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Journal of Resources and Ecology >

2022 , Vol. 13 >Issue 6: 1116 - 1127

DOI: https://doi.org/10.5814/j.issn.1674-764x.2022.06.016

Land Resource and Land Use

Exploring the Scale Effects of Trade-offs and Synergies of Multifunctional Cultivated Land—Evidence from Wuhan Metropolitan Area

  • YANG Fengyanzi , 1, 2 ,
  • HU Weiyan , 1, *
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  • 1. College of Public Administration, Huazhong Agricultural University, Wuhan 430070, China
  • 2. Wuhan Planning and Research and Exhibition Center, Wuhan 430014, China
* HU Weiyan, E-mail:

YANG Fengyanzi, E-mail:

Received date: 2020-12-28

  Accepted date: 2021-08-30

  Online published: 2022-10-12

Supported by

The National Natural Science Foundation of China(71673105)

The Fundamental Research Funds for the Central Universities(2662016PY116)

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Abstract

The purpose of this paper is to explore the trade-offs and synergies of multifunctional cultivated land (MCL) at multiple scales. The study area is Wuhan Metropolitan Area, China. The entropy method and the method of Spearman's rank correlation were employed for the analysis of combined land use/cover data, administrative division data, population data and statistical yearbook data, from the multi-scale perspectives of cities, counties and townships. The results showed that: (1) The multi-functionality of cultivated land had obvious spatial differences and its overall spatial patterns were relatively robust, which did not change very much at the single scale. (2) At each single scale, the MCL's trade-offs and synergies had spatial heterogeneity. (3) Scale effects existed in the MCL's trade-offs and synergies. From the prefecture-level city scale, to the county scale, and to the township scale, the MCL's trade-offs were changed to synergies, and some synergic relationships were enhanced. This article contributes to the literature by deepening the multiscale analysis of trade-offs and synergies of multifunctional cultivated land. The conclusions might provide a basis for helping policy-makers to implement protection measures for the multi-functionality of cultivated land at the right spatial scale, and to promote the higher-level synergies of multifunctional cultivated land to realize its sustainable use.

Key words： sustainable cultivated land use; multifunctional cultivated land; trade-offs and synergies; scale effects; Wuhan Metropolitan Area

Cite this article

YANG Fengyanzi , HU Weiyan . Exploring the Scale Effects of Trade-offs and Synergies of Multifunctional Cultivated Land—Evidence from Wuhan Metropolitan Area[J]. Journal of Resources and Ecology, 2022 , 13(6) : 1116 -1127 . DOI: 10.5814/j.issn.1674-764x.2022.06.016

1 Introduction

Cultivated land is one of the most important factors for agricultural production and a scarce resource and environmental element. It has multi-functional characteristics, including food production functions, ecological adjustment functions, social security functions, and landscape cultural functions (OECD, 2001; Song and Ouyang, 2012). Globally, single-function productive agriculture has had a huge impact on soil quality, food security, ecological environment and rural vitality since the 1970s. As the most important element of agricultural operations, multifunctional cultivated land has been used as a strategy for maintaining agricultural and rural development in a sustainable way (Lee et al., 2009; Huang et al., 2015). This is especially true in China, where 22% of the world's population was fed by only 7% of the world's cultivated land (Liu et al., 2017). However, with the rapid development of industrialization, urbanization, informatization and agricultural modernization, a large amount of cultivated land resources is being lost, pollution is serious, and the quality of cultivated land is degraded (Zhang and Chen, 2014; Qian et al., 2016). In this situation, the Chinese government has attached great importance to the improvement and protection of the production function of
cultivated land, and adopted the world's most stringent cultivated land protection policy in terms of both quantity and quality. In recent years, the Chinese government has gradually strengthened its understanding of the multi-functionality of cultivated land, especially the ecological functions and social security functions. The protection of cultivated land has gradually shifted from the protection of quantity and quality to a more comprehensive protection in terms of quantity, quality and ecology (Qi et al., 2018). In addition, since 2013, the Chinese government has clearly implemented several strategies and programs, such as the ecological civilization construction strategy, the rural revitalization strategy, and the territory spatial development and protection plan, which were proposed to realize the value of multiple functions in the countryside, and to foster the sustainable use of the multiple functions of limited cultivated land resources. However, due to the diversity of cultivated land function types, the imbalance of spatial distribution and the selectivity of human use, the functions of cultivated land are often mutually promoted or inhibited, that is to say, there are trade-offs and synergies in the functions of cultivated land (Rodriguez et al., 2006; Swallow et al., 2009; Wu et al., 2013). Considering the trade-offs and synergies between multiple functions in the decision-making and spatial planning of cultivated land protection and utilization is beneficial for avoiding negative effects, for promoting the coordinated development of various functions, and is of great significance for deepening cultivated land protection, and its sustainable use and management.
Trade-offs and synergies can be classified by spatial scale, temporal scale, and reversibility (Deng et al., 2016). Trade- offs and synergies of multifunctional cultivated land have been assessed at many different spatial scales, such as the grid scale. Based on land use/cover data and statistical yearbook data, Dong and Zhao analyzed the trade-off and synergy of multifunctional cultivated land in Qingpu District, Shanghai, and they found synergistic relationships in the production and ecology functions and the production and landscape functions, but a trade-off relationship in the ecology and landscape functions (Dong and Zhao, 2019). Zhu et al. (2018) used socio-economic, soil and meteorological data of 2000, 2005, 2010 and 2013, to reveal the dynamic spatial-temporal pattern of trade-offs and synergies of multifunctional cultivated land. The results indicated that there were many synergic relationships among the cultivated land functions; the relationships among some functions even changed from synergy to trade-off and the synergy degree declined while the trade-off gradually increased. The versatility of cultivated land can be investigated at various scales, e.g., farm scale, regional scale, national scale, etc. (Lee et al., 2009). Raudsepp-Hearne et al. used a case study in Québec, Canada, to analyze the scales of production, consumption, and management of 12 ecosystem services and to analyze how interactions among these ecosystem services change across three scales of observation (1, 9, and 75 km²) (Raudsepp-Hearne and Peterson, 2016). Stürck and Verburg tested different multifunctionality indicators at various spatial scales, and the results indicated that the analysis scale determines the interpretation of landscape multifunctionality (Stürck and Verburg, 2017). However, the existing literature on the scale effect of the multiple functions of cultivated land remains less comprehensive (Raudsepp-Hearne and Peterson, 2016; Liu et al., 2017; Cao et al., 2020), and the research on the administrative multi-scale is poorly understood.
The Chinese government implements the management of cultivated land through the establishment of a proxy-agent mechanism. Under this mechanism, the provincial governments transfer their powers to cities, counties, and townships through a semi-vertical management system of layered entrusted and hierarchical agency. Due to the long principal-agent chain, there are significant differences in the willingness, behavior and goals of the different actors in protecting cultivated land (Wang et al., 2008), and the trade- offs and synergies of multifunctional cultivated land may also have a significant scale effect. To this end, we conducted this research from the administrative management scale. The overriding question to be answered in this article is: Is there an administrative scale effect in the trade-offs and synergies of multifunctional cultivated land? Exploring the scale effect of the trade-offs and synergies is conducive to formulating agricultural spatial control policies, effectively managing the trade-offs among cultivated land multifunctionality, and improving the sustainable use of cultivated land.

2 Materials and methods

2.1 Study area and research framework

The study area is Wuhan Metropolitan Area in central China, in the east of Hubei Province, and occupies an area of 5.78×104 km2 (Fig. 1). There are 9 cities of Wuhan, Huangshi, Huanggang, Ezhou, Xiaogan, Xianning, Qianjiang, Xiantao and Tianmen, including 39 counties, and 474 townships. According to statistics, the Wuhan Metropolitan Area had a permanent population of 31.6209 million in 2017 and a regional GDP of 2262.8 billion yuan, accounting for 56.6% of the province's total permanent population and 61.9% of the province's total GDP, respectively. It is the core area of Hubei's economic development. In 2007, the Wuhan Metropolitan Area was approved by the State Council as the “National Resource-saving and Environmentally Friendly Society Construction Comprehensive Supporting Reform Pilot Zone”. At the end of 2016, Wuhan was officially approved as the “National Central City Construction”.
Fig. 1 Location of the Wuhan Metropolitan Area in China
With all those establishments of programs, the study area is in the process of all-round development at a rapid rate. The demand for construction land in the Wuhan Metropolitan Area has increased. The area of cultivated land has dropped from 3.029 million ha in 1990 to 2.773 million ha in 2015. According to the “Investigation and Evaluation of Cultivated Land Quality Grades in China (National Volume)”, the quality of cultivated land in Wuhan Metropolitan Area is excellent (Liu et al., 2018), and it serves as an important commodity grain, cotton and oil production base in China. In 2017, the “Territory Planning Outline (2016-2030)” issued by the State Council of China classified the “Wuhan Metropolitan Area” as a “Human Settlement Ecology and Quality Farmland Maintenance Zone”. This means that in the process of economic development, the Wuhan Metropolitan Area is facing tremendous pressure regarding cultivated land protection.
As one of the largest urban groups in central China, the urban ripple effect and regional development pattern of Wuhan Metropolitan Area make the cultivated land not only have the functions of agricultural production, social security and ecological regulation, but it also has the landscape leisure function highlighted by the development of multi- functional modern agriculture with cultivated land as the carrier. Determining how to promote the coordinated development of multifunctional cultivated land in Wuhan Metropolitan Area, actively guide the territory development plan, optimize the functional relationships among urban space, agricultural space and ecological space, and strengthen cultivated land protection in quantity, quality and ecology have become important research topics.
This paper describes the construction of an evaluation index system of multifunctional cultivated land at the city, county and township scales, and discusses the relationships between the multi-functional trade-offs and synergies of cultivated land in the study area. The technical route is shown in Fig. 2.
Fig. 2 Technical roadmap of the trade-offs and synergies of multifunctional cultivated land
The multifunctional cultivated land that was only quantified at the city or county scale is marked with an asterisk, additional functions were quantified at all scales; y1ij, y2ij, y3ij and y4ij represent the total grain output, vegetable output, melon and fruit yield and agricultural chemical fertilizer application amount of the jth Township in the ith county administrative region, Y1i, Y2i, Y3i and Y4i represent the total grain output, vegetable output, melon and fruit yield and agricultural chemical fertilizer application amount of the ith county, Aij represents the total cultivated land area of the jth township in the ith county, and Si represents the total cultivated land area of the ith county.

2.2 Evaluation index system of multifunctional cultivated land

Referring to existing relevant research (Wiggering et al., 2006; Brandão et al., 2010; Xie et al., 2010; Fan et al., 2018; Gong et al., 2019), and considering the particular features of the cultivated land in Wuhan Metropolitan Area and also the access to data, we divided the cultivated land function into four functions: production function, ecological function, social function and landscape function. A multi-functional evaluation index system of cultivated land was established for the city, county and township at the three levels of administrative scale. The specific index interpretation is shown in Table 1.
Table 1 Evaluation system of multifunctional cultivated land in the Wuhan Metropolitan Area
Function type Evaluation index Property Calculation method** Weights
City County Township
F1:
Production function		 F11: Grain yield (t) +
${{y}_{1ij}}={{Y}_{1i}}\times \frac{{{A}_{ij}}}{{{S}_{i}}}$. 0.0769 0.1028 0.1102
F12: Vegetable yield (t) + ${{y}_{2ij}}={{Y}_{2i}}\times \frac{{{A}_{ij}}}{{{S}_{i}}}$. 0.1308 0.1388 0.2296
F13: Fruit yield(t) + ${{y}_{3ij}}={{Y}_{3i}}\times \frac{{{A}_{ij}}}{{{S}_{i}}}$. 0.1399 0.1347 0.2423
F14: Land reclamation rate (%) + Cultivated land area / total land area 0.0504 0.0611 0.0592
F2:
Ecological function		 F21: Fertilizer application rate (t) - ${{y}_{4ij}}={{Y}_{4i}}\times \frac{{{A}_{ij}}}{{{S}_{i}}}$. 0.0278 0.0331 0.0109
F22: Carbon fixation and oxygen release (t ha-1) + CO2 Absorption + O2 Release 0.0786 0.1030 0.1107
F23: Habitat fragmentation (/) - (Area fragmentation index + distribution fragmentation index)/2 0.0379 0.0436 0.0326
F24: Per capita ecological carrying capacity of cultivated land (/)* + Per capita cropland resource endowment × cropland yield factor × cropland equilibrium factor 0.0441 0.0438
F3:
Social function		 F31: Food self-sufficiency ratio (%) + Food output/ (resident population × 400 kg) 0.0434 0.0610 0.0772
F32: Per capita cultivated land area
(m2 person-1)		 + Cultivated land area / resident population 0.0470 0.0391 0.0567
F33: Proportion of agricultural output value (%)* + Agricultural output value/GDP 0.0878 0.0782
F34: Proportion of employed population in primary industry* (%) + Number of employees in primary industry / total number of employees 0.0547
F4:
Landscape function		 F41: Aggregation index (/) + Fragstats 4.2 (AI） 0.0415 0.0396 0.0233
F42: Shannon's diversity index (/) + Fragstats 4.2 (SHDI) 0.0527 0.0372 0.0161
F43: Contagion index (/) + Fragstats 4.2 (CONTAG) 0.0318 0.0393 0.0164
F44: Perimeter area fractal dimension (/) - Fragstats 4.2 (PAFRAC） 0.0548 0.0446 0.0148

Note: (1) F24、F33、F34 marked with an asterisk mean the multifunctional cultivated land that were only quantified at the city or county scale and the other functions were quantified at all scales; (2) In the calculation method, y1ij, y2ij, y3ij and y4ij represent the total grain output, vegetable output, melon and fruit yield and agricultural fertilizer use amount of the j-th township in the i-th county administrative region, respectively; Y1i, Y2i, Y3i and Y4i represent the total grain output, vegetable output, melon and fruit yield and agricultural fertilizer use amount of the i-th county, respectively; Aij represents the total cultivated land area of the j-th township in the i-th county, and Si represents the total cultivated land area of the i-th county.

2.2.1 Production function of cultivated land

The production function of cultivated land refers to the ability of human beings to control the growth and development of crops through labor in order to obtain agricultural products such as grains, vegetables, melons and fruits (Fan et al., 2018). As an important agricultural supply, the production capacity of grain, vegetables, and fruits is an important manifestation of the production function of cultivated land. The land reclamation rate reflects the degree of regional cultivated land development and utilization, and has an important impact on the stability of the structure and production function of the cultivated land system. Hence, this article uses the indicators of grain output, vegetable output, melon and fruit output and land reclamation rate to measure the production function of cultivated land.

2.2.2 Ecological function of cultivated land

The ecological function of cultivated land refers to the ability of the cultivated land ecosystem to maintain the balance of the ecosystem together with forest land, grassland, and water areas (Jiang et al., 2011). All kinds of crops continuously absorb CO2 and release O2 during the growth period to maintain the balance of carbon and oxygen in the cultivated land ecosystem. Since cultivated land is a natural/artificial composite ecosystem, the use of chemical fertilizers and pesticides in the production process of crops will cause damage to the agricultural ecological environment, and the interference of human use will also cause the fragmentation of biological habitat. Hence, this article comprehensively selects the amount of agricultural chemical fertilizers, the amounts of carbon fixation and oxygen release, the degree of habitat fragmentation and the ecological carrying capacity of cultivated land per capita to measure the ecological functions of cultivated land.

2.2.3 Social function of cultivated land

The social function of cultivated land refers to the ability of cultivated land to ensure food security and to provide services such as employment and pension for farmers. In China, the social security system for farmers is not yet sound. When farmers' material base is insufficient or lacks non- agricultural employment opportunities, cultivated land can maintain the basic level of farmers and enhance their ability to resist social risks and crises, which is important for the stability of society (Liu, 2013). The livelihoods of farmers in the Wuhan Metropolitan Area are still largely dependent on self-produced food, and their cultivated land has a social security function. Hence, this paper selects the self-sufficiency rate of grain, per capita cultivated land area, the proportion of agricultural output value, and the proportion of the population employed in the primary industry to characterize the social functions of cultivated land, such as food security and employment guarantee.

2.2.4 Landscape function of cultivated land

The landscape cultural function of cultivated land refers to the provision of aesthetic enjoyment, leisure and recreation, cultural education and other services for the people based on the cultivated land landscape, which is mainly manifested in two aspects: the quality of cultivated land landscape natural resources and the convenience of access (Peng et al., 2016). Based on the conditions of the cultivated land landscape, considering the regularity and concentration of cultivated land, this paper selected the cultivated landscape Aggregation Index (AI), Landscape Diversity Index (SHDI), Landscape Spread Index (CONTAG) and the shape of the cultivated land plot to quantify the cultivated landscape functional degree. The shape of the cultivated land plot is expressed by the fractal dimension in the landscape pattern index.

2.3 Data sources

In this study, the research is conducted on three administrative scales: city, county, and township. After merging the streets in the central city, it includes 9 cities, 39 counties, and 474 townships (Fig. 1). This study uses multi-source datasets to evaluate the multiple functions of cultivated land, including land use/cover datasets, satellite image datasets, administrative division datasets, population datasets, statistical datasets and related auxiliary datasets. The detailed descriptions of the data sources are shown in Table 2, and the basic land use data processing method follows three steps. 1) Image processing is performed on remote sensing image data based on field survey data and related geographic maps, land use data is obtained through human-computer interaction interpretation, and the accuracy of the data are verified. The accuracy of the cultivated land data is not less than 85%, and the accuracy of the non-cultivated land data is not less than 80%. 2) Combined with the vector data of city, county and township administrative divisions, ArcGIS 10.4 is used for raster clipping to obtain land use data of the administrative units at all scales, and cultivated land and non-cultivated land are reclassified, assigning cultivated land to 1 and non-cultivated land to 0. 3) The raster calculator in the 3D analyst tool is used to obtain the basic data of the cultivated land of administrative units at all scales. In addition, the population grid data is connected to the cities, counties, and townships by using ArcGIS 10.4 spatial connection tools, and summarized to each city, each county and each township through statistical data tools.
Table 2 Data sources and descriptions
Type Source Format
Land use/cover Bureau of Natural Resources and Planning of Hubei Province Vector
Administrative division data NGCC (http://www.ngcc.cn/ngcc/) Vector
Population data Resource and Environment Science and Data Center (http://www.resdc.cn/) Raster
Socioeconomic statistics Hubei Provincial Bureau of Statistics (http://tjj.hubei.gov.cn/) Spreadsheet
Agricultural production data Hubei Provincial Bureau of Statistics (http://tjj.hubei.gov.cn/) Spreadsheet

2.4 Data processing

2.4.1 Standardization and determining the weights of

indicator data
Due to the different dimensions of the cultivated land function evaluation index, the range standardization method was used to process the evaluation index non-dimensionally. For the positive index, it was as follows:
${{y}_{ij}}=\frac{{{x}_{ij}}-\min ({{x}_{ij}})}{\max ({{x}_{ij}})-\min ({{x}_{ij}})}$
For the negative index, it was as follows:
${{y}_{ij}}=\frac{\max ({{x}_{ij}})-{{x}_{ij}}}{\max ({{x}_{ij}})-\min ({{x}_{ij}})}$
where ${{x}_{ij}}$ is the original indicator value and ${{y}_{ij}}$ is the normalized index value.
The entropy method was used to calculate the weight value of each evaluation index on the different scales. The specific calculation formula is shown in Equation (3):
${{w}_{j}}=\frac{1-{{e}_{j}}}{n-\sum\limits_{j=1}^{n}{{{e}_{j}}}}$
where, $~{{e}_{j}}=-k\sum\limits_{i=1}^{m}{{{P}_{ij}}\ln {{P}_{ij}}}$, k=lnm, ${{P}_{ij}}={{y}_{ij}}/\sum\limits_{i=1}^{n}{{{y}_{ij}}}$, wj is the weight value of the j-th index, m is the number of evaluation units, n is the number of the evaluation index, ${{e}_{j}}$ is the entropy of the j-th index, $~{{P}_{ij}}$ is the ratio of the standardized value of the ith evaluation unit index in the jth evaluation unit index to the entire evaluation index sequence, and we suppose that when ${{P}_{ij}}=0$, define $\underset{{{P}_{ij\to 0}}}{\mathop{\lim }}\,{{P}_{ij}}\ln {{P}_{ij}}=0$.

2.4.2 Single function measurements of cultivated land

The weighted scores of the production function, ecological function, social function and landscape function index of cultivated land were calculated by the linear weighted model method. The specific calculation formula is as follows:
${{F}_{bi}}=\sum\limits_{j=1}^{n}{{{w}_{j}}\times {{y}_{ij}}} (b=1, 2, 3, 4) $
In the equation, Fbi represents the single function score of cultivated land; wj represents the index weight value, n is the number of cultivated land function classifications, and n represents the number of single function evaluation indexes of cultivated land.

2.4.3 Measurement of multifunctional cultivated land

In the literature, there are many approaches to quantifying multifunctional cultivated land, mainly including the weighted comprehensive index method (Fleskens et al., 2009), Shannon's diversity index (Plieninger et al., 2013) and Simpson's reciprocal index (Stürckand Verburg, 2017; Raudsepp-Hearne et al., 2010). Among them, the comprehensive index method takes the multifunctionality of the cultivated land as a whole, considering the relative importance of each index in the whole, and mainly measures the multifunctional cultivated land in the total amount; and Shannon's diversity index can better measure the diversity of types, but it has defects in reflecting structural characteristics such as quantity uniformity, while Simpson's reciprocal index can better characterize the uniformity of the multifunctional quantity of cultivated land (Stürck and Verburg, 2017). On the basis of the above-mentioned individual function evaluations, we adopted the weighted comprehensive index method and the Simpson's reciprocal index to measure the multifunctionality of cultivated land from the total and structural perspectives, respectively. The calculation formula is as follows:
Weighted comprehensive index method:
${{F}_{i}}=\sum\limits_{b=1}^{4}{{{F}_{bi}}}$
where Fi is the total score of multifunctional cultivated land.
Simpson's reciprocal index:
$SR{{I}_{\theta }}=\frac{1}{\sum\limits_{i=1}^{m}{\sum\limits_{j=1}^{n}{{{\left( \frac{{{y}_{ij}}}{4} \right)}^{2}}}}}$
In the equation, SRIθ is Simpson's reciprocal index at location θ, which reflects the diversity of cultivated land functional types and the uniformity of the quantity. The larger the value of SRIθ, the more diverse cultivated land function types and the more uniform the quantity; yij represents the normalized value of the j-th evaluation index on the i-th research scale.

2.4.4 Correlation analysis approach

Correlation analysis methods mainly include Pearson's correlation (Pearson and Lipman, 1988) and Spearman's rank correlation (Spearman, 2010), which are the most common methods used in trade-off research (Peng et al., 2016). Spearman's rank correlation coefficient uses the rank size of two variables for linear correlation analysis, and does not require any particular distribution of the original variables. It is a non-parametric statistical method and has a wider range of applications. Therefore, we used Spearman's correlation coefficient to analyze the trade-offs and synergies of multifunctional cultivated land. A positive correlation between two cultivated land functions indicates synergy between them, while a negative correlation between a pair of cultivated land functions indicates a tradeoff. If the correlation is not significant, it means that there is an independent relationship between two functions. If the correlation coefficient $0.5<r<1\ \text{or}-1<\ r<-0.5$, it indicates that there is a high correlation between two functions, if $-0.5<r<-0.3$ and $0.3<r<0.5$ it indicates a medium correlation between two functions, and if $0<r<0.3\ \text{or}-0.3<r<0$, it indicates a weak correlation between two functions (Chan et al., 2006; Egoh et al., 2008). The calculation formula is as follows:
${{\rho }_{s}}=\frac{\sum\limits_{i=1}^{N}{({{R}_{i}}-\bar{R})({{S}_{i}}-\bar{S})}}{{{\left[ \sum\limits_{i=1}^{N}{{{({{R}_{i}}-\bar{R})}^{2}}}\sum\limits_{i=1}^{N}{{{({{S}_{i}}-\overline{S})}^{2}}} \right]}^{\frac{1}{2}}}}=1-\frac{6\sum\limits_{i=1}^{N}{d_{i}^{2}}}{N({{N}^{2}}-1)}$
where ${{R}_{i}}$ and ${{S}_{i}}$ represent the value levels of observation i; $\bar{R} $ and $\bar{S} $ represent the average levels of variables x and y; N is the total number of observations; and ${{d}_{i}}={{R}_{i}}-{{S}_{i}}$.

3 Results

3.1 Evaluation of multifunctional cultivated land

We used ArcGIS 10.4 to realize the spatial expression of the single function and multifunctional comprehensive evaluation of cultivated land in Wuhan Metropolitan Area at the three administrative scales of city, county, and township. The evaluation results are shown in Fig. 3, and the specific results are described here. As shown in Fig. 3(1a-1d), at the city level, the high-value areas of cultivated land production functions are located in Wuhan, Xiaogan and Huanggang cities, while the productive functions of cultivated land are weak in Ezhou and Huangshi; the high-value areas for the ecological functions of cultivated land are located in Xiaogan and Huanggang, while the ecological functions of cultivated land are weak in Wuhan and Huangshi; the high-value areas of social functions are located in Huanggang, Tianmen, and Xiantao, while the social functions of cultivated land in Wuhan and Huangshi are weak; and the high value areas of landscape functions of cultivated land are located in Wuhan, Ezhou and Xiaogan, while the landscape functions of cultivated land in Qianjiang and Xianning are weak.
Fig. 3 Multiscale spatial distribution patterns of the single functions of cultivated land in Wuhan Metropolitan Area

Note: From column 1 to column 4, a-d, is used to represent the production function, ecological function, social function and landscape function of cultivated land, respectively; while line 1 to line 3 uses 1-3 to represent city scale, county scale and township scale, respectively.

Figure 3 (2a-2d) shows that, at the county scale, the high values of cultivated land production functions are mainly concentrated in the counties in the Jianghan Plain in the central and western parts of Wuhan Metropolitan Area, and the counties with lower production functions are located in the north and south of Wuhan Metropolitan Area. The high- value counties of ecological functions are mainly concentrated in the east and west of the Wuhan Metropolitan Area, and the low-value counties are mainly located in the middle of the Wuhan Metropolitan Area. The counties with high social functions are mainly concentrated in the periphery of Wuhan Metropolitan Area, showing an obvious spatial pattern of “high periphery and low middle”, while the landscape function values of cultivated land in each county gradually declined from the center of the study area to the periphery.
Figure 3 (3a-3d) shows that, at the township scale, the townships with high values of cultivated land production function are mainly concentrated in the central and western parts of the Wuhan Metropolitan Area; the townships with high ecological functions are mainly concentrated in the western and southern-eastern areas; the townships with high social functions are mainly concentrated in the western, northwestern, southwestern and eastern parts of Wuhan Metropolitan Area in the periphery; and the townships with high values of landscape function are mainly concentrated in the east and west of Wuhan Metropolitan Area and the northern area.
Our analysis demonstrates that the multifunctional degree of cultivated land in Wuhan Metropolitan Area has spatial differences at different administrative scales, and also has obvious spatial differentiation characteristics. Social functions and landscape functions of cultivated land changed evenly across the scales. For other functions, the pattern observed at the smallest scale (township scale) was partially hidden at the largest scale (city scale). From the city scale to the county scale, and then to the township scale, the multifunctionality of cultivated land can be expressed more accurately in space, but the trend of displaying a functional distribution is more obvious on a larger scale. As shown in a-f of Fig. 4, at all scales, the multifunctional cultivated land measured by the weighted composite index method and the Simpson's reciprocal index method have opposite spatial distribution patterns. Our results indicate that the study area still focuses on the single function utilization of cultivated land, and the degree of structural synergy between the various cultivated land functions is low.
Fig. 4 Multiscale spatial distribution pattern of multifunctional cultivated land in Wuhan Metropolitan Area

Note: a-c is the multifunctional degree of cultivated land measured by the weighted comprehensive index method at the city scale, county scale and township scale; d-f is the multifunctional degree of cultivated land measured by Simpson's reciprocal index method at the city scale, county scale and township scale.

3.2 Scale effects of trade-offs and synergies of multifunctional cultivated land

In order to characterize the interactions among the functions of cultivated land at different scales, we used SPSS 24.0 and the “corrgram” package of R to realize the calculation and expression of the trade-offs and synergies of multifunctional cultivated land. The results are shown in Fig. 5, in which different colors are used to indicate the relationships between the functions. Red indicates that the two functions are in a synergistic relationship, and blue indicates that the two functions are in a trade-off relationship. The darker the color, the greater the correlation between the two functions. In the pie chart in the upper right corner of the figure, the filling size of the pie chart represents the correlation coefficient value, i.e., the greater the correlation, the larger the filled area. If the two functions are in a synergistic relationship, the pie chart is filled in the clockwise direction, and for a trade-off relationship it is filled in the counterclockwise direction.
Fig. 5 Scale effect of trade-offs and synergies of multifunctional cultivated land in Wuhan Metropolitan Area

Note: a, b, and c represent the city scale, county scale, and township scale, respectively; *, and ** indicate a significance level of 0.05, and 0.01, respectively.

Our results demonstrate that among the six pairs of correlations on the city scale, the coefficient of the Spearman's rank correlation between production function and ecological function is 0.633, showing a significant synergistic relationship. Meanwhile, the coefficient of the Spearman's rank correlation between social function and landscape function is -0.600, which indicates a significant trade-off relationship. On the county scale, the coefficients of the Spearman's rank correlations between the production function and the ecological function and social function are 0.712 and 0.427, respectively, showing significant synergistic relationships; the ecological function and social function of cultivated land are also in a significant synergistic relationship, with a correlation coefficient of 0.634; and the coefficient of the Spearman's rank correlation between social function and landscape function is -0.380, indicating a significant trade-off relationship. At the township scale, the production function and the other functions (ecological function, social function, and landscape function) all have significant synergistic relationships, with correlation coefficients of 0.749, 0.492, and 0.295, respectively. Similarly, the coefficients of the Spearman's rank correlations between the ecological function and the social function and landscape function are 0.657 and 0.201, respectively, showing significant synergistic relationships.
In our analysis, most trade-offs and synergies among multifunctional cultivated land are robust across the scales, but the relationships between some functions changed with the change of scale. Moreover, the matching relationship between the functions at the township scale is significantly stronger than at the city scale. There are 5 pairs of functions on the township scale that show significant correlations (P<0.01), and there are only 2 pairs of functions on the city scale that express significantly correlated relationships (P<0.05). The relationship between the production function and the ecological function of cultivated land is synergistic at all scales, and the synergy intensity is in the order of: township scale> county scale> city scale. The social functions and landscape functions of cultivated land show an obvious trade-off relationship at the city scale and county scale, and the trade-off intensity is: city scale> county scale. The production function and social function, as well as the ecological function and social function of cultivated land have synergistic relationships at the county and township scales, and the synergy intensity of the township scale is higher than the county scale. In addition, except for the significant trade-off between social functions and landscape functions of cultivated land, there are significant synergistic relationships among other functions. The strength of the trade-off between the social functions and landscape functions of cultivated land decreases with a decrease of the scale, while the synergy among other functions increases with a decrease of the scale.

4 Discussion

The results of trade-offs and synergies of multifunctional cultivated land are affected by the evaluation index of the multifunctional cultivated land. Based on the existing research results and considering the characteristics of the study area, we divided the total functionality of cultivated land into four functions: production function, ecological
function, social function and landscape function. Combined with the current situation of cultivated land use and the availability of data in the Wuhan Metropolitan Area, a multi-level evaluation index system of cultivated land consisting of 13 indicators was established. The multifunctional cultivated land was evaluated at the city scale, county scale, and township scale, and research was carried out on the trade-offs and synergies of the cultivated land.
The results show that the social functions and landscape functions of cultivated land changed evenly across the scales, while the patterns of production functions and ecological functions of cultivated land changed with scale, and the patterns of production functions and ecological functions of cultivated land observed at the township scale were partially hidden at the city scale. These are similar to the findings of the research by Raudsepp-Hearne and Peterson (Raudsepp-Hearne and Peterson, 2016). There are several possible reasons for these results. On the one hand, at some scales, the information of cultivated land functional characteristics cannot be obtained or are entirely absent, which would affect the research results; on the other hand, the connotation of cultivated land function is also variable due to differences in the natural environmental factors such as topography and socio-economic development status at different scales. Further preliminary research shows that the production function and landscape function, as well as the production function and social function of cultivated land in mountainous areas have a higher degree of synergy than in plain areas, while the production function and ecological function of cultivated land in plain areas have higher synergy than in mountainous areas. Relatively speaking, the synergy degree of cultivated land functions in less developed regions is higher, while economically developed areas present a trade-off between production function and landscape function, as well as between social function and landscape function of cultivated land. In the future, we can carry out further research on the feedback mechanism of the scale effect of natural environmental factors and socio-economic development factors in the trade-offs and synergies of multifunctional cultivated land.
In addition, our results demonstrate that whether at the city scale, county scale, or township scale, there is an opposite spatial distribution pattern between the multifunctional cultivated land in total and that in structure. Among them, the cultivated land in the Jianghan Plain has strong multifunctionality in total, but the structure of the multifunctional cultivated land needs to be further optimized, while the Dabie mountain area, Wuhan, Ezhou and Huangshi have great potential for improving the multifunctional cultivated land. Figuring out how to implement the policy of cultivated land protection and utilization and promote the transition of multifunctional cultivated land from trade-offs to synergies are also topics that need further discussion.
Finally, we used linear correlation analysis to discuss the trade-offs and synergies of multifunctional cultivated land, with reference to the most widely used method in the literature. In many cases, however, there may be non-linear relationships between the multiple functions of the cultivated land. Due to the limitations of available research data, we only considered the three administrative scales of city, county and township in exploring the scale effects of trade-offs and synergies of multifunctional cultivated land. The trade-offs and synergies of multifunctional cultivated land in ecological cultivated land construction and at multiple time scales and plot scales also need to be studied further.

5 Conclusions

Based on the land use data and statistical data, we first divided the functions of cultivated land into functions of production, ecological, social, and landscape from the multi- scale perspective of administrative management. Then, a multi-level evaluation index system of multifunctional cultivated land was established to evaluate the multifunctionality of the cultivated land. Lastly, we carried out research on the trade-offs and synergies of cultivated land, and revealed the changes and spatial differences of the multifunctional trade-offs and synergies at different scales. The results show that the multifunctional cultivated land of Wuhan Metropolitan Area has obvious spatially differentiated characteristics at different administrative scales; and there are both scale effects and spatial differences in the trade-offs and synergies of multifunctional cultivated land. The contributions of this paper are that we improved the evaluation index system for multifunctional cultivated land, and carried out research on the trade-offs and synergies of cultivated land at multiple scales. We hope that this research will help to guide the territory development plan, optimize the functional relationships among urban space, agricultural space and ecological space in different scales, and strengthen the “Trinity” protection of cultivated land quantity, quality and ecology. Additionally, we hope it will effectively provide a basis for those working at different administrative levels to try to explore the linkage policies of multifunctional protection of cultivated land, reduce the trade-offs between various functions of cultivated land as much as possible, and promote the synergies and sustainable use of multifunctional cultivated land.

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