software, the weights, absolute fitness values, relative fitness values, and comprehensive fitness values of the elements in each sub-problem domain (see Table 5) are obtained by the unified co-evolution model (steps 1–4; Equations (1)–(8)). According to the comprehensive fitness value of each element, the fitness degree and coordination index of each sub-problem domain of the water safety system in the study area (see Table 6) are obtained using operation step 5 (Equation (9)), and the fitness of the entire problem domain (see Table 7) is obtained using step 6 (Equation (10)).

Table 5

Weight and fitness of each element in the study area water security system

Element (Index) Weight Absolute fitness Relative fitness Comprehensive fitness Element (Index) Weight Absolute fitness Relative fitness Comprehensive fitness 
X1 0.0275 0.773 0.555 0.558 X18 0.0409 0.637 0.435 0.449 
X2 0.0338 0.915 0.779 0.784 X19 0.0265 0.692 0.469 0.474 
X3 0.0335 0.700 0.476 0.486 X20 0.0283 0.715 0.491 0.494 
X4 0.0286 0.836 0.643 0.650 X21 0.0343 0.704 0.480 0.488 
X5 0.0257 0.645 0.438 0.444 X22 0.0341 0.670 0.452 0.462 
X6 0.0252 0.913 0.776 0.780 X23 0.0289 0.589 0.423 0.427 
X7 0.0255 0.771 0.553 0.556 X24 0.0308 0.594 0.424 0.429 
X8 0.0301 0.664 0.448 0.454 X25 0.0300 0.988 0.944 0.941 
X9 0.0320 0.634 0.434 0.437 X26 0.0342 0.678 0.458 0.470 
X10 0.0397 0.597 0.424 0.434 X27 0.0254 0.401 0.386 0.387 
X11 0.0329 0.850 0.664 0.677 X28 0.0243 0.472 0.406 0.404 
X12 0.0229 0.610 0.427 0.430 X29 0.0336 0.917 0.784 0.790 
X13 0.0270 0.868 0.693 0.688 X30 0.0317 0.644 0.438 0.445 
X14 0.0416 0.668 0.451 0.468 X31 0.0299 0.514 0.413 0.416 
X15 0.0231 0.882 0.718 0.721 X32 0.0305 0.780 0.565 0.570 
X16 0.0253 0.536 0.417 0.419 X33 0.0338 0.611 0.427 0.448 
X17 0.0284 0.508 0.412 0.410      
Element (Index) Weight Absolute fitness Relative fitness Comprehensive fitness Element (Index) Weight Absolute fitness Relative fitness Comprehensive fitness 
X1 0.0275 0.773 0.555 0.558 X18 0.0409 0.637 0.435 0.449 
X2 0.0338 0.915 0.779 0.784 X19 0.0265 0.692 0.469 0.474 
X3 0.0335 0.700 0.476 0.486 X20 0.0283 0.715 0.491 0.494 
X4 0.0286 0.836 0.643 0.650 X21 0.0343 0.704 0.480 0.488 
X5 0.0257 0.645 0.438 0.444 X22 0.0341 0.670 0.452 0.462 
X6 0.0252 0.913 0.776 0.780 X23 0.0289 0.589 0.423 0.427 
X7 0.0255 0.771 0.553 0.556 X24 0.0308 0.594 0.424 0.429 
X8 0.0301 0.664 0.448 0.454 X25 0.0300 0.988 0.944 0.941 
X9 0.0320 0.634 0.434 0.437 X26 0.0342 0.678 0.458 0.470 
X10 0.0397 0.597 0.424 0.434 X27 0.0254 0.401 0.386 0.387 
X11 0.0329 0.850 0.664 0.677 X28 0.0243 0.472 0.406 0.404 
X12 0.0229 0.610 0.427 0.430 X29 0.0336 0.917 0.784 0.790 
X13 0.0270 0.868 0.693 0.688 X30 0.0317 0.644 0.438 0.445 
X14 0.0416 0.668 0.451 0.468 X31 0.0299 0.514 0.413 0.416 
X15 0.0231 0.882 0.718 0.721 X32 0.0305 0.780 0.565 0.570 
X16 0.0253 0.536 0.417 0.419 X33 0.0338 0.611 0.427 0.448 
X17 0.0284 0.508 0.412 0.410      
Table 6

Comprehensive fitness and coordination index of each sub-problem domain in the study area water security system

Year WA SA EA WAC SAC EAC 
2002 0.646 0.278 0.500 0.404 0.439 0.404 
2003 0.693 0.265 0.703 0.413 0.395 0.521 
2004 0.714 0.271 0.600 0.470 0.406 0.405 
2005 0.736 0.366 0.524 0.497 0.261 0.353 
2006 0.756 0.317 0.565 0.532 0.326 0.365 
2007 0.776 0.327 0.654 0.534 0.290 0.424 
2008 0.953 0.333 0.640 0.811 0.258 0.372 
2009 0.858 0.401 0.737 0.610 0.179 0.479 
2010 0.845 0.425 0.651 0.609 0.164 0.385 
2011 0.971 0.471 0.616 0.791 0.129 0.325 
Year WA SA EA WAC SAC EAC 
2002 0.646 0.278 0.500 0.404 0.439 0.404 
2003 0.693 0.265 0.703 0.413 0.395 0.521 
2004 0.714 0.271 0.600 0.470 0.406 0.405 
2005 0.736 0.366 0.524 0.497 0.261 0.353 
2006 0.756 0.317 0.565 0.532 0.326 0.365 
2007 0.776 0.327 0.654 0.534 0.290 0.424 
2008 0.953 0.333 0.640 0.811 0.258 0.372 
2009 0.858 0.401 0.737 0.610 0.179 0.479 
2010 0.845 0.425 0.651 0.609 0.164 0.385 
2011 0.971 0.471 0.616 0.791 0.129 0.325 

WA’ denotes the comprehensive fitness of the water resources system; ‘SA’ denotes the comprehensive fitness of the socioeconomic system; ‘EA’ denotes the comprehensive fitness of the eco-environmental system; ‘WAC’ denotes the adaptive coordination index of the water resources system; ‘SAC’ denotes the adaptive coordination index of the socioeconomic system, and ‘EAC’ denotes the adaptive coordination index of the eco-environmental system.

Table 7

Fitness values of the problem domain of the study area water security system

Year 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 
Fitness value 0.453 0.528 0.503 0.517 0.520 0.558 0.600 0.634 0.610 0.632 
Year 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 
Fitness value 0.453 0.528 0.503 0.517 0.520 0.558 0.600 0.634 0.610 0.632 

Adaptability analysis of the water safety system in the study area

According to the absolute fitness, relative fitness, and comprehensive fitness values in Table 5, the fitness bar graph of each element of the study area's water security system is obtained (see Figure 3). Based on the data in Table 6, the comprehensive fitness and coordination index change curves of each sub-problem domain are also obtained (see Figure 4). Finally, the comprehensive fitness change curve of the study area's water security system problem domain is determined (see Figure 5).

Figure 3

Bar chart of each fitness value of each element in the problem domain of the study area's water security system.

Figure 3

Bar chart of each fitness value of each element in the problem domain of the study area's water security system.

Figure 4

Sample fitness value and coordination index value in each sub-problem domain.

Figure 4

Sample fitness value and coordination index value in each sub-problem domain.

Figure 5

Line chart of the problem domain fitness values for the study area's water security system.

Figure 5

Line chart of the problem domain fitness values for the study area's water security system.

Element (index)

Figure 3 shows that the absolute fitness values of each element are significantly greater than their relative fitness values. This indicates that each element itself has a strong adaptability to the environment, which is directly related to the good natural foundation in the study area (Liu 2013). The ability of the elements to interact with each other to adapt to environmental change is weak, which is due to the various elements focusing on their own development; mutual interaction is caused by the effects of production. The comprehensive fitness value can fully reflect the ability of each factor to adapt to environmental changes. The result shows that the comprehensive fitness values of X1, X2, X4, X6, X7, X11, X13, X15, X25, X29, and X32 all exceeded 0.5 (mean value of 0.701), which is because the absolute fitness (mean value of 0.863) and relative fitness (mean value of 0.698) of these elements are higher; these elements also have a stronger ability to recover themselves and resist external disturbances. However, the overall fitness values of the remaining factors are below 0.5 (mean value of 0.444), which is due to the absolute fitness (mean value of 0.613) and relative fitness (mean value of 0.438) of these elements being low; these elements tend to mutate when subjected to external conditions or other elements. Therefore, it is an effective measure for improving the comprehensive fitness of each element to strengthen the construction of each element and to improve the coordinated development relationship among the various factors.

Sub-problem domain

For the period 2002–2011, Figure 4(a) shows that the average annual comprehensive fitness values of the water resources, socioeconomic, and eco-environmental system in the study area are 0.795, 0.345, and 0.619, respectively, indicating that the water resources system has good adaptability. The adaptability of the ecological environment system at the medium level during this period, and the adaptability of the socioeconomic system is low. The comprehensive fitness of the studied water resources system shows a rising trend, with an average annual increase of 5.03%, which is mainly due to the abundant water resources (average annual water resources amount of 4.35 × 109 m3) in the study area. Moreover, over the studied period, the comprehensive supply of groundwater increases (maximum increase of 39.64%), the processing capacity of wastewater treatment facilities increases (average annual growth rate of 85%), and the cost of wastewater treatment facilities increases (average annual increase was 13.71%), improving the adaptability of the water resources system. The comprehensive fitness of the socioeconomic system shows an upward trend, with an average annual increase of 6.94%; this is due to the decrease in the natural growth rate of the population (an average annual decrease of 5.33%), which reduces the pressure on the social and economic development of the study area. Moreover, the proportion of investments in environmental protection accounted for by the GDP increases with an average annual growth rate of 2.02%, which reduces the pollution level of the enterprises in the study area. The grain yield per unit area and regional agricultural production density increases with an average annual growth rate of 3.26% and 3.81%, respectively, which improves the efficiency of agricultural economic development. However, due to the small change in each element and their low comprehensive fitness values, the adaptability of the sub-problem domain is low. The comprehensive fitness of the eco-environmental system fluctuates upward and downward. In 2002–2003, the comprehensive fitness of the system shows a rising trend due to a decrease in the extent of flood damage (decrease of 26.08%) and an increase in vegetation coverage (increase of 0.66%), which reduces the amount of soil erosion in the study area. In 2004–2005, the comprehensive fitness of the system shows a downward trend due to the increase of cultivated land area (increase of 37.25%), which leads to an increase in the fertilizer application rate (increasing range of 7.75%) and an increase in the content of soil toxic substances in the study area; the number of local livestock increases (increase of 4.98%); and the afforestation area decreases (decrease of 49.44%), aggravating the degree of desertification in the study area. In 2006–2011, the comprehensive fitness of the system increases with a maximum increase of 40.65%; the effective irrigation area and the actual irrigation area in the study area increases (average annual increases of 12.60% and 12.85%, respectively), reducing the ecological environment carrying capacity; the local drought and flood disaster degree decreases (average annual decreases of 14.12% and 15.81%, respectively); and the number of livestock grazing decreases (average annual decrease of 2.28%), improving the ability of the eco-environmental system to protect itself against natural disasters.

Figure 4(b) shows that in 2002–2011, the contribution degree of water resources system to the study area's water security system adaptability increases (average annual increase of 9.58%), and the average annual coordination index value is 0.567. The contribution degree of the socioeconomic system to the water security system adaptability decreases (average annual decrease of 7.06%), and the average annual coordination index value is 0.285. The contribution degree of the eco-environmental system to the water security system adaptability exhibits a fluctuating downward trend (maximum decrease of 37.62%), and the average coordination index value is 0.403. The results show that the water resources system enhances the ability of the study area's water security system to adapt to the environmental changes, while the socioeconomic system and the eco-environmental system decrease annually.

Problem domain

Figure 5 shows that in 2002–2011, the comprehensive fitness of water security system in the study area fluctuates upward (maximum increase of 39.96%), and the annual comprehensive fitness is 0.556, which indicates the system adaptability is at level II. The system is barely able to adapt to changes in the environment. Despite the comprehensive fitness of the water resources system and the contribution degree to the problem domain being high, the comprehensive fitness of the socioeconomic and the eco-environmental system (especially the socioeconomic system) and their contribution degree to the problem domain are low; and their contribution to the problem domain decreases each year, which further decreases the comprehensive fitness of the water security system in the study area. Therefore, to improve the water security system adaptability, the healthy development of the water resources system should be promoted. Moreover, vigorous improvements in the sustainable development of the society and economy and the protection and improvement of the quality of the ecological environment are needed.

Suggestions and measures

This study shows that the main reason for the reduced adaptability of the water security system to the changing environment is the low comprehensive fitness of the socioeconomic and the eco-environmental system, and the two systems' contributions to the sustainable development of the water safety system decrease every year. Therefore, effective measures should be taken to improve the fitness and contribution of these two systems; the specific suggested measures are as follows:

  1. Based on the low comprehensive adaptability of the socioeconomic system and the low contribution of the system to the problem domain, the study area should adjust the three major industrial structures and diversify the production methods, which can increase the per capita GDP and reduce the pressure on the water security system caused by the rapid socioeconomic development. The study area also needs to mobilize all social forces to enhance environmental protection and water conservancy construction funds for diversified, multi-channel, and multi-level financing mechanisms related to environmental protection and water conservancy investments. Moreover, the area should improve the relationship between economic development and the use of water resources and the protection of the ecological environment in the study area.

  2. According to the relatively low comprehensive adaptability of the eco-environmental system and the relatively low contribution of the system to the problem domain, the local government should carry out practical farmer fertilizer technical guidance and scientific breeding training, improve farmer fertilizer application technology and grain pest disaster prevention level, and promote farmers to use pollution-free organic fertilizer on farmland, improve soil organic matter content, and increase the effective area of cultivated land. In the fenced grazing areas, controlling livestock grazing quantity, increasing afforestation efforts, continuing to reclaim wasteland, reducing land desertification degree, and reducing the loss of water and soil are all needed.

  3. Although the comprehensive adaptation degree of the study area's water resources system is high in the study period, if we ignore the development scenario of the water resources system, the ability of the water security system to adapt to the changing environment will be seriously hindered. Therefore, to strengthen the social and economic development and ecological environmental protection at the same time, the study area needs to rely on scientific and reasonable development and utilization of water resources, make full use of rainwater resources to replace groundwater surface water, improve the quality and yield of rice using surface water irrigation, and store surface runoff decreased by groundwater exploitation (the groundwater to vertical replenishment effect can also improve the local ecological environment). Moreover, the way in which wastewater is discharged should be addressed, and the construction of farm sewage treatment facilities should be strengthened. Centralized wastewater treatment emissions act to scatter emissions; strictly controlling new pollution sources of water and a finite period of governance are needed.

CONCLUSIONS

Based on the complex adaptive features in water security systems, the co-evolution theory has been introduced. The adaptability of water security systems is defined as the problem domain, and 33 elements (indicators) and sub-problem domains based on water resources, the social economy, and ecological environment are used. An evaluation index system of water security systems is established. Based on reliable survey data, the unified co-evolution model is used to study the adaptability conditions of a water security system. The results show that the adaptability of the water security system in the study area is low, and the comprehensive fitness shows an upward trend. In the sub-problem domains, the adaptability of the water resources system is high, and the comprehensive adaptability of the system increases every year. Moreover, the adaptability of the socioeconomic and the eco-environmental system is low, the comprehensive fitness of the socioeconomic system exhibits an increasing trend, and the comprehensive fitness of the eco-environmental system fluctuates (average increasing trend). The Euclidean grey weighted correlation method is used to calculate the absolute fitness of each element; this method considers the importance of each element in the system and the fluctuation coefficient, which is the fluctuation in each point correlation coefficient based on its average value. The method fully reflects the influence of the correlation degree between the reference sequence and comparison sequence on the overall correlation degree. The relative fitness of each element is used in the improved co-evolution method, and the method is based on the individual variation in each element in the system based on the principles of competitive exclusion and feature substitution (Shang 2002).

In summary, the unified co-evolutionary model proposed in this paper has good practical significance for studying the adaptability of regional water security systems. Moreover, it provides a reliable basis for improving the adaptability of water security systems.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Grant no. 51479032 and 51579044) and the Natural Science Foundation of Heilongjiang Province, China (Grant no. E201321).

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