2.2.1. System Dynamics Model
System dynamics was proposed by Professor J. W. Forrester of Massachusetts Institute of Technology in 1956. It is a discipline that quantitatively studies nonlinear, high-order, multi-feedback complex systems based on theories related to cybernetics, information theory, and decision theory, and with computer simulation techniques as means [
35,
36]. The demand for arable land is influenced by the regional population, per capita food demand, food yield, the replanting index of arable land, and the grain-to-crop ratio [
25]. It has been used to forecast resource demand, economic development, food demand, etc. [
25,
37,
38] The variables such as population, per capita food demand, and food yield are driven by their related subvariables, and there is some mutual feedback effect of each variable among each and influencing factors. The use of a system dynamics model allows the dynamics of the variables and their associated drivers to be taken into account in an integrated manner, and the prediction results may be more satisfying. The model was run for 2001–2035. Specifically, 2001–2020 was the reference and validation period for the model simulation, which provides a reference for the rationality and accuracy of the model simulation, while 2021–2035 was the forecast period for arable land demand. The system dynamics model of arable land demand was constructed and the variables of interest were determined as follows.
We constructed a model of arable land demand forecasting system based on the structure and function of the determinants of the arable land demand system, in order to forecast the arable land demand in China in the context of ensuring food security (
Figure 1). The model consists of three subsystems: population development subsystem, per capita food demand subsystem, and the grain yield subsystem. The total regional food demand is divided by the food production capacity per unit of arable land area to get the area of arable land demand. Of course, it is also necessary to consider the replanting index of arable land and the proportion of arable land used for growing food crops. Therefore, the arable land demand forecast formula in this paper is as follows.
where
denotes the minimum area of arable land demanded in year
x +
t,
x represents the base year, and
t is the difference between the forecast year and the base year.
denotes the food self-sufficiency rate in year
x +
t;
represents the total population in year
x +
t.
is the per capita food demand in year
x +
t;
is the food production per unit area in year
x +
t;
is the grain-to-crop ratio in year
x +
t;
is the replanting index in year
x +
t.
Regional population change mainly contains two parts: natural population growth and population migration, and the direction and intensity of their effects together determine the direction of population change in a region. The natural population growth is mainly influenced by the birth rate and the death rate of the population, and the combination of the above factors can better predict the total population in different future periods with the following formula.
where
denotes the birth rate in year
x +
t;
represents the population mortality rate in year
x +
t;
is the Chinese population migrating abroad in year
x +
t;
is the overseas population migrating to China in year
x +
t.
Birth and death rates are closely related to local fertility and marriage attitudes, regional policies, medical conditions, and other factors [
39]. In recent years, as China’s economy has grown, the cost of raising children has also risen, which has led to a steady decline in the willingness of Chinese families to have children [
40]. With the increase in the number of young Chinese individuals that have received higher education, it has become increasingly evident that young Chinese individuals are marrying and having children at an older age [
41]. The number of registered married couples and the proportion of the population of childbearing age have a key impact on the birth rate of the population [
42]. Therefore, in this study, we selected the variables of per capita disposable income (
), the number of registered married couples (
), the number of postgraduate students (
), the percentage of the population aged 22–35 (
), and per capita education expenditure (
) as variables of interest to predict the fertility rate in China. Mortality in China is also affected by the quality of life of the population, medical technology, and population aging [
43,
44]. Therefore, in this study,
, the number of medical technicians per 10,000 people (
), and the proportion of the population in the 70 + age group (
) were selected as variables of interest to predict future population mortality in China. The increase in the depth and breadth of China’s participation in the globalization process has made China an increasingly attractive destination country for migrants. Meanwhile, the cross-border reverse and circular flows of Chinese citizens have become increasingly diverse in recent years; thus, migration is a key variable influencing demographic change [
45] (
Table 1,
Table 2 and
Table 3).
- 2.
Per capita food demand subsystem
Food consumption demand is primarily composed of two parts: food for living and food for production. The former is primarily for food rations for residents, while the latter primarily includes feed grains, industrial grains, and seed grains. With the change of residents’ income, living standards, and population age structure, the dietary structure will change accordingly [
47,
48]. As a result, the direct consumption of food rations for residents will exhibit a decreasing trend, while the consumption of meat, eggs, milk, and aquatic products will exhibit a continuous growth trend. Because industrial food and the level of industrial development is closely related, in the future, industrial food demand will grow along with the development of industry. The changes in multiple factors imply that the structure of demand for food will change dramatically in the new era. The formula for forecasting food demand is as follows:
where
,
,
,
represent food rations for residents, feed grains, industrial grains, and seed grains, respectively.
represents meat, egg, and milk consumption,
represents the corresponding food conversion factor,
represents the ratio of edible food, and
represents losses in the process.
- 3.
Food yield subsystem
The quality of arable land, degree of mechanizable cultivation, and degree of irrigatability are factors directly affecting the planting and growth of crops, which will directly affect the yield of crops. Moreover, fertilizers and pesticides are the “food” of food, and the amount of fertilizers and pesticides applied is significantly related to the yield of food crops. Advancements in agricultural science and technology in the broad sense, including crop breeding, technology diffusion, and application, are also instrumental in improving grain yields. Thus, in this study, we selected four variables, namely, year-end ownership of agricultural mechanization, fertilizer and pesticide application, irrigable area, and fixed asset investment in agricultural science and technology, as the variables of interest to predict future grain yields in China.
- 4.
Settings of other parameters
Grain-to-crop ratio is mainly predicted by analyzing changes in the grain-to-crop ratio in the past years, in combination with relevant industrial planning, agricultural restructuring, market demand, and other factors. China’s Grain-to-crop ratio decreased from 0.69 in 2000 to 0.65 in 2003, then increased to 0.69 in 2006, and has since remained stable. Owing to the importance attached to the use of arable land for non-farming purposes, China’s grain-to-crop ratio will gradually decrease as the agricultural structure rationalizes in the future. Thus, in this study, we set a stable grain-to-crop ratio of 0.69 for 2020–2035. Replanting index was primarily predicted by analyzing changes in the replanting index in the past years in combination with changes in climate, agricultural restructuring, cropping systems, production technology, and other factors. Replanting index fluctuated at approximately 1.20 from 2000 to 2006. It exhibited a slow upward trend, stabilized at approximately 1.30 from 2007 to 2013, and then declined to 1.23 in 2015. In this study, we set the future replanting index at 1.21, considering all policies and the implementation of a crop rotation fallow system.
2.2.2. Gray-Markov Model
The future supply area of arable land in China is equal to the existing area of arable land minus the area of arable land lost. The area of arable land lost is equal to the difference between the area of arable land converted to other land and the area of other land converted to arable land. There are numerous drivers of interconversion between arable land and other types of land in China. Economic growth and urbanization are considered to be one of the most important drivers of arable land loss in China [
49], with both economic development and urbanization leading to the conversion of significant amounts of arable land into urban construction land. China is also one of the countries with severe desertification and natural disasters, which cause a substantial amount of arable land to be degraded to wasteland every year [
7]. To alleviate the deterioration of the natural environment, China has implemented the project of “returning farmland to forest and grass”, converting arable land with steep slopes of 25 degrees or more into forest or grass land [
50]. In recent years, in order to promote the development of rural industries and achieve rural revitalization, agricultural restructuring has also led to changes in land use. To curb the loss of arable land, China has put forward the arable land protection policy of “balance of occupation and compensation”, which makes an entity occupying arable land responsible for replenishing arable land of the same quantity and quality as the arable land it occupies [
51]. In summary, the main ways of converting arable land out are construction land occupation, disaster destruction, returning farmland to forest, and agricultural restructuring, while the main way of replenishing arable land is “balance of land occupation and replenishment”.
Equidistant observations are used in Gray-Markov model to predict systems with uncertain factors [
52,
53]. Using the transfer-out data and transfer-in data of various types of arable land in China from 2001 to 2017 as basic data, a gray model was used to predict the future transfer-out and transfer-in of arable land in China. By subtracting the future amount of arable land change from the existing arable land holdings in China, the future arable land holdings can be obtained. The difference between the data of China’s second national land survey and the change data of the first national land survey and other external factors are avoided. The basic modeling steps are as follows.
Construct the original data sequence. Let X(0)(1), X(0)(2), ..., X(0)(x) be the original data of the index to be predicted.
- 2.
Accumulate the original data. To reduce the randomness of the original series, we processed the original data sequence for cumulative generation to obtain new series.
- 3.
Construct accumulation matrix B and column vector Y.
- 4.
The differential equation for Gray-Markov model is .
- 5.
Derive the values of parameters a and b. The values were fitted using the least squares.
- 6.
Construct the Gray-Markov model time response function.
- 7.
Solve the original series x(0) time-response function. The cumulative reduction of the above was performed to derive the reduced value of the original number.