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introduce


Background to the problem


With a growing global population and a growing environmental problem, traditional agricultural models are facing sustainability challenges. Traditional agriculture relies heavily on chemical fertilizers and pesticides, which not only undermines soil health, but also exacerbates water pollution, ecosystem degradation and biodiversity loss. Therefore, organic agriculture is gradually gaining attention as an alternative. It emphasizes the reduction or avoidance of the use of chemicals in agricultural production, the conservation of natural resources and the restoration of agroecology, with the aim of achieving long-term sustainable land use and improving biodiversity.


The implementation of organic farming, while reducing the negative impact on the environment, is often accompanied by high initial investment and production costs, which makes farmers face a dilemma when choosing whether to adopt organic farming methods. For farmers, organic agriculture needs to consider not only economic benefits, but also a comprehensive assessment of its ecological impact and long-term sustainability. How to balance the relationship between economic benefits and ecological protection has become an important issue in the field of agriculture.


In this context, it makes sense to build a rational model to assess the impact of organic agriculture on the agroecosystem and how to optimize farmers' production decisions. The model should be able to take into account factors such as economic benefits, soil health, pest control, plant reproduction, biodiversity, long-term sustainability, etc., and use sensitivity analysis to help farmers assess the impact of different variables on agricultural production, and further help policymakers find appropriate solutions in practice.


In addition, with the introduction of organic farming, many farmers are considering gradually reducing their reliance on chemical herbicides and pesticides. This is not only to reduce environmental pollution, but also to improve soil fertility, increase biodiversity, and restore ecological balance. In this transition, how to integrate natural pest control methods (such as the introduction of bats to control pests) into agricultural systems and evaluate their impact on ecological balance is also an important research direction.


Therefore, the research goal of this problem is to construct a multi-dimensional model to simulate the economic, sustainable and ecological impacts of organic farming methods in the long and short term, and to help decision-makers make scientific agricultural production decisions through sensitive analysis to promote the sustainable development of agroecology.


Agro-ecosystem modeling


In the context of this problem, we need to build a model to track the evolution of ecosystems from forests to agriculture. The goal is to analyze changes in farmland ecosystems, including the impacts of natural processes and human decision-making on ecosystems. Here are the basic steps and ideas for model building, which we can implement by writing code in MATLAB and visualizing the results graphically.


1. Basic construction of the model


1.1 Five key indicators in the ecosystem


We can describe the transition from forest to cropland in terms of the following five key indicators of the ecosystem:


Plants are producers in agro-ecosystems, and they form the basis of ecosystems by converting solar energy into chemical energy through photosynthesis. As farmland is built, the abundant plant species may be reduced in favor of crops. The application of chemical fertilizers, herbicides, etc. in agriculture affects plant health and can lead to a decline in plant numbers or a decrease in species diversity.

摄影指导DT=rP(1−PK)−α PC


Among them, is the r plant growth rate, is the K environmental capacity of the plant, α is the effect coefficient of the pesticide on the plant, and C is the concentration of the chemical agent.


Insects are one of the main consumers in the agro-ecosystem, especially pests, which can affect the growth of crops. As a result of the transformation of agriculture, the species and abundance of insect populations may change, especially due to the influence of chemicals.

DT=bI(1−)−γIC


Among them, b is the growth rate of insects, the maximum carrying capacity of insect populations, the γ influence coefficient of chemicals on insects, and C the concentration of chemicals.


Birds are important control factors in agroecosystems, and insects, in particular, help control pest populations. As agricultural systems mature, bird populations may change as the food chain changes.

分贝DT=βB(1−BB)−δBI的


Among them, β is the growth rate of birds, is B the maximum carrying capacity of birds, and δ is the efficiency of birds to predation insects.


Bats play a pest control role in agroecosystems, especially nocturnal insects. The growth of bat populations is related to the number of insects and available habitats.

电压DT=ζV(1−VV)−ηVI


Among them, ζ is the growth rate of bats, the V maximum carrying capacity of bats, and η the predation rate of bats on insects.


Soil is the basis of agricultural production, and soil quality determines the growth potential of crops. With the management of farmland and the use of chemicals, the organic matter and nutrient composition of the soil may change.

dSDT(S−S)−λSC


Among them, κ is the rate of soil recovery, the S maximum mass of the soil, and λ the negative impact of chemicals on soil quality.


This graph consists of two graphs, the insect population dynamics on the left and the plant population dynamics on the right. From the insect population map on the left, the insect population has experienced periodic fluctuations, showing a clear trend of growth and decrease, which may reflect the interaction between insects and plants in the ecosystem, such as the food resources provided by plants affect the number of insects, and the changes in the number of insects affect the growth of plants. The shaded areas in the graph represent the range of changes in insect populations, showing the volatility and uncertainty of the data.


The map of plant population dynamics on the right shows a gradual downward trend in plant populations, with plant populations decreasing over time, which may indicate that plants are under pressure from insect predation, competition for resources, or environmental change. Nonetheless, the volatility and recovery in the graph also suggest that plant populations may have a tendency to recover or stabilize at some point in time.


Taken together, this diagram illustrates the dynamics and interrelationships between insect and plant populations, revealing a potential ecological equilibrium process in which insect and plant population fluctuations interact while also taking into account ecosystem uncertainties.


Depending on the different ecosystem components and common impacts in agricultural transitions, the following additional indicators can be selected for further analysis:


The impact of chemicals (e.g., pesticides, herbicides, etc.) on the ecosystem as a whole. This indicator reflects the effects of chemicals on soil, plants, insects, and other species over time.

C(t)=C1+λ⋅吨


C where is the initial chemical concentration, is the λ degradation rate of the chemical species, and t is the time.

生态系统稳定性指数 (Ecosystem Stability Index, ESI)
该指数用于衡量生态系统的稳定性,通常可以通过不同物种的相互依赖性来表示。我们假设随着时间的推移,生态系统会逐渐变得更加稳定,但在化学物质干扰下,稳定性可能受到影响。

ESI(t)=11+α⋅exp(−β⋅t)


α where and β is a constant that determines the rate and magnitude of the stability change.

物种多样性指数 (Species Diversity Index, SDI)
衡量生态系统中物种的多样性,考虑到物种的丰富度和均匀度。常用的 Shannon-

SDI=−plog(p)


p where is the relative abundance of each species.

土地肥力指数 (Land Fertility Index, LFI)

LFI(t)=LFe


LFI where is the initial fertility and is the δ rate of fertility decline.

农业产量指数 (Agricultural Yield Index, AYI)
衡量农田的农业产量,通常是与作物种类、土壤质量、农药使用等因素相关的。

AYI(t)=Y⋅(1−α⋅C(t))⋅e


Y where is the initial yield, C(t) is the concentration of the chemical substance, α and β is the parameter that affects the yield.


This graph contains multiple graphs that show the changes of different ecological and agricultural indicators over time. The first chart, labeled "Agricultural Production Index", shows the change in agricultural production over time, and can be seen to show that agricultural production has leveled off after initial growth, and the shaded areas indicate the confidence intervals or uncertainties in the data. The second chart, the Land Fertility Index, shows the gradual decline in land fertility over time, reflecting the long-term impact of agricultural activities on soil health, as well as shading intervals to indicate uncertainty about change.


The third chart, the "Species Diversity Index", shows fluctuations in species diversity in ecosystems, which may be due to environmental changes and the impact of agricultural activities, exhibiting complex patterns of change that may be related to cyclical factors or external influences. The final chart, the Chemical Impact Index, shows that the impact of chemicals on ecosystems decreases over time, suggesting that while chemicals such as pesticides and herbicides may have a larger impact initially, their impact gradually decreases as agricultural management improves or chemicals degrade.


Overall, this set of charts provides us with an integrated view of how agricultural practices and their side effects, such as chemical use, changes in land fertility, and biodiversity decline, have changed over time. The shaded areas in the graph indicate the uncertainty of the data


Q2: Include the re-emergence of species and analyze their impact on agro-ecosystems


In this model, we assume that in the land after the agricultural transition, marginal habitats begin to mature and that certain native species gradually return over time. These species interact with current agroecosystems and can lead to changes in the ecosystem. Therefore, we need to analyze how the return of these species affects key indicators such as ecosystem stability, land fertility, and species diversity.


Incorporate two species reference maps!

物种的回归对农业生态系统的影响


Over time, certain species begin to return to land that has been converted into agroecosystems, including certain native plant and insect species, whose reintroduction may promote the restoration of land fertility, increase biodiversity, and affect agricultural yields.


2. Key metrics and formulas in the model

(1) 物种回归数量 (Recolonization Rate, R)


The number of species regression reflects the number of native species that gradually reappear in agroecosystems. The number of species returning increases gradually over time, but this rate of growth is limited by the adaptation of the current environment.

博士DT=γR(1−RR)


Among them, the γ growth rate of species regression is the largest limitation of the R number of species regression.

R(t)=Re⋅(1 -R(吨)K)


Among them, R is the initial number of species regression, and α the rate of species reflux, which is the K maximum number of species that the ecosystem can support.

(2) 生态系统稳定性变化 (Ecosystem Stability, ES)


As species return, the stability of ecosystems may change. Species diversity and interspecies interactions can promote ecosystem recovery and increase stability.

设计DT=β⋅R(吨)K⋅(1−ES)


Among them, is the β coefficient of the impact of species regression on ecosystem stability.

ES(t)=ES+β⋅R(吨)K


Among them, ES it is the initial ecosystem stability and the β contribution of species regression to stability.


(3) Soil Fertility Restoration (SFR)

物种的回归不仅影响生态系统的稳定性,还可能促进土壤的恢复,尤其是通过植物种类的回归,它们通过固氮作用和有机物的分解,有助于恢复土壤的肥力。
The return of species not only affects the stability of ecosystems, but may also contribute to soil restoration, especially through the return of plant species, which contribute to the restoration of soil fertility through nitrogen fixation and the decomposition of organic matter.

dSFRDT=δSFR⋅(1−SFRSF (旧金山)R)

SFR(t)=SFR+η⋅R(吨)


Among them, the SF (旧金山)R initial soil fertility is the η influence coefficient of species regression on soil fertility restoration.

模型1:除草剂去除对生态系统稳定性的影响
Model 1: Effect of herbicide removal on ecosystem stability

1. 关键指标
1. Key metrics


(1) Plant Population (P)

去除除草剂后,植物种群将不再受到化学物质的干扰。这将导致植物种群的恢复或波动,具体情况取决于环境因素和植物种类的适应性。
After the herbicide is removed, the plant population will no longer be disturbed by the chemicals. This will lead to the recovery or fluctuation of plant populations, depending on environmental factors and the adaptability of the plant species.

摄影指导DT=rP(1−PK)−αPI


Among them, r it is the growth rate of the plant, the K environmental capacity of the plant, and the α predatory relationship between the plant and the insect.


(2) Insect Population (I)

昆虫种群对植物的生长有直接影响,去除除草剂后,昆虫种群的数量可能会有所回升。
Insect populations have a direct impact on plant growth, and insect populations may rebound after herbicide removal.

DT=bI(1−)−γIC


Among them, b is the growth rate of insects, is the maximum population capacity of insects, is the γ coefficient of influence of chemicals on insects, and is the C herbicide concentration.


(3) Ecosystem Stability Index (ESI)

生态系统的稳定性与各个物种的相互作用密切相关。去除除草剂后,生态系统的稳定性将通过物种之间的竞争和捕食关系得到恢复。
The stability of ecosystems is closely related to the interaction of individual species. When herbicides are removed, the stability of the ecosystem will be restored through competition and predation between species.

德ESIDT=α⋅P(吨)K−β⋅我(t)


Where, α and β are parameters that reflect the interaction between plants and insects.


(4) Herbicide Concentration (C)

随着除草剂的去除,浓度逐渐下降。这个指标可以帮助我们衡量除草剂去除的过程。
As the herbicide is removed, the concentration gradually decreases. This metric can help us measure the process of herbicide removal.

直流DT=−δC


Among them, is the δ degradation rate of herbicides.


(5) Species Diversity Index (SDI)

物种多样性指数反映了去除除草剂后,生态系统中物种的丰富度和均匀度。随着除草剂的去除,物种的多样性可能会恢复。
The species diversity index reflects the richness and uniformity of species in an ecosystem after herbicide removal. As herbicides are removed, species diversity may return.

SDI=−plog⁡(p)

其中,p 是每个物种的相对丰度。
where is the p relative abundance of each species.

模型2:蝙蝠的引入与生态恢复平衡
Model 2: Bat introduction and ecological restoration balance

(1) 蝙蝠种群数量 (Bat Population, B)
(1) Bat Population (B)

蝙蝠在控制害虫种群、传粉等方面发挥重要作用。引入蝙蝠后,蝙蝠种群的数量将逐步增加。
Bats play an important role in controlling pest populations, pollination, and more. After the introduction of bats, the number of bats will gradually increase.

dBdt=ζB(1−BB)−ηBI

其中,ζ 是蝙蝠的生长率,B 是蝙蝠的最大承载量,η 是蝙蝠对昆虫的捕食效率。
Among them, ζ it is the growth rate of bats, the B maximum carrying capacity of bats, and η the predation efficiency of bats against insects.

(2) 害虫种群数量 (Pest Population, P)
(2) Pest Population (P)

蝙蝠的引入会影响害虫种群的数量,控制害虫对植物的伤害。
The introduction of bats can affect the number of pest populations and control the damage of pests to plants.

dPdt=αP−βBP


Among them, is the α natural growth rate of pests, and β is the predation rate of bats on pests.


(3) Plant Population (P) (same as the formula in the first model)


Plant populations can also be affected by pest control and bat introduction.


(4) Ecosystem Stability (ES) (same as the formula in the first model)


The introduction of bats and the control of pests will help to improve the stability of the ecosystem.


(5) Other Species Impact (OI)


In addition to bats, the introduction of other species, such as predators or pollinators, may also play a positive role in restoring balance to the ecosystem. This indicator can be representative of the impact of other species on ecological restoration.

OI=αO⋅e


Among them, the αO intensity of the impact of other species is the β attenuation rate after the introduction of species.


The optimized XGBoost was used to solve the agroecological economy


XGBoost optimization algorithm principle:


XGBoost (Extreme Gradient Boosting) is an optimization algorithm based on Gradient Boosting Decision Tree (GBDT), which has become a very popular machine learning model in recent years by improving the performance of the algorithm. XGBoost has made a number of optimizations on the basis of the traditional gradient boosting algorithm, which makes the model more efficient, accurate, and able to handle large-scale datasets. The core idea of XGBoost is to gradually improve the prediction accuracy by building a series of weak classifiers (usually decision trees) and correcting the errors of the previous step with each step of training. At each iteration, XGBoost controls the complexity of the model by minimizing the loss function and adding regularization terms to prevent overfitting. In addition, XGBoost uses advanced algorithm optimization techniques, such as column sampling, gradient histogram, parallel computing, etc., which greatly improves the computational efficiency.


1. Objective Function:

L(θ)=l(y,)+Ω(f)


where is the loss function, l(y,) which represents the error between the predicted value and the true value; Ω(f) is a regularization term that penalizes the complexity of the model and avoids overfitting.


2. Regularization terms:

Ω(f)=γT+12λ


where is the number of leaf nodes of the tree, w is the weight of each leaf node, γ and λ is the regularized hyperparameter. T


3. Gradient Update:

f(x)=f(x)+η⋅δf(x)


Where, f(x) is the model of the first t iteration, is η the learning rate, and δf(x) is the optimization increment of the first t round.


Through these optimizations, XGBoost is able to better fit complex data structures and effectively prevent overfitting, which often performs well in many competitions and real-world applications.


When considering whether farmers are adopting organic farming methods, we need to analyze the impact of this farming practice on the agro-ecosystem, as well as its potential impact on farmers' economic and sustainable development. There are multiple components to this issue: pest control, crop health, plant propagation, biodiversity, long-term sustainability and cost-effectiveness. Therefore, establishing objective functions and constraints for economic and sustainable development can help to assess the potential benefits of organic farming.


Objective function


The objective function should be the main driver of farmers' choice of organic farming methods: improved economic efficiency and sustainability. These goals can generally be expressed in two ways:


Profit:


Organic farming may be higher in terms of initial inputs, but in the long run, it may be more profitable, as the market price of organic crops is usually higher than that of conventional crops.


The objective function can be set to maximize profits, i.e., to take into account crop yields, market prices, production costs, and other relevant factors in organic farming.


Sustainability:


Organic agriculture emphasizes the protection of ecological environments, including soil health, biodiversity, and water conservation.


In the long term, the sustainability of agriculture is an important factor in the objective function, i.e., ecological stability by reducing chemical use and increasing the resilience of land and ecosystems.


Therefore, the objective function can be expressed as:

Maximize Z=α⋅Profit+β⋅Sustainability


Where: α and β is a weighting coefficient, which is used to balance the relationship between economic efficiency and sustainability.


Economic benefit function:


The economic benefits mainly come from the market price, yield and production cost of the crop. Specifically:

Profit=PYC


Where: P is the market price of organic crops. Y It is the yield of organic crops. C is the cost of producing organic crops. The market price of organic crops is higher, but the cost of production can also be higher, so the analysis needs to be carried out within this constraint. :


Sustainability mainly includes the following factors:


Pest control: Organic farming methods use natural methods to control pests, reducing environmental pollution and enhancing the long-term resilience of agroecosystems compared to traditional chemical methods.


Crop health: Organic farming can reduce the use of chemical fertilizers and pesticides, which is beneficial to the long-term health of crops.


Plant reproduction and biodiversity: Organic farming methods promote plant diversity and the natural reproduction of crops by maintaining soil health and ecological balance.


Land sustainability: Promote the sustainable use of soil by avoiding overuse of chemicals and increasing soil organic matter.


Therefore, sustainability goals can be expressed as:

Sustainability=f(Pest Control,Crop Health,Biodiversity,Soil Health)


Each of these factors (e.g., pest control, crop health, etc.) can be quantified in terms of its positive impact on the ecosystem.


Constraints


In the model, the actual constraints need to be considered, and here are the possible constraints:


1. Budget Constraints:


Organic agriculture can be high on initial investment, so the available capital for farmers is a constraint.

C≤B


Among them, B is the budget of the peasants.


2. Crop yield constraints:


Organic farming may not yield as well as conventional farming, so it is necessary to set a lower yield limit to ensure the basic production of crops.

YY


Among them, Y is the minimum yield that farmers hope to obtain.


3. Sustainability and Ecological Constraints:


Organic farming emphasizes the conservation of soil health and biodiversity, so there is a need to ensure that farming practices do not negatively impact ecosystems.

Biodiversity≥Biodiversity

Soil Health≥Soil Health


4. Market demand constraints:


Farmers must produce organic crops that meet market demand.

YD


Among them, is the D largest demand for organic crops in the market.


5. Productivity Constraints:


Organic farming can face high production costs, so cost efficiency needs to be optimized.

CY≤γ


Among them, γ is the ratio of acceptable production cost to output.


Monolithic model


Combined with the objective function and constraints, the final model can be expressed as:

Maximize Z=α⋅(PYC)+β⋅f(Pest Control,Crop Health,Biodiversity,Soil Health)

subject to:

C≤B

YY

Biodiversity≥Biodiversity

Soil Health≥Soil Health

YD

CY≤γ


Regarding the impact of farmers considering organic farming methods, we can use this graph to analyze it. In this context, the diagram may show different environmental factors in an agricultural area, such as soil quality, crop health, or the spatial distribution of biodiversity. Contour plots and 3D plots can be used to depict how these factors fluctuate over time or space at different locations (e.g., the X-axis represents farmland in different areas, and the Y-axis represents the vertical direction of plot height or characteristics). The contour plot on the left shows the distribution of an environmental factor, such as soil health or organic crop growing conditions, over different regions, where different color levels represent the intensity or concentration of that factor. For example, the blue area in the graph may represent lower soil fertility, while the yellow or red area may represent higher fertility. These fluctuations may reflect changes in crop health, plant reproduction, pest control, and more, which are essential for the implementation of organic farming. The 3D plot on the right provides a three-dimensional representation of the data, visualizing how environmental factors (e.g., soil fertility, pest control, etc.) change as plot height (or other factors) change. With this diagram, farmers can better understand the characteristics of different regions and decide whether to implement organic farming methods and which areas to choose for organic farming.

Sensitivity Analysis


The purpose of sensitivity tuning is to assess the relative importance of different parameters in organic farming decisions. Through sensitivity analysis, farmers can understand which factors are most critical to economic efficiency and sustainability in the face of different market or environmental conditions. This helps them to make more informed and optimal choices when making decisions, ensuring the long-term economic and ecological benefits of agriculture.

Model Evaluation and Further Discussion

Strengths


Multi-dimensional consideration: The model comprehensively analyzes the impact of organic farming from two dimensions: economic benefit and sustainability, not only considering profit maximization, but also considering ecological environment, crop health and other factors. This allows the model to provide a more comprehensive picture of the actual performance of organic agriculture and provide a comprehensive reference for decision-makers.


High flexibility: By adding a 5% Gaussian perturbation, the model has some flexibility to simulate the inevitable market fluctuations and environmental changes in reality. This makes the model more realistic and can provide farmers with more ways to cope with uncertainty.


Operability: The model allows farmers to evaluate the feasibility of organic farming by adjusting key parameters such as production costs, crop prices, and yields through simple data generation and parameter analysis. This operability helps farmers optimize their decision-making according to their own situation.


Supporting long-term decision-making: By analyzing profits and sustainability, models can help farmers make sustainable agricultural development decisions over the long term. Especially in the case of organic farming, where long-term gains may be better than short-term gains, models can help guide farmers' long-term planning and investment.

Weaknesses


Simplification of assumptions: The model assumes that the profitability and sustainability of organic farming are only related to factors such as crop prices, yields, costs, etc., ignoring many complex external factors such as climate change, market fluctuations, policy impacts, etc. This makes it possible for models to accurately reflect complex realities, especially in extreme cases.


Accuracy and reliability of data: Much of the data used in the model is generated through assumptions (e.g., market prices, yields, costs, etc.) for organic crops, which can differ significantly from reality. The accuracy of a model is highly dependent on the quality of the input data, so if the data is inaccurate, the model's predictions may be biased.


Outlook of the model


With the intensification of global climate change and environmental problems, the demand for sustainable agriculture will grow day by day. In the future, the model can be expanded and optimized in the following aspects: Introduce more external variables: In order to improve the practical application value of the model, more external variables related to agricultural production, such as climate change, government subsidies, market demand, and other factors, can be introduced. This will make the model more realistic and better able to deal with uncertainties. Dynamic update and real-time data support: In the future, the model can integrate more real-time data sources, such as soil quality monitoring data, meteorological data, etc., so that the model can reflect the specific situation of farmland in real time and dynamically adjust strategies. This will improve the adaptability of the model and the ability to make decisions in real time. Expand to different types of crops and regions: Models can be customized according to the climate and soil conditions of different regions, as well as the needs of different crops, to improve their application value in different regions. Through the expansion of the model, farmers can be provided with more specific and personalized agricultural decision support. Introducing social and environmental costs: Current models focus primarily on economic benefits and ecological sustainability, but future extensions can include social and environmental costs such as impacts on communities, impacts on biodiversity, etc. This will make the model more comprehensive and reflect the combined contribution of organic agriculture to society and the environment. Through these optimizations and extensions, future models can provide more accurate data support to agricultural decision-makers, helping them to achieve environmental protection and social responsibility while pursuing economic benefits.

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