# Exploring the Dynamic Mechanisms of Farmland Abandonment Based on a Spatially Explicit Economic Model for Environmental Sustainability: A Case Study in Jiangxi Province, China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}(Figure 1). This area belongs to a subtropical zone with a humid monsoon climate, an annual average temperature of 16–18 °C and an annual average rainfall of 1300–2000 mm. Due to its terrain is narrow and long, there are large differences between the climate in the southern region and that in the northern region of the study area. The annual average Sunshine is 1473.3–2077.5 h, and the total radiation amount is 97–114.5 kcal/cm

^{2}. The study area is surrounded by three mountains with a chain of undulating hills located in the middle portion. Based on the digital elevation model, 54% of the study area is located at elevations <200 m, 33% at 200–500 m, and 23% at >500 m. The soils are predominantly red soil, yellow soil, and hydromorphic paddy soil. The main vegetation types include subtropical evergreen broadleaf forest, coniferous forest, and broadleaf mixed forests. The main crops in the Jiangxi province include rice, wheat, soybeans, and sweet potatoes. In 2010, the crop planting area covered 3 × 10

^{6}ha, and the study area had a population of 44.56 million and a food productivity of 4.00 × 10

^{7}t. Recently, many people in the study area have participated in non-farm employment due to the development of urbanization and industrialization, and farmland abandonment has become a common phenomenon in the mountainous areas.

#### 2.2. Data

#### 2.2.1. Land Use Data

Land use/land cover class | Land use/land cover subclass |
---|---|

Farmland | Paddy field |

Dry field | |

Forest | Woodland |

Shrubland | |

Open woodland | |

Grassland | High covered grass |

Medium covered grass | |

Low covered grass | |

Water area | River and trench |

Lake | |

Reservoir | |

Permanent glacier | |

Beach | |

Bottomland | |

Built areas | City or town region |

Village residential area | |

Rest construct land | |

Other covers | Sand land |

Gobi | |

Salted land | |

Swamp | |

Bare ground | |

Bare rock | |

Rest of used land |

#### 2.2.2. Data of Biophysical Variables

#### 2.2.3. Socio-Economical Data

#### 2.3. Methods

#### 2.3.1. Spatial Economical Model

^{*}.

^{*}is the proxy for farmland abandonment, and R is the agricultural land rent. If the agricultural land rent is zero or negative, the farmland will be abandoned; otherwise it will be maintained.

Variable Description | Spatial Resolution | Expected Sign * |
---|---|---|

Yield of agricultural product(y)-related variables | ||

Cumulative temperature above 10 °C (day × °C) | 100 m | − |

Annual precipitation (mm/year) | 100 m | − |

Distance to forest edge (m) | 100 m | − |

Soil depth (cm) | 100 m | − |

Content of soil coarse sand (%) | 100 m | + |

Slope (°) | 100 m | + |

Elevation (m) | 100 m | + |

Wage of agricultural labor(w)-related variables | ||

Proportion of employees in the primary sector (%) | County | − |

Rural labor force participation rate (%) | County | − |

Rate of change of rural labor (%/year) | County | − |

Rate of population urbanization (%) | County | + |

Proportion of secondary sector’s output value (%) | County | + |

GDP per capita (￥/capita) | County | + |

Transportation cost(v)-related variables | ||

Distance to central town(m) | 100 m | − |

Distance to village (m) | 100 m | − |

Distance to primary road (m) | 100 m | − |

Structural characteristics in agriculture | ||

Net income of farmer per capita (￥/capita) | County | ? |

Average agricultural area per farmer (ha/farm) | County | + |

Rate of change of farmer (%/year) | County | ? |

Rate of change of employees in the primary sector (%/year) | County | ? |

*****The expected sign refers to the expected relationship between the response and covariates negative, (+) positive, (?) undetermined.

#### 2.3.2. Multivariate Logistic Regression Model

_{ki}in predicting the probability of having p

_{i}. If we assume that x is the response variable and p is the response probability, then the regression model is:

_{i}= P(y

_{i}= 1|x

_{1i}, x

_{2i}, …, x

_{ki}) is the occurrence probability of farmland abandonment when given x

_{1i}, x

_{2i}, …, x

_{ki}, α is the intercept and β is the slope.

_{1}x

_{1}+ β

_{2}x

_{2}+ … + β

_{n}x

_{n})

^{2}, and significance of coefficients. A positive coefficient value means that the odds ratio will increase for a unit increase of the independent variable and vice versa. Whenever the relationship among data can be estimated from a parametric model, the Wald test can be used to test the true value of the parameter [52]. Once we have estimated the model, we must to evaluate this model to assess how and to what extent it is able to describe the dependent variables and data effectively. If we increase the number of independent variables (especially after the continuous independent variables are included in the model), Pearson’s χ

^{2}and Deviation D should not be used to estimate MLE. The Akaike information criterion (AIC) statistic becomes a more useful MLE for estimating logistic regression models with continuous independent variables. Therefore, in this study we use the AIC statistic to estimate the MLE of farmland abandonment in the logistic regression model. The AIC is defined as [53]:

#### 2.3.3. Sampling

_{1}− ln p

_{2}) where p

_{1}and p

_{2}are frequencies of 0 and 1 of the dependent variables [56].

## 3. Results

**Figure 4.**Frequency of observations in areas where agriculture has been maintained (absence) and where farmland abandonment has been observed (presence) along the slope, elevation and distance-to-town gradients in the first period (1990–1995).

**Figure 5.**Frequency of observations in locations where agriculture has been maintained (absence) and where farmland abandonment has been observed (presence) along the slope, distance-to-village and cumulative-temperatures-above-10-degrees gradients in the second period (1995–2005).

^{2}can be used to judge the importance of independent variables. The more the value of Wald’s χ

^{2}for an independent variable, the more important the independent variable is. The results from the spatially explicit logistic regressions for farmland abandonment in the first period indicate that topographic characteristics, level of population urbanization, status of rural labor supply and market accessibility are the most important spatial determinants of farmland abandonment (Table 3). For example, farmland abandonment was more likely on steeper slopes and at higher elevation. The odds ratio for slope is 1.22, which means that an additional slope degree rendered abandonment 22% more likely. For every 100 m of altitude, the risk of abandonment increased by 3% at the 1% significance level. Content of soil coarse sand has a strong positive bearing on abandonment, and an additional percentage point increased abandonment by 6% at the 0.1% significance level. Another important independent variable in the first period is rate of urbanization and the result shows that population urbanization and economic development increased the likelihood of farmland abandonment. The variable Distance to town is positively related to abandonment at the 0.1% significance level, which shows that farmland abandonment was more likely with increasing distance to town. The rate of change of rural labor decreased abandonment by 9% at the 5% significance level.

**Table 3.**Final prediction model of farmland abandonment based on sampling observations in the first period (1990–1995) (Observation: n = 1000).

Variables | Estimator (β) | Standard Error (SE) | Wald χ^{2} Statistics | p Value | EXP (β) |
---|---|---|---|---|---|

Wald-Chi-square: 523.987(p < 0.0001) | |||||

Constant | 21.209 | 5.887 | 12.981 | 0.000 | 2 × 10^{9} |

Cumulative temperature above 10 degrees | −0.001 | 0.000 | 12.439 | 0.000 ^{***} | 0.999 |

Annual precipitation | −0.009 | 0.004 | 5.852 | 0.016 ^{*} | 0.991 |

Distance to forest edge | −0.001 | 0.000 | 9.273 | 0.002 ^{**} | 0.999 |

Soil depth | −0.005 | 0.011 | 0.191 | 0.662 | 0.995 |

Content of soil coarse sand | 0.056 | 0.012 | 22.604 | 0.000 ^{***} | 1.058 |

Slope | 0.201 | 0.025 | 66.942 | 0.000 ^{***} | 1.223 |

Elevation | 0.003 | 0.001 | 8.126 | 0.004 ^{**} | 1.003 |

Proportion of employees in the primary sector | −0.013 | 0.007 | 3.203 | 0.074 | 0.987 |

Rural labor force participation rate | −0.008 | 0.004 | 2.959 | 0.085 | 0.993 |

Rate of change of rural labor | −0.090 | 0.048 | 3.611 | 0.050 ^{*} | 0.914 |

Rate of urbanization | 0.058 | 0.009 | 41.730 | 0.000 ^{***} | 1.060 |

Distance to town | 7.0 × 10^{−5} | 0.000 | 17.243 | 0.000 ^{***} | 1.000 |

Distance to village | 8.0 × 10^{−5} | 0.000 | 1.476 | 0.224 | 1.000 |

Distance to primary road | 2.0 × 10^{−5} | 0.000 | 1.256 | 0.262 | 1.000 |

Net income of farmer per capita | −0.003 | 0.001 | 15.816 | 0.000 ^{***} | 0.997 |

Average agricultural area per farm | 2.404 | 1.203 | 3.993 | 0.046 ^{*} | 11.068 |

Rate of change of employees in the primary sector | 0.059 | 0.042 | 1.931 | 0.165 | 1.060 |

^{2}, distance to village, soil depth, cumulative temperature above 10 degrees, slope, rate of change of employees in the primary sector, and net income of farmer per capita are important variables for farmland abandonment in the second period (Table 4). Farmland abandonment was more likely on the poor-quality land and in the developed areas in the second period. For example, farmland abandonment was also more likely on steeper slopes in the study area. Soil depth had a strong negative effect on abandonment and an additional 1 cm decreased abandonment by 5% at the 0.1% significance level (see Table 4). For the additional percentage for rate of urbanization and proportion of secondary sector’s value, the risk of farmland abandonment increased by 3% at the 1% significance level.

**Table 4.**Final prediction model of farmland abandonment based on sampling observations in the second period (1995–2005) (Observation: n = 1000)

Variables | Estimator (β) | Standard Error (SE) | Waldχ^{2} Statistics | p Value | EXP (β) |
---|---|---|---|---|---|

Wald-Chi-square: 210.703 (p < 0.0001) | |||||

Constant | 12.046 | 2.372 | 25.787 | 0.000 | 1.7× 10^{5} |

Cumulative temperature above 10 degrees | −0.001 | 0.000 | 17.084 | 0.000 ^{***} | 0.999 |

Annual precipitation | −1.9 × 10^{−4} | 0.001 | 0.032 | 0.859 | 1.000 |

Distance to forest edge | 2.6 × 10^{−4} | 0.000 | 6.556 | 0.010 ^{**} | 1.000 |

Soil depth | −0.051 | 0.011 | 23.670 | 0.000 ^{***} | 0.950 |

Content of soil coarse sand | −0.027 | 0.015 | 3.168 | 0.075 | 0.973 |

Slope | 0.080 | 0.022 | 13.382 | 0.000 ^{***} | 1.083 |

Elevation | −0.001 | 0.001 | 1.184 | 0.277 | 0.999 |

Proportion of employees in the primary sector | −0.015 | 0.006 | 5.736 | 0.017 ^{*} | 0.985 |

Rural labor force participation rate | −0.014 | 0.005 | 8.751 | 0.003 ^{**} | 0.986 |

Rate of change of rural labor | −1.113 | 0.724 | 2.364 | 0.124 | 0.329 |

Rate of urbanization | 0.031 | 0.011 | 7.639 | 0.006 ^{**} | 1.032 |

Proportion of secondary sector’s output value | 0.031 | 0.015 | 4.561 | 0.033 ^{*} | 1.032 |

GDP per capita | 7.1 × 10^{−}^{5} | 0.000 | 6.279 | 0.012 ^{*} | 1.000 |

Distance to town | 4.4 × 10^{−}^{5} | 0.000 | 11.315 | 0.001 ^{**} | 1.000 |

Distance to village | 3.5 × 10^{−}^{5} | 0.000 | 26.371 | 0.000 ^{***} | 1.000 |

Distance to primary road | 1.5 × 10^{−}^{5} | 0.000 | 1.102 | 0.294 | 1.000 |

Net income of farmer per capita | −0.002 | 0.001 | 17.766 | 0.000 ^{***} | 0.998 |

Average agricultural area per farm | 2.851 | 0.909 | 9.835 | 0.002 ^{**} | 17.297 |

Rate of change of farm | 0.263 | 0.172 | 2.330 | 0.127 | 1.301 |

Rate of change of employees in the primary sector | −2.380 | 0.618 | 14.838 | 0.000 ^{***} | 0.093 |

Model | AIC | PC | AUC | Kappa |
---|---|---|---|---|

First period model | 0.89 | 0.81 | 0.80 | 0.45 |

Second period model | 1.22 | 0.70 | 0.70 | 0.41 |

## 4. Discussion

## 5. Conclusions

## Acknowledgements

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Xie, H.; Wang, P.; Yao, G.
Exploring the Dynamic Mechanisms of Farmland Abandonment Based on a Spatially Explicit Economic Model for Environmental Sustainability: A Case Study in Jiangxi Province, China. *Sustainability* **2014**, *6*, 1260-1282.
https://doi.org/10.3390/su6031260

**AMA Style**

Xie H, Wang P, Yao G.
Exploring the Dynamic Mechanisms of Farmland Abandonment Based on a Spatially Explicit Economic Model for Environmental Sustainability: A Case Study in Jiangxi Province, China. *Sustainability*. 2014; 6(3):1260-1282.
https://doi.org/10.3390/su6031260

**Chicago/Turabian Style**

Xie, Hualin, Peng Wang, and Guanrong Yao.
2014. "Exploring the Dynamic Mechanisms of Farmland Abandonment Based on a Spatially Explicit Economic Model for Environmental Sustainability: A Case Study in Jiangxi Province, China" *Sustainability* 6, no. 3: 1260-1282.
https://doi.org/10.3390/su6031260