Fragmentation Reduction through Farmer-Led Land Transfer and Consolidation? Experiences of Rice Farmers in Wuhan Metropolitan Area, China

: Land fragmentation has become a serious obstacle to agricultural production, and land transfer and consolidation are traditionally emphasized as the two most effective solutions to this quandary. To identify the extent of land fragmentation accurately and systematically, this study selected the number of plots, the average size of plots, and the average distance between plots to calculate the land fragmentation index (LFI). Taking the Wuhan metropolitan area as a case study, this study examined the effectiveness of farmer-led land transfer and consolidation on land fragmentation. The main results are as follows: (a) most of the transferred plots and contracted plots were not spatially adjacent, suggesting that the tenants could not merge and consolidate both plots; (b) land transfer caused the LFI to increase by 2.85%, suggesting that land transfer had intensiﬁed the degree of land fragmentation to some extent; (c) if the transferred and contracted plots were non-adjacent or adjacent but unmerged and unconsolidated, then the LFI might increase or decrease; (d) if the transferred and contracted plots were spatially adjacent, merged, and consolidated, then the LFI decreased signiﬁcantly.


Introduction
Land fragmentation (LF) is a universal trait of all agricultural systems that affects farmland productivity, and as yet, no one has documented a rural society where there was no LF [1]. LF is a complex concept that encompasses four aspects: (i) number of plots; (ii) sizes of plots; (iii) shape of plots; and (iv) distances between plots, or distance between plots and homesteads [2][3][4]. Fragmented landholding exerts both positive and negative effects on agricultural performance. On the one hand, it may increase the utilization of labor resources, optimize the internal structure of planting agriculture, and disperse the natural and market risks in production process [5][6][7][8][9][10]. On the other hand, it may hinder the use of agricultural machinery, increase the costs of agricultural production, arouse the dispute over land ownership, and lessen the marginal productivity of agricultural labor [11][12][13][14][15][16].
As a largely agricultural country with a huge but economically poor rural population, China is confronted by highly severe LF in its rural areas [14,17]. The Household Contract Responsibility System (HCRS) implemented in 1978 contributed to rapid rural and agricultural development by stimulating the farmers' enthusiasm for agricultural production, but also led to each household having possession of numerous small and separate plots of cultivated land [10,18]. According to a report from the Rural Fixed Observation Point of the Ministry of Agriculture in China, the average number of plots per household declined obviously during 2000 to 2015, but the average size of plots per household did not increase accordingly [18]. This finding is somewhat unexpected and concerning.
With the continuous progress of agricultural modernization and mechanization, it has been generally believed that the negative effects of LF have become increasingly obvious

Theoretical Analysis and Hypotheses
To analyze the effectiveness of farmer-led land transfer and consolidation on LF, the first step is to clarify how to measure the degree of LF. There are two main methods for measuring the degree of LF: the single index method and comprehensive index method [7,12]. The single index method usually uses the number of plots, the average size of plots, and the average distance between plots or the average distance between plots and homesteads. It is straightforward and easy to understand, but too one-sided. The comprehensive index method combines information from individual indexes. Simpson's, Januszewski's, and Igbozurike's indexes are the three most commonly used comprehensive indexes [1,14,15]. Simpson's and Januszewski's indexes combine information on the number and sizes of plots but have difficulty discerning which indicator is the dominant one and ignore the distances between plots or the distances between plots and homesteads. Although Igbozurike's index introduces the variable of distance, the regulation of distance is rather vague, so scholars vary in their adoption of the distances between plots or between plots and homesteads. In sum, the traditional indexes are not always suitable, so there is a need for new indexes.
The selection of the measurement indicators of the degree of LF should be based on the characteristics of LF, namely, the number, sizes, and distribution of plots. It is worth noting that the distribution of plots is derived from the distances of each plot to other plots, but the distances between plots and homesteads cannot accurately reflect the spatial distribution of the plots. Therefore, we selected the number of plots (n), the average size of plots (a), and the average distance between plots (d) as the measurement indicators of the degree of LF. Next, we introduced the farmers' grading method to determine the weight coefficients of the three individual indicators and employed the comprehensive index method to calculate the LFI. Because the individual indicators have inconsistent scales or distributions, we normalized the data by the minimum-maximum standardization method, for which a is a negative indicator, whereas n and d are positive indicators.n,â, andd are their respective normalized values while w 1 , w 2 and w 3 are their respective weight coefficients. The formula for LFI can be expressed as: where LFI it represents the LFI of i-th farmer at year t, whose value ranges from 0 to 1. The closer the value to 1, the higher is the degree of LF and vice versa. The livelihoods of the landlord (whose plots have been transferred-out) are less dependent on agricultural production; hence this study focused on the coupling effects of farmer-dominated land transfer and consolidation on the fragmentation degree of the tenants (whose plots have been transferred-in from the landlord). n i0 , a i0 , and d i0 represent the number of plots, the average size of plots, and the average distance between plots, respectively, before land transfer and consolidation, whereas n i1 , a i1 , and d i1 represent the respective values after land transfer and consolidation. To ensure the comparability of the degree of LF, all the values before and after land transfer and consolidation are combined for normalization. The respective normalized values are represented byn i0 ,â i0 , andd i0 , then byn i1 ,â i1 , andd i1 after land transfer and consolidation. Therefore, the LFIs before and after land transfer and consolidation are LFI i0 and LFI i1 , respectively. Now, we discuss three scenarios below for the coupling effects of land transfer and consolidation on LF.
Scenario 1: The transferred and contracted plots are not spatially adjacent, so the tenants are unable to merge and consolidate their transferred and contracted plots. Hence, the number of plots operated by the tenants increases (n i1 −n i0 > 0). Since the number and sizes of the transferred plots cannot be determined, the average size of the plots operated by the tenants may increase or decrease, so (â i1 −â i0 ) cannot be determined. Because the transferred and contracted plots are not spatially adjacent, the average distance between Scenario 2: The transferred and contracted plots are spatially adjacent but have not been merged and consolidated. The possible outcomes of Scenario 2 are similar to those of Scenario 1, e.g., the number of plots operated by the tenants increases, but the sizes of the plots and the average distance between the plots operated by the tenants cannot be determined. Therefore, LFI i1 − LFI i0 is also uncertain.
Scenario 3: The transferred and contracted plots are spatially adjacent, so they have been partially or completely merged and consolidated. The possible outcomes are also similar to those of Scenarios 1 and 2. With complete merging and consolidation, the number of plots operated by the tenants may remain unchanged or decrease (n i1 −n i0 ≤ 0), the average size of the plots operated by the tenants increases (â i1 −â i0 < 0), and the average distance between plots operated by the tenants may become shorter or remain unchanged Based on the above analysis, the following hypothesis can be put forward: land transfer affects LF, but the direction of its action depends on the spatial relationship between contracted and transferred plots, as well as on the extent of merging and consolidation. Only when transferred and contracted plots are spatially adjacent, as well as completely merged and consolidated, can land transfer effectively reduce the degree of LF.

Study Area
Consisting of one provincial capital city, five prefecture-level cities, and three countylevel cities, the Wuhan metropolitan area is located in the central-eastern part of Hubei province ( Figure 1). The Wuhan metropolitan area accounts for only 31.2% of the total area of Hubei province but constituted 53.8% of the total population and 60.3% of the province's gross domestic product (GDP) in 2020 [40]. It possesses a varied and complicated topography with plains, hills, and mountains, which account for 50%, 30%, and 20%, respectively, of the total area [41]. However, the widespread conversion of cultivated land to construction land has intensified LF across the region and has strongly affected agricultural production [42].
transferred and contracted plots are not spatially adjacent, the average distance between plots may shorten or extend, so ) ( is also uncertain. Scenario 2: The transferred and contracted plots are spatially adjacent but have no been merged and consolidated. The possible outcomes of Scenario 2 are similar to those of Scenario 1, e.g., the number of plots operated by the tenants increases, but the sizes o the plots and the average distance between the plots operated by the tenants cannot be determined. Therefore, is also uncertain. Scenario 3: The transferred and contracted plots are spatially adjacent, so they have been partially or completely merged and consolidated. The possible outcomes are also similar to those of Scenarios 1 and 2. With complete merging and consolidation, the number of plots operated by the tenants may remain unchanged or decrease ) 0 , the average size of the plots operated by the tenants increases ) 0 < ( , and the average distance between plots operated by the tenants may become shorter or remain unchanged ) 0 ( Based on the above analysis, the following hypothesis can be put forward: land trans fer affects LF, but the direction of its action depends on the spatial relationship between contracted and transferred plots, as well as on the extent of merging and consolidation Only when transferred and contracted plots are spatially adjacent, as well as completely merged and consolidated, can land transfer effectively reduce the degree of LF.

Study Area
Consisting of one provincial capital city, five prefecture-level cities, and three county level cities, the Wuhan metropolitan area is located in the central-eastern part of Hube province ( Figure 1). The Wuhan metropolitan area accounts for only 31.2% of the tota area of Hubei province but constituted 53.8% of the total population and 60.3% of the province's gross domestic product (GDP) in 2020 [40]. It possesses a varied and compli cated topography with plains, hills, and mountains, which account for 50%, 30%, and 20% respectively, of the total area [41]. However, the widespread conversion of cultivated land to construction land has intensified LF across the region and has strongly affected agri cultural production [42].

Paired Sample t-Test
A paired sample t-test is used to determine whether there is statistical evidence that the mean difference between paired observations on a particular outcome is not equal to zero [43]. This test emphasizes homogeneous test subjects to ensure that the influences of other variables are eliminated so that the relationships between the independent variable and the dependent variables are better represented [44]. Since there are only 138 samples of tenants, it is not suitable to employ regression analysis method to conduct quantitative testing, but it is possible to use paired sample t-test to carry out statistical testing [45]. By comparing whether the mean difference of the LFIs before and after land transfer and consolidation were significantly far from zero, we were able to deduce if land transfer and consolidation had reduced the degree of LF.

Farmers Grading Method
Drawing on expert grading methods, farmers can be selected as the experts who determine the weight coefficients of the measurement indicators of the degree of LF. To ensure the credibility of the farmers' grading, our questionnaires were mainly given to those familiar with the situations of land management and agricultural production. Based on the survey data collected from 775 rice farmers, we summarized the farmers' ratings of the three indicators affecting agricultural production, and the n it , a it and d it have obtained score of 2996, 2974 and 2978, respectively ( Table 1). The weights of each indicator is equal to the score of each indictor divided by the total scores of the three indicators. Therefore, the weights of n it , a it and d it were 0.335, 0.332, and 0.333, respectively. The formula for LFI can be expressed as follows:

Data Source
The data were collected by a survey questionnaire presented to rice farmers in the Wuhan metropolitan area. According to the principle of relative equilibrium and random sampling, 7, 9, 6, and 5 towns in Jiangxia District, Xian'an District, Tongshan County, and Chongyang County, respectively, were selected for the survey. In each town, 3 to 5 villages were selected, and in each village, 10 to 20 rice farmers were selected as the subjects. After excluding 146 invalid samples, in which rice had not been planted, we obtained 775 valid samples from 97 villages in 27 towns in 4 counties. The valid samples of landlords, tenants, and contractors (who neither transferred-out nor transferred-in land) were 56, 138, and 581, respectively. The sample data were tested for reliability and validity before data processing. The results showed that the Cronbach's Alpha coefficient is 0.764, greater than 0.7; the Kaiser-Meyer-Olin value is 0.685, higher than 0.6; the spherical degree of Bartlett's test for sig. value is 0, at 0.01 significant level, indicating that the questionnaire is highly reliable.

Spatial Characteristics of Contracted Land Fragmentation
Since the surveyed area is in the transition zone from plain to hilly and mountain, there is much difficulty in distinguishing between hillocks and plains, and low mountains and hills. Hence, the landform types of the study area are finally divided into two categories: low hillock and plain, low mountain and hill. Table 2 shows the regional difference in the fragmentation degree of contracted land. The average LFI value of the survey areas is 0.376, and the average LFI value of low mountain and hill areas is 3.78% higher than that of low hillock and plain areas. In terms of individual indicator, although the average number of plots in low mountain and hill areas is 12.62% less than that of low hillock and plain areas, the average size of plots is 34.94% smaller than that of low hillock and plain areas, and the average distance between plots is 8.26% greater than that of low hillock and plain areas. These implies that the LF in low mountain and hill areas is more severe than that in low hillock and plain areas. Figure 2 depicts the spatial distribution of LF degree in different landform types. Grading similar individual index value and comprehensive index value of LF into the same group is conducive to comparison. Therefore, using the Jenks natural breaks classification method in ArcGIS, the individual and comprehensive index value of LF were divided into three groups: low, medium, and high. As shown in Figure 2, towns with high and medium LFI value were mostly concentrated in low mountain and hill areas. In terms of single index, towns with the largest average number of plots but largest and medium average size of plots are mostly scattered in low hillock and plain areas, while towns with the furthest average distance between plots were mainly located in low mountain and hill areas.  Table 3 shows the relationship between the transferred plots and the contracted plots. The results show that only 37.68% of the transferred plots are adjacent to the contracted plots. Of the adjacent plots, only 28.85% have been merged and consolidated.  Table 4 represents the changes in the degree of LF before and after land transfer. The LFI after land transfer increased by 0.011 with an increased rate of 2.85%. In terms of individual indicators, the average number of plots increased by 3.043 with an increased rate of 66.44%, the average size of plots increased by 0.017 hectares with an increased rate of 23.61%, and the average distance between plots increased by 17.816 m with an increased rate of 4.13%. These findings imply that land transfer has not reduced the degree of LF but has increased the degree of LF to some extent. The main reasons are the non-adjacency of most of the transferred plots. Even for adjacent plots, the issue of land ownership and    Table 3 shows the relationship between the transferred plots and the contracted plots. The results show that only 37.68% of the transferred plots are adjacent to the contracted plots. Of the adjacent plots, only 28.85% have been merged and consolidated.   Figure 3 describes the relationship between the scale of land management and the degree of LF. No obvious linear relationship exists before land transfer, but a negative correlation that does not pass the significance test appears after land transfer. These findings reveal neither positive nor negative relationships. To further reveal the relationship between the scale of land management and the degree of LF, the group average clustering method was used to divide the rice farmers into three groups: small-scale farmers (<0.5 hectares), medium-scale farmers (0.5-1 hectares), and large-scale farmers (≥1 hectare). As shown in Table 5, before land transfer, the largescale farmers had the highest LFI, followed by the small-scale farmers, then by the medium-scale farmers. After land transfer, the small-scale farmers had the highest LFI, followed by the medium-scale farmers, then by the large-scale farmers. These results are consistent with the findings in Figure 3. However, when the small-and medium-scale farmers transformed into large-scale farmers, the LFI was significantly reduced, indicating that rice farmers paid close attention to the reduction of LF in the pursuit of moderate scales of operation. To further reveal the relationship between the scale of land management and the degree of LF, the group average clustering method was used to divide the rice farmers into three groups: small-scale farmers (<0.5 hectares), medium-scale farmers (0.5-1 hectares), and large-scale farmers (≥1 hectare). As shown in Table 5, before land transfer, the large-scale farmers had the highest LFI, followed by the small-scale farmers, then by the medium-scale farmers. After land transfer, the small-scale farmers had the highest LFI, followed by the medium-scale farmers, then by the large-scale farmers. These results are consistent with the findings in Figure 3. However, when the small-and medium-scale farmers transformed into large-scale farmers, the LFI was significantly reduced, indicating that rice farmers paid close attention to the reduction of LF in the pursuit of moderate scales of operation.  Table 6 summarizes the results of the paired sample t-tests for the change in the degree of LF in Scenario 1. Regardless of an increase or decrease in the degree of LF, the correlation coefficients of the LFI and the three individual indicators are greater than 0.67 and pass the significance test, indicating a significant correlation between the data before and after land transfer, so the paired sample t-test can be employed.
Consistent with the theoretical analysis, the t-tests confirm that the LFI in Scenario 1 may increase or decrease. Specifically, the number and average size of plots increase, whereas the average distance between plots may shorten or lengthen. Since the transferred plots are not adjacent to the contracted plots, the tenants are unable to merge and consolidate them. The change in the average distance between the plots is uncertain. Both situations lead to unsatisfactory outcomes for land transfer in the solution to LF.  Table 7 presents the results of the paired sample t-test for the change in the degree of LF in Scenario 2. When the degree of LF increases, the correlation coefficients of the LFI and the three individual indicators are greater than 0.49 and pass the significance test. When the degree of LF decreases, the correlation coefficients of the LFI and the other two individual indicators, in addition to the number of plots, are greater than 0.88 and pass the significance test. These results indicate that an increase or decrease in the degree of LF results in the data's high correlation before and after land transfer, so the paired sample t-test can be employed.
Consistent with the theoretical analysis, the t-tests demonstrated that the LFI in Scenario 2 may increase or decrease. The average number and size of the plots increase while the average distance between the plots may shorten or lengthen. The adjacency of the transferred plots to the contracted plots is a necessary condition but not a sufficient condition for the reduction in the degree of LF. However, even if the transferred and contracted plots are spatially adjacent, the problems of land ownership and the normalization of land transfer hinder merging and consolidation by the tenants. Therefore, land transfer aimed at preventing LF may be unsuccessful.  Table 8 shows the results of the paired sample t-test for both the presence of changes (increase or decrease) and lack of changes in the number of plots in Scenario 3. When the number of plots increases, the correlation coefficients of the LFI and the average size of plots are greater than 0.56 but do not pass the significance test, whereas the correlation coefficients of the number of plots and the average distance between plots are greater than 0.78 and pass the significance test. When the number of plots does not change or decrease, the correlation coefficients of the LFI and the three individual indicators are greater than 0.73 and pass the significance test, indicating that regardless of the presence or absence of a change in the number of plots, there is a significant correlation between the data before and after land transfer and consolidation, so the paired sample t-test can be employed.
Inconsistent with the theoretical analysis, the t-tests demonstrated that the LFI in Scenario 3 decreases significantly. When the average number of plots increases, the average size of the plots enlarges and the average distance between plots shortens, contributing to a significant decrease in the LFI. However, the theoretical analysis shows that when the number of plots increases, the change in the LFI is uncertain. The main reason for such an outcome is the small scale of operation and fragmented holdings of cultivated land, which result in lower agricultural productivity and incomes. When the transfer of cultivated land is allowed and the rent is within the acceptable range, farmers have incentives to transfer in the larger plots that are adjacent to the contracted plots, then merge and consolidate them. However, the keys to solving the problem of LF lie in the willingness of the landlords to let the tenants merge and consolidate their contracted plots, as well as the willingness of the tenants to do so. Therefore, the coupling effects of land transfer and consolidation are limited by strict matching conditions, as only 10.87% of the tenants have partially or completely merged and consolidated their transferred and contracted plots.

The Advantage of the New LFI
There are two perspectives by which to measure the degree of LF: micro-farmer perspective [3,5] and macro-region perspective [8,10]. From the perspective of the microfarmer, the measurement indicators of LF include the number, sizes, and distribution of plots. From the perspective of the macro-region, the selection of measurement indicators is generally based on GIS technology and landscape ecology. In addition to the number, size, and distribution of the landscape, its shape is considered. However, the macroregion perspective describes only the physical fragmentation of land and does not consider ownership fragmentation. In contrast, the micro-farmer perspective takes both the physical and ownership fragmentation into consideration. Additionally, farmers are the main force in land management and the core subject of fragmentation treatment in China, so it is more reasonable to select the measurement indicators of the degree of LF from the micro-farmer perspective.
The selection of the measurement indicators should be based on the attribute characteristics of LF, and the distribution of plots is based on the distances of each plot from other plots. Compared with the distances between plots and homesteads, the distances between plots can better reflect how the plots are spatially distributed. Therefore, we selected the number of plots, the average size of plots, and the average distance between plots as the measurement indicators of the degree of LF, then introduced the farmers' grading method to determine the weight coefficients of the three individual indicators, and finally employed the comprehensive index method to calculate the LFI. Compared with Simpson's, Januszewski's, and Igbozurike's index, the new index not only combines information on the number and sizes of plots but also combines information on the distribution of plots. In addition, this new index can also identify the contribution of a single indicator to the composite index. Therefore, the new index significantly outperforms the existing indices, which will lay a foundation for the study of degree, effect, and governance of LF.

Policy Implications and Limitations
The average LFI value of low mountain and hill areas is higher than that of low hillock and plain areas. In the low hillock and plain areas, the main causes of LF were property factors such as the land equalization system under the HCRS, followed by natural factors such as hydrological conditions; both of these ultimately left each household in possession of numerous small and separate plots of cultivated land. In the low mountain and hill areas, the main causes of LF were natural factors such as geomorphic conditions, followed by the property factors, which ultimately left each household in possession of many rugged and irregular-shaped plots of cultivated land. Therefore, the treatment measures for LF must be targeted and differentiated. In the low hillock and plain areas, the key to solving the fragmentation problem lies in promoting the benign interaction between labor force transfer and cultivated land transfer by strengthening the development of factor markets in rural areas, especially the labor force market and land transfer market. In the low mountain and hill areas, under the premise of minimizing excessive disturbance to the ecological environment, the land leveling projects should be carried out in accordance with local conditions, so as to form a unique and well-scattered landscape of "terraced filed" and "low slope hills". Additionally, it is necessary to accelerate the development of small agricultural machinery suitable for hilly and mountainous operations, and vigorously cultivate agricultural machinery specialized service households and agricultural machinery cooperative organizations.
The farmer-led land transfer and consolidation focus on solving the problem of LF faced by farmers, who decide for themselves whether to participate in land transfer and consolidation rather than being forced to join by the government, the village cadres, or the new types of agricultural business entities (NABE), such as leading agricultural enterprises and specialized farmers cooperatives. A community of shared interests is formed under the condition that farmers participate voluntarily so that land transfer and consolidation become an internal requirement of farmers. The control of LF has a broader public awareness. Farmer-led land transfer and consolidation internalize the complex problem of LF, which requires rational decisions made by different farmers after comprehensive weighing. However, intended to accelerate the cultivation of NABE, preferential policies, regardless of land transfer or consolidation, issued by the Chinese government tend to support the development of NABE while not paying enough attention to farmers. Although the NABE do play an important role in the treatment of LF, farmers are and will remain the main force in land management and the core subject of fragmentation treatment for a long time to come [46,47]. Therefore, the land transfer and consolidation dominated by the NABE could not be regarded as a solution to the problems faced by farmers. While maintaining smallholder operations, the government should provide more funding and technical support to farmers in order to encourage their participation in land transfer and consolidation as a solution to LF.
This study focus on the quantitative evaluation of LI Change before and after land transfer and consolidation led by rice farmers. However, the development degree of land transfer market in Wuhan metropolitan area is relatively low, and only 138 farmers participated in land transferred-in, accounting for 17.81% of the total number of samples. Therefore, it is not going to be possible to draw any robust conclusions from that small number of cases. However, this study aims to explain the observed phenomenon and reveal the underlying mechanism. The rationality of conclusions should be verified by using large-scale data covering different natural and socio-economic conditions.

Conclusions
Wuhan metropolitan area presents a particularly interesting case for investigating LF, as it is a consequence of the The HCRS carried out in 1978 in China. The HCRS is considered as the most important cause of small operation and fragmented holding of cultivated land, and these two problems have persisted to the present day. Although there have been several studies on whether land transfer or consolidation reduces LF, no evidence exists for the effectiveness of farmer-led land transfer and consolidation. Hence, our study fills a gap in the literature by taking the Wuhan metropolitan area as a case study and analyzing the effectiveness of farmer-led land transfer and consolidation on LF. The main conclusions are summarized as follows.
No matter whether it is from individual indicators or from comprehensive index, there are spatial differences in degrees of LF. However, from the perspective of individual indicators, it is impossible to judge the degree of LF in different landform types. Contrarily, from the perspective of comprehensive index, it can be intuitively found that the fragmentation of low mountain and hill areas is higher than that of low hillock and plain areas.
There are neither positive nor negative relationships between the scale of land management and the degree of LF. Before and after land transfer, no obvious linear correlation exists between them. However, when small-and medium-scale farmers transform into large-scale farmers, the LFI is significantly reduced, indicating that farmers pay close attention to the treatment of LF in their pursuit of economies of scale in agricultural production.
The treatment of LF depends on the coupling effects of land transfer and consolidation. Land transfer caused the LFI to increase by 2.85%, which means that relying solely on land transfer does not reduce LF and may even intensify it. The main reason is the non-adjacency of most transferred plots and contracted plots, so the tenants are unable to merge and consolidate them. Only spatially adjacent transferred plots and contracted plots that have been merged and consolidated can effectively reduce LFI.

Data Availability Statement:
The data that support the findings of this study are available from the first author Chaozheng Zhang, upon reasonable request.