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Problem Chosen
E
问题选择E

2025
MCM/ICM

Summary Sheet
摘要表

Team Control Number
2425059
团队控制号码
2425059

Going green in farming, going away from deforestation
在农业中走向绿色,远离森林砍伐

Summary
总结

In recent years, as population explodes, the area of agricultural land expands and deforestation takes place, causing an imbalance in the environment. To find a way to get rid of the deforestation, we study the converted forest.
近年来,随着人炸,农业用地面积扩大,森林砍伐发生,导致环境失衡。为了找到摆脱森林砍伐的方法,我们研究了改建后的森林。

For Task one, we adopted a dynamic changing model and a differential equation to show the change of the area of the agricultural area in a converted forest.
对于任务 1,我们采用动态变化模型和微分方程来显示转换森林中农业区面积的变化。

Then we established an N×N interactive matrix to quantize the strengths and directions of interactions between different species and used the networkz library to make a matrix into a DiGraph. We also applied Matplotlib to achieve image rendering. We assessed the fluctuation of the populations of current producers and consumers over time to analyze interspecific relationships.
然后,我们建立了一个 N×N 交互式矩阵来量化不同物种之间相互作用的强度和方向,并使用 networkz 库将矩阵制作成 DiGraph。我们还应用 Matplotlib 来实现图像渲染。我们评估了当前生产者和消费者种群随时间的波动,以分析种间关系。

After that, we considered seasonal and agricultural cycles to study the dynamic changes. We simulated the growth of crops by introducing the variable of time and seasonal factors.In the end, we constructed a differential equation to study the accumulation and decomposition of chemicals. We assessed them by introducing the input rate of chemicals, the decomposing coefficient and cumulant.
之后,我们考虑了季节性和农业周期来研究动态变化。我们通过引入时间和季节性因素的变量来模拟农作物的生长。最后,我们构建了一个微分方程来研究化学物质的积累和分解。我们通过引入化学品的输入速率、分解系数和累积量来评估它们。

For Task 2, to illustrate the reemergence of species as the agri-cultural system matures, we first built a f(agriculture-impact) model to study the reemergence rate of species. And to express the maturity rate of edge habitats we take the factor of time and the agricultural activity seasonal fluctuations into account. We also applied logistic increasing models to predators and pollinators to study the impact of the maturity of the ecosystem to producers and consumers.
对于任务 2,为了说明随着农业文化系统的成熟而物种的重新出现,我们首先建立了一个 f(农业影响)模型来研究物种的重新出现率。为了表达边缘栖息地的成熟率,我们考虑了时间因素和农业活动、季节性波动。我们还将 Logistic-Increasing 模型应用于捕食者和传粉者,以研究生态系统成熟度对生产者和消费者的影响。

For Task 3, we applied dynamic equations to show the populational change in producers and consumers as the herbicide is removed progressively to assess the impact of the removal of chemicals on the stability of the ecosystem.
对于任务 3,我们应用动态方程来显示随着除草剂逐渐去除,生产者和消费者的种群变化,以评估去除化学品对生态系统稳定性的影响。

For Task 4, we incorporated bats into the food web. We assessed their interspecific relationships with other species to evaluate bats’ role in stabilizing the ecosystem as an insectivore and a pollinator. We then used birds as an alternative species to assess their inter-specific relationships and finally compared both of their impacts on the ecosystem. All the differential equations are solved by numpy and scipy in Python.
在任务 4 中,我们将蝙蝠纳入食物网。我们评估了它们与其他物种的种间关系,以评估蝙蝠作为食虫者和传粉者在稳定生态系统中的作用。然后,我们使用鸟类作为替代物种来评估它们的种间关系,最后比较它们对生态系统的影响。所有的微分方程都是用 Python 中的 numpy 和 scipy 解决的。

For Task 5, we adopted the optimizing strategy to gain the maximum benefit as we found the balance between the yield maximization and the minimization of environmental and chemical costs. We used Python codes to generate synthetic data and trained a Random Forest model to predict the yield and the environmental cost. We also applied the algorithm NSGA-II to optimize multiple goals including the balance factors above. We utilized 2D and 3D Advanced Visualization Deployment Objectives Trade-offs, and Python libraries as Pandas, NumPy, Matplotlib, sklearn, Seaborn and pymoo to process and model the data, and apply optimization analysis.
对于任务 5,我们采用了优化策略以获得最大收益,因为我们在产量最大化与环境和化学成本最小化之间找到了平衡。我们使用 Python 代码生成合成数据,并训练随机森林模型来预测产量和环境成本。我们还应用了算法 NSGA-II 来优化多个目标,包括上述平衡因素。我们利用 2D 和 3D 高级可视化部署目标权衡以及 Python 库(如 Pandas、NumPy、Matplotlib、sklearn、Seaborn 和 pymoo)来处理和建模数据,并应用优化分析。

Keywords: logistic increasing model, interactive matrix, dynamics, differential equation, optimizing strategy
关键词:逻辑递增模型 交互矩阵 动力学 微分方程 优化策略

Team # 1111111 Page 2 of 11

Contents
内容

1 Introduction3
1 介绍3

1.1 Problem Background3
1.1 问题背景3

1.2 Restatement of the Problem4
1.2 问题重述4

1.3 Literature Review4
1.3 文献综述4

1.4 Our Work4
1.4 我们的工作4

2 Assumptions and Justifications5
2 假设和理由5

3 Notations6
3 符号6

4 Natural Process6
4 自然过程6

4.1 Data Description6
4.1 数据描述6

4.2 The Establishment of Model 16
4.2 模型 1 的建立6

4.3 The Solution of Model 17
4.3 模型1 的解决方案 7

5 The name of model 27
5 型号名称 27

6 The name of model 37
6 型号名称 37

7 Sensitivity Analysis8
7 敏感性分析8

8 Model Evaluation and Further Discussion8
8 模型评估和进一步讨论8

8.1 Strengths8
8.1 优势8

8.2 Weaknesses8
8.2 弱点8

8.3 Further Discussion8
8.3 进一步讨论8

8 Letter of Advice9
8 建议信9

References10
参考资料10

10 Report on Use of AI11
10 AI 使用报告11

Introduction
介绍

Problem Background
问题背景

According to FAO, the loss of primary forests remained high at around 4 million hectares per year during the 2000s. Primary, or old-growth, forests today account for only 36 percent of global forest cover (1.35 billion hectares), while secondary and naturally regenerating forests make up 57 percent (2.15 billion hectares). The balance— 9 percent or 264 million hectares — consists of planted forests, including industrial plantations. And according to FAO on the UN climate change conference, the lion part for the loss of forest is the factor of agriculture, which comprises nearly 90 percent.
根据粮农组织的数据,在 2000 年代,原始森林的损失仍然很高,每年约为 400 万公顷。如今,原生林或老树林仅占全球森林覆盖率的 36%(13.5 亿公顷),而次生林和自然再生林占 57%(21.5 亿公顷)。其余 9% 或 2.64 亿公顷由人工林组成,包括工业人工林。根据联合国粮农组织在联合国气候变化会议上的说法,森林损失的主体是农业,占近 90%。

Net change in forest areas by country, 2005-2010 (hectares per year). Image courtesy of FAO.
2005-2010 年按国家/地区划分的森林面积净变化(每年公顷)。图片由粮农组织提供。

Reasons of deforestation, according to FAO
根据 FAO 的说法,森林砍伐的原因

The enormous loss of forests poses a complicated threat for the ecosystems around the globe. For the lion part of the loss, forests were converted to agricultural areas. However, that doesn’t mean the yield or harvest is much better. Loss of forests can lead to the flourishment of pests, which would definitely make our ecosystem more fragile and our agriculture worse. The natural change is on the way, but we humans can make decisions to change or not. Farmers need to explore the best practice method of farming to ensure the yield and protect the environment to achieve the sustainability of the agriculture.
森林的巨大损失对全球生态系统构成了复杂的威胁。对于损失的大部分,森林被转化为农业区。然而,这并不意味着产量或收成要好得多。森林的丧失会导致害虫的繁殖,这肯定会使我们的生态系统更加脆弱,我们的农业变得更糟。自然的变化正在进行中,但我们人类可以决定是否改变。农民需要探索最佳的耕作方法,以确保产量并保护环境,以实现农业的可持续性。

Therefore, there is a growing need for models that accurately illustrate the change that takes place in the converted forest and the process the new agricultural areas reach its balance. Models that indicate the impacts of human decisions are also in need. These models will help farmers take farming methods more seriously and explore an optimal method of organic farming.
因此,越来越需要能够准确说明转换森林中发生的变化以及新农业区域达到平衡的过程的模型。还需要表明人类决策影响的模型。这些模型将帮助农民更认真地对待耕作方法,并探索有机农业的最佳方法。

Restatement of the Problem
重述问题

Considering the background information and restricted conditions identified in the problem statement, we need to solve the following problems
考虑到问题陈述中确定的背景信息和限制条件,我们需要解决以下问题
:

Problem 1: The converted forest area has a new food web and a new systematic ecological dynamics caused by deforestation, leading to the change of ecosystem stability.
问题 1:转化后的林区拥有新的食物网和森林砍伐引起的新的系统性生态动态,导致生态系统稳定性发生变化。

Problem 2: Edge habitats begin to mature and there are reemergence of original species, changing the agricultural ecosystem.
问题 2 边缘栖息地开始成熟,原始物种重新出现,改变了农业生态系统

Problem 3: Herbicide is removed, changing the stability of the ecosystem in the aspects of producers and consumers.
问题 3除草剂被去除,改变了生态系统在生产者和消费者方面的稳定性。

Problem 4: Bats and another species are incorporated into the system respectively, which benefits the restoration of the ecosystem balance.
问题 4 蝙蝠和其他物种分别被纳入系统,有利于恢复生态系统平衡。

Problem 5: Different components of organic farming included, which has a beneficial effect to both the individuals and the ecosystem as a whole in terms of economic and environmental benefits.
问题 5 包括有机农业的不同组成部分,在经济和环境效益方面对个人和整个生态系统都有有益的影响。

Literature Review
文献综述

Literature Review:文献综述就是把关于当前问题的现有研究成果做个概述。首先需要阅读大量解决该问题的论文,其次得用自己的话总结出来。
文献综述:文献综述就是把关于当前问题的现有研究成果做个概述。首先需要阅读大量解决该问题的论文,其次得用自己的话总结出来。

除非想冲O奖,否则别写这部分。一来竞赛时间有限,不可能去阅读大量论文;二来能力有限,不一定能写好总结。

小技巧:去搜相关论文,一般发表的论文都会有文献综述部分,照着别人的综述用自己的话描述一遍即可。

Our Work
,你的

The work we have done is mainly shown in Figure 3.
我们所做的工作主要如图 3 所示。

Our Work
,你的

Assumptions and Justifications
假设和理由

Assumption1: The total area of the forest and the agricultural area is a constant.
假设 1:森林和农业面积的总面积是一个常数。

Justification: In reality, the conversion from forest to the agricultural land is a complicated issue as there are other biomes involved, but their influences are subtle so we focus on the forest and the agricultural area, supposing their total area is a constant.
理由:实际上,从森林到农业用地的转换是一个复杂的问题,因为涉及其他生物群落,但它们的影响是微妙的,因此我们专注于森林和农业区域,假设它们的总面积是恒定的。

Assumption 2: The number of the reappeared species is certain.
假设 2:重新出现的物种的数量是确定的。

Justification: The maturity of the edge habitat is a gradual process. And the initial stage can be directly seen as the reemergence of certain species.
理由: 边缘栖息地的成熟是一个渐进的过程。而初始阶段可以直接看作是某些物种的重新出现。

Assumption 3: The data we use is true and reliable.
假设 3:我们使用的数据真实可靠。

Justification: Our data sources include international statistical agencies, academic databases, and reputable insurance companies. Therefore, we can confidently state that the data we use is accurate and reliable for modeling purposes.
理由我们的数据来源包括国际统计机构、学术数据库和信誉良好的保险公司。因此,我们可以自信地声明,我们使用的数据对于建模目的来说是准确可靠的。

Notations
符号

The key mathematical notations used in this paper are listed in Table 1.
表 1 列出了本文中使用的关键数学符号

Notations used in this paper
本文中使用的符号

Symbol
象征

Description
D描述

在此处键入公式。

4 Natural Process
4 自然过程

4.1Build a Dynamic Changing Model to Illustrate the Current Ecosystem
4.1构建动态变化模型来说明当前的生态系统

The conversion from a forest to an agricultural area is measured in terms of the rate agricultural area expands, the change in the population of the related species and the population itself. The process agricultural ecosystem takes place of a heavily forested region is an important case to study to know about the effect the environmental change has on the ecosystem. Therefore, we take these three main aspects as primary indicators.
从森林到农业区的转变是根据农业区扩大的速度、相关物种种群的变化以及种群本身来衡量的。农业生态系统发生在森林茂密地区的过程是了解环境变化对生态系统影响的重要案例。因此,我们将这三个主要方面作为主要指标。

4.1.1 Building a dynamic changing model to illustrate the change in the area of agricultural land
4.1.1 构建动态变化模型来说明农业用地面积的变化

As the farming land expands, the rate of its expansion varies with time. For the dynamic change of the area of agricultural land, we synthesized various factors, such as the soil fertility and the brightness in the ecosystem. We selected three factors for our research.
随着耕地的扩大,其扩张的速度会随着时间的推移而变化。对于农业用地面积的动态变化,我们综合了土壤肥力和生态系统亮度等各种因素。我们选择了三个因素进行研究。

农业用地面积动态变化(A(t))

dAdt=r×(F-A)-m×I×α

where:
A(t):The area of agricultural land
F:Current forest coverage area(F+Ais a constant)
m:
I: The number of the insect population

αThe portion of pests in the insect population

Agricultural land use change modelling: Given that it is a forest to farmland change, we first establish a model that is about agricultural land use change. We notice that the sum area of agricultural land and the forest is a constant. We take into account their difference in area and the pest portion in the insect population.
农业土地利用变化模型:鉴于这是森林到农田的变化,我们首先建立一个关于农业土地利用变化的模型。我们注意到,农业用地和森林的面积之和是一个常数。我们考虑了它们的面积差异和昆虫种群中的害虫部分。

4.1.2 Building a logistic increasing model for the food web
4.1.2 构建食物网的 logistic 递增模型

4.1.2.1

Plant Population (P(t))

dPdt=r×P×(1-PK)-α×I-α×D(t)×P

where:
r:growth rate of plants
Kenvironmental carrying capacity of plants

α:the influence coefficent of insects to plants

α:the influence coefficent of herbicide to plants

D(t):amount of herbicide usage

Insect Population I(t)

dIdt=r×I×(1-IK)+β×P-δ×I-α×P×I

β:support coefficent of plants to insects

δ:death rate of insects

Bat population (B(t))

dBdt=r×B×(1-BK)+α×I-γ×B

α:support coefficent of insects to plants

γ:natural death rate of bats

BirdPopulation(A(t))

dAdt=r×A×(1-AK)+α×A×I-γ×A

α:support coefficent of insects to birds

γ:influence coefficent of pesticide tp birds

Crop growth model(C(t))

dCdt=r*C*(1-CK)-P×I×α

-r:Growth rate of crops
-P:destruction coefficent of pests

Chemical Accumulation(C)

dCdt=μ-δ×C

C(t):the dose of chemical accumulation

μ:theinputrateofchemicals(aconstant)

δ:decomposing coefficent of chemicals

We established an ecological model based on the food chain, simulating producers(plants), primary consumers(insects)and secondary consumers(predators like bats, birds and so on). In the process of conversion, their population varies over time. It shows that we need to take into account their interspecific relations like predation, competition and mutualism.
我们建立了一个基于食物链的生态模型,模拟生产者(植物)、初级消费者(昆虫)和次级消费者(蝙蝠、鸟类等捕食者)。在转换过程中,他们的人口会随着时间的推移而变化。它表明我们需要考虑它们的种间关系,如捕食、竞争和共生关系。

To study the dynamic change of the agricultural system, considering the seasonal changes and agricultural production, we introduce the variable of time and seasonal factors to simulate the influence on the population and ecosystem and establish related produce models.
为了研究农业系统的动态变化,考虑到季节变化和农业生产,我们引入了时间和季节因素的变量,以模拟对种群和生态系统的影响,并建立相关的生产模型。

The effect of herbicides and pesticides: modelling through the use of chemicals, and analyze how the use of chemicals influence ecological balance combined with the different effects these chemicals have on different species in the ecosystem. For example, pesticides reduce insect herds and herbicides affect the growth of plants.
除草剂和杀虫剂的影响:通过使用化学品进行建模,并分析化学品的使用如何影响生态平衡,以及这些化学品对生态系统中不同物种的不同影响。例如,杀虫剂可以减少虫群,而除草剂会影响植物的生长

4.1.2.2Additionally, we build an interactive matrix for this
4.1.2.2 此外,我们为此构建了一个交互式矩阵

An interactive matrix is used to quantize the strengths and directions of interactions between different points of species in the ecosystems.
交互式矩阵用于量化生态系统中不同物种点之间相互作用的强度和方向。

From right to left, from up to down, they are bats, plants, pests, pollinators and predators
从右到左,从上到下,它们是蝙蝠、植物、害虫、传粉者和捕食者

If an location is negative it means a negative effect like bats preying pests.
如果某个位置是负面的,则意味着负面效果,例如蝙蝠捕食害虫。

If it is positive it means a positive effect like bats pollinating plants.
如果它是积极的,则意味着像蝙蝠为植物授粉一样的积极影响。

The interspecific relationships between different species in the same ecosystem, including predation, competition and symbiosis. Therefore we used a matrix to show the correlation between species.
同一生态系统中不同物种之间的种间关系,包括捕食、竞争和共生。因此,我们使用矩阵来显示物种之间的相关性。

The joint means different species and the direction side means interaction, the width of which means the strengths.
关节意味着不同的物种,方向侧意味着相互作用,其宽度意味着强度。

4.2The reemergence of species
4.2物种的重新出现

As the ecosystem of farmland comes to maturity, part of the vanished species might reappear. So we built a model to showcase the reemergence of the original species after the maturity of the habitats, and established an increasing model to compare the effects the reemergence of the two species has on the whole ecosystem.
随着农田生态系统的成熟,部分消失的物种可能会重新出现。因此,我们建立了一个模型来展示栖息地成熟后原始物种的重新出现,并建立了一个递增模型来比较这两个物种的重新出现对整个生态系统的影响。

Reemergence of species and ecological restoration:
The expression of species reemergence

dNdt=r×(1-NK)×f(agriculture-impact)

N:population of insects

r:species reemergence rate(decrease progressively)
K:population environmental carrying capacity(a constant)

Agriculture does have an impact on the species reemergence rate, so we use a function to illustrate the limitation agriculture exerts on the rate. That’s an external factor of the population. The internal one is the population of the species. Along with another external factor-the environmental carrying capacity of the population, it confines the species reemergence rate.
农业确实对物种重新出现率有影响,因此我们使用一个函数来说明农业对重新出现率的限制。这是人口的外部因素。内部的 A 是物种的种群数量。它与另一个外部因素——种群的环境承载能力一起,限制了物种的重新出现率。

f(agriculture-impact):therestrictiontospeciesreemergencefrom

agricultural influence , range between 0 and 1

f(agriculture-impact)=1-θ×A(t)

θ:sensitive coefficent of agricultural activities to species, a constant less than 1
A(t):agricultural activity strength with period,low in winter
A(t)=A×(1+sin(2πtT))
A:standard agricultural activity strength, a constant less than 1
T:activity cycle(day)
sin(2πtT):to show seasonal fluctuatiions

From this, we could know that when the agricultural intensity is lower, the f(agriculture-impact) is higher and the species reemergence rate is higher. On the contrary, it is lower. We find out that the species reemergence rate is inversely correlated with the agricultural intensity.
由此可以知道,当农业强度较低时,f(agriculture-impact) 较高,物种重新出现率较高。相反,它更低。我们发现物种重新出现率与农业强度呈负相关。

The influence of edge habitat maturity and species reemergence on agricultural ecosystem:
边缘生境成熟度和物种重新出现对农业生态系统的影响:

The emergence rate of species

P(t): producer number, a normal logistic model
C(t):consumer number , a normal logistic model

S(t):the number of reemergence species1 which prey on pests

S(t):number of reemergence species2 which are pollinators

H(t):edge habitat maturity

r:reproduction rate ofspecies1,less than1,

drop as the number of species 1 increase reach 0 at K

r:the growth rate of producers

r:thegrowthrateofconsumers

r:reproduction rate of species2

β:efficiency of returning species1 preying on consumers,intially less than 1

and drop to 0 as the number increases

β:the promotion of returning species2 to producers

γ:the maturity rate of edge habitat

δ:edge habitat maturity support coefficent to the population restoration of species 1

δ:edge habitat maturity support coefficent to the population resttoration of species 2

Dynamic equation for returning species 1:

dSdt=r×S×(1-SK)+δ×H+β×S×C

for species 2:

dSdt=r×S×(1-SK)+δ×H+β×S×P

Edge habitat maturity

dHdt=γ×(1-H)

γis the growth rate, which tends to stabilize when H=1

Suppose that species 1 refer to seven-starred ladybugs, and species 2 refer to bees
假设物种 1 指的是七星瓢虫,物种 2 指的是蜜蜂

We found that as the edge habitat comes to maturity, the two species rise in their populations continuously, compared to the model in the previous question, instead of reaching their maximums and falling afterwards.
我们发现,与上一个问题的模型相比,随着边缘栖息地的成熟,这两个物种的种群数量不断增加,而不是达到最大值并在之后下降。

5.Human decisions
5.人工决策

Humans play an important part in nature. We look into the role of humans in two aspects: one is the removal of herbicides, the other is the practice of organic farming.
人类在自然界中扮演着重要的角色。我们从两个方面来研究人类的作用:一是除草剂的去除,二是有机农业的实践。

1.Removal of herbicide
1. 除草剂

What comes with the maturity of the ecosystem is the less dependance of farmers on herbicide. To study the effect of the removal of herbicide, we would access it in terms of the producers and consumers
随着生态系统的成熟,农民对除草剂的依赖程度降低。为了研究去除除草剂的效果,我们将从生产者和消费者的角度来获取它

D(t):除草剂的量
D:除草剂的初始量
λ:除草剂的去除速率(常数)
D(t)方程:
D(t)=D×e
## 生产者动态方程:

$$\frac{dP}{dt}=r_P\times P(1-\frac{P}{K_P})-\alpha\times C\times P-\beta_P\times D(t)\times P$$

## 消费者动态方程:

$$\frac{dC}{dt}=r_C\times C(1-\frac{C}{K_C})+\alpha\times C\times P-\beta_C\times D(t)\times C$$

- $\alpha$:消费者捕食生产者的效率(初始值小于1且随消费者数量上升而下降最后变成0(快速降为0))

- $\beta_P$:化学品对生产者的抑制系数(010之间的一个常数)

- $\beta_C$:化学品对消费者的抑制系数(010之间的一个常数)

We could see that with the herbicide account dropping to zero, both the populations of consumers and producers rise to its maximum, in a curve similar to the Logistic Model of Increase. It showcases that the stability of the ecosystem is restored after the removal of the herbicide.
我们可以看到,随着除草剂账户下降到零,消费者和生产者的人口都上升到最大值,曲线类似于 Logistic Model of Increase。它表明,去除除草剂后,生态系统的稳定性得到了恢复。

5.2 Bats play a double role in the ecosystem back into balance, as they are not only insectivores that control pest populations, but also pollinators that support plant reproduction.
5.2 蝙蝠在生态系统恢复平衡中发挥着双重作用,因为它们不仅是控制害虫种群的食虫动物,也是支持植物繁殖的传粉者。

# 选择引入蝙蝠(只引入蝙蝠不考虑鸟类)

## 方程

### P(t):植物数量

### I(t):昆虫数量

### C(t):捕食者数量

### B(t):蝙蝠数量

## 植物变动

$$\frac{dP}{dt} = r_P\times P(1-\frac{P}{K_P})-\beta_I\times I \times P+\gamma_B\times B\times P$$

## 参数

- $r_P$:植物种群增长率(小于1,随植物种群数量增长而下降,在到达$K_P$之前不会降为0)

- $K_P$:植物种群最大容量

- $\beta_I$:昆虫对植物的破坏系数(初始值小于1且随植物数量上升而下降最后变成0)

- $\gamma_B$:蝙蝠对植物的促进系数(初始值小于1且随蝙蝠数量上升而上升但上升速度会逐渐变慢)

## 昆虫变动

$$\frac{dI}{dt} = r_I\times I(1-\frac{I}{K_I})-\alpha_B\times B \times I$$

## 参数

- $r_I$:昆虫种群增长率(小于1,随昆虫种群数量增长而下降,在到达$K_I$之前不会降为0)

- $K_I$:昆虫种群最大容量

- $\alpha_B$:蝙蝠对昆虫的捕食系数(初始值小于1且随蝙蝠数量上升而上升但不会超过1)

## 捕食者变动

$$\frac{dC}{dt} = r_C\times C(1-\frac{C}{K_C})+\eta_{C_B}\times C\times B-\epsilon_C$$

## 参数

- $r_C$:捕食者种群增长率(小于1,随捕食者种群数量增长而下降,在到达$K_C$之前不会降为0)

- $K_C$:捕食者种群最大容量

- $\eta_{C_B}$:蝙蝠对捕食者的促进系数(初始值小于1且随捕食者数量上升而下降,也会随蝙蝠数量下降而下降)

- $\epsilon_C$:捕食者死亡率(小于1的常数)

## 蝙蝠变动

$$\frac{dB}{dt} = r_B\times B(1-\frac{B}{K_B})+\eta_B\times B\times I-\epsilon_B-\alpha_C\times C\times B$$

## 参数

- $r_B$:蝙蝠种群增长率(小于1,随蝙蝠种群数量增长而下降,在到达$K_B$之前不会降为0)

- $K_B$:蝙蝠种群最大容量

- $\eta_B$:昆虫对蝙蝠的促进系数(初始值小于1且随蝙蝠数量上升而下降)

- $\epsilon_B$:蝙蝠死亡率(小于1的常数)

- $\alpha_C$:捕食者对蝙蝠的捕食系数(初始值小于1且随蝙蝠数量上升而下降)

We could see that the number of plants and the bats’ predators rises while the number of insects drops on an overall level, which means the overall stability of the ecosystem is risen. And specifically, the insects first increase and decrease afterwards.
我们可以看到,植物和蝙蝠的捕食者数量在整体水平上增加,而昆虫数量在整体水平上下降,这意味着生态系统的整体稳定性有所提高。具体来说,昆虫首先增加,然后减少。

Bats are effective pest hunters, so the insects drop drastically after a short period of increase. As insects, especially pests drop in number, the hazards of the plants decrease and the overall health and quality of the plants level up and they reproduce and increase, which flourishes other species as birds or some herbivore insects. And the predators preying on bats increase as well. Therefore, a new balance is reached and the overall stability of the ecosystem is enhanced.
蝙蝠是有效的害虫捕食者,因此昆虫在短暂增加后会急剧下降。随着昆虫,尤其是害虫数量的减少,植物的危害减少,植物的整体健康和质量提高,它们繁殖和增加,这让鸟类或一些食草昆虫等其他物种蓬勃发展。捕食蝙蝠的捕食者也有所增加。因此,达到了新的平衡,生态系统的整体稳定性得到了增强。

We introduced birds as an alternative species to bats as they both feed on pests, and they can both increase the reproduction rate of plants, promoting their reproduction.
我们引入了鸟类作为蝙蝠的替代物种,因为它们都以害虫为食,它们都可以提高植物的繁殖速度,促进它们的繁殖。

The\ equation\ considers\ birds\ only,\ regardless\ of\ the\ bats.
方程式只考虑 \ 只鸟\ \ 不管\ \ 蝙蝠\ 。

The\ equation\ of\ the\ variation\ of\ plants:
\ 植物的 \ 方程\ \ 变体\ :

P(t):植物数量

### I(t):昆虫数量
### C(t):捕食者数量
### B(t):鸟类数量
## 植物变动

dPdt=r×P(1-PK)-β×I×P+γ×A×P

## 参数

- $r_P$:植物种群增长率(小于1,随植物种群数量增长而下降,在到达$K_P$之前不会降为0)

- $K_P$:植物种群最大容量

- $\beta_I$:昆虫对植物的破坏系数(初始值小于1且随植物数量上升而下降最后变成0)

- $\gamma_A$:鸟类对植物的促进系数(初始值小于1且随鸟类数量上升而上升但上升速度会逐渐变慢)

## 昆虫变动

$$\frac{dI}{dt} = r_I\times I(1-\frac{I}{K_I})-\alpha_A\times A \times I$$

## 参数

- $r_I$:昆虫种群增长率(小于1,随昆虫种群数量增长而下降,在到达$K_I$之前不会降为0)

- $K_I$:昆虫种群最大容量

- $\alpha_A$:鸟类对昆虫的捕食系数(初始值小于1且随鸟类数量上升而上升但不会超过1)

## 捕食者变动

$$\frac{dC}{dt} = r_C\times C(1-\frac{C}{K_C})+\eta_{C_A}\times C\times A-\epsilon_C$$

## 参数

- $r_C$:捕食者种群增长率(小于1,随捕食者种群数量增长而下降,在到达$K_C$之前不会降为0)

- $K_C$:捕食者种群最大容量

- $\eta_{C_A}$:鸟类对捕食者的促进系数(初始值小于1且随捕食者数量上升而下降,也会随鸟类数量下降而下降)

- $\epsilon_C$:捕食者死亡率(小于1的常数)

## 鸟类变动

$$\frac{dA}{dt} = r_A\times A(1-\frac{A}{K_A})+\eta_A\times A\times I-\epsilon_A-\alpha_C\times C\times A$$

## 参数

- $r_A$:鸟类种群增长率(小于1,随鸟类种群数量增长而下降,在到达$K_A$之前不会降为0)

- $K_A$:鸟类种群最大容量

- $\eta_A$:昆虫对鸟类的促进系数(初始值小于1且随鸟类数量上升而下降)

- $\epsilon_A$:鸟类死亡率(小于1的常数)

- $\alpha_C$:捕食者对鸟类的捕食系数(初始值小于1且随鸟类数量上升而下降)

The interspecific relationships in birds’ cases follow a similar pattern to bats. The number of plants increases while the number of insects increases at first and decreases afterwards and all their numbers are inconsistent. It is noted that there are a range of fluctuations in the bats’ case, not in the birds.
鸟类的种间关系遵循与蝙蝠相似的模式。植物的数量增加,而昆虫的数量一开始增加,然后减少,它们的数量都不一致。值得注意的是,蝙蝠的情况存在一系列波动,而不是鸟类的情况。

Bats are nocturnal animals, while birds are normally diurnal animals. They form a distribution in time. Both of them feed on insects to reduce their populations and therefore can increase the populations of plants, which provide food to other species. As other species increase, the overall stability of the ecosystem is levitated. Bats can pollinate while birds mainly increase the reproduction rate of plants through dispersing seeds as they fly. Their effects are inconsistent as the study points out. Birds have a higher level of flying, and can fly to a wider range of habitats and disperse seeds on a wider range.
蝙蝠是夜行动物,而鸟类通常是昼夜动物。它们在时间上形成分布。它们都以昆虫为食以减少其数量,因此可以增加为其他物种提供食物的植物数量。随着其他物种的增加,生态系统的整体稳定性是悬浮的。蝙蝠可以授粉,而鸟类主要通过在飞行时传播种子来提高植物的繁殖率。正如研究指出的那样,它们的效果并不一致。鸟类的飞行水平更高,可以飞到更广泛的栖息地,并在更广阔的范围内传播种子。

As both birds and bats can decrease the insects, including pests, and increase the plants, including the crops, they can reduce the use of pesticide to increase the yield. And both of them have multiple roles in the ecosystem, so they add stability to the ecosystem as they can adjust interspecific relationships on a more macroscopic level.
由于鸟类和蝙蝠都可以减少昆虫(包括害虫)并增加植物(包括农作物),因此它们可以减少农药的使用以提高产量。而且它们都在生态系统中扮演着多种角色,因此它们可以在更宏观的层面上调整种间关系,从而增加生态系统的稳定性。

Going green
走向绿色

Organic farming is a new trend nowadays as people pursue for a greener and healthier way of farming. Therefore, we adopted optimizing strategy to help organic farming, or going green by finding the balance between the maximum of yield and the minimum of the costs of the environment and chemical use. The maximum of produce, or yield, can satisfy the food needs, while the minimum of the latter two can help protect biodiversity and controlling the use of chemicals help to reduce economic costs as well.We established an objective function and realized the maximum profit through the optimizing strategy by constructing an objective function Z.
有机农业是当今的一种新趋势,因为人们追求更绿色、更健康的耕作方式。因此,我们采用优化策略来帮助有机农业,或者通过在最大产量与环境和化学品使用成本最低之间找到平衡来走向绿色。农产品或产量的最大可以满足粮食需求,而后两者中的最小值可以帮助保护生物多样性,控制化学品的使用也有助于降低经济成本。我们建立了一个目标函数,并通过构建目标函数 Z 通过优化策略实现了最大利润。

# 走向绿色
## 在产量最大化与环境成本和化学药品使用成本最小化之间找到平衡
- 如何最大化产量Y,以满足粮食供给
- 如何最小化环境成本$C_E$,保护物种多样性
- 如何控制学药品使用成本D,减轻经济负担

## 构造目标函数Z,通过优化策略实现效益最大化

Z=a×Y-b×C-c×D

### 参数
- a,b,c:是权重系数,用于反映决策者对各项指标的重视程度
- Y:产量,通常是资源的投入函数
-C:环境成本
- D:化学药品使用成本,取决与使用量

产量Y:Y=f(R,M,P)

### 参数
- R:自然资源(如水,土和生物)
- M:不合理管理策略的强度
- P:化学品使用量
η资源的产量效率系数

Y=R×η×(1-d×p)×(1-β×M)

参数

-d害虫对产量的抑制系

- R×η:资源的基础产量贡献

-β管理策略的损耗系

-(1-d×p):害虫对产量的负面影响

-(1-β×M):管理策略对产量的影响

环境成本C:C=g(p,Y)

C=Y×P+Y×YK

### 参数
-Y:化学药品对环境的影响系数
-Y:产量对环境的影响系数(如资源消耗)
-K产量的环境承载力
- P:化学药品使用量
- Y:产量

Z=a×f(R,M,P)-b×g(P,f(R,M,P))-c×k×P

## 约束条件
-RR资源限制
-PP化学药品使用上限
-CC管理策略限制

## 参考权重:b>a>c 具体数据可主观设置a+b+c=1

We take three factors into account in the optimizing strategy: yield, environmental costs and the costs for chemical usage. It provides the solution to the optimal use of chemical. To individuals, organic farming by using the most appropriate amount of chemicals is cost-effective since they won’t be that reliant on chemicals as herbicide or pesticide and there will be a higher yield or gain. For the whole ecosystem, the benefits are huge. Organic farming usually takes natural measures to control pests like introducing natural enemies. As pest control can be done more effectively and efficiently, crop health is ensured as well as the yield. As interspecific relationships exist if adopting organic farming, we can protect the biodiversity of the nature. For example, bats and birds as we mention above can continue to help reduce pests. And in turn chemicals are used less and we can continue to save the costs of chemicals and protect the environment from the pollution and hazards on the long run. A sustainable mode of farming is established.
我们在优化策略中考虑了三个因素:产量、环境成本和化学品使用成本。它为化学品的最佳使用提供了解决方案。对于个人来说,使用最适量的化学品进行有机农业具有成本效益,因为他们不会那么依赖除草剂或杀虫剂等化学品,并且会有更高的产量或收益。对于整个生态系统来说,好处是巨大的。有机农业通常采取自然措施来控制害虫,例如引入天敌。由于可以更有效地进行害虫防治,因此可以确保作物健康和产量。由于采用有机农业存在种间关系,我们可以保护自然界的生物多样性。例如,正如我们上面提到的,蝙蝠和鸟类可以继续帮助减少害虫。反过来,化学品的使用量减少,从长远来看,我们可以继续节省化学品的成本,并保护环境免受污染和危害。建立了可持续的农业模式。

Sensitivity Analysis
敏感性 A分析

模型的分析 :在建模比赛中模型分析主要有两种,一个是灵敏度()分析,另一个是误差分析。灵敏度分析是研究与分析一个系统(或模型)的状态或输出变化对系统参数或周围条件变化的敏感程度的方法。其通用的步骤是:控制其他参数不变的情况下,改变模型中某个重要参数的值,然后观察模型的结果的变化情况。误差分析是指分析模型中的误差来源,或者估算模型中存在的误差,一般用于预测问题或者数值计算类问题。
模型的分析:在建模比赛中模型分析主要有两种,一个是灵敏度分析,另一个是误差分析。灵敏度分析是研究与分析一个系统(或模型)的状态或输出变化对系统参数或周围条件变化的敏感程度的方法。其通用的步骤是:控制其他参数不变的情况下,改变模型中某个重要参数的值,然后观察模型的结果的变化情况。误差分析是指分析模型中的误差来源,或者估算模型中存在的误差,一般用于预测问题或者数值计算类问题。

模型的检验:模型检验可以分为两种,一种是使用模型之前应该进行的检验,例如层次分析法中一致性检验,灰色预测中的准指数规律的检验,这部分内容应该放在模型的建立部分;另一种是使用了模型后对模型的结果进行检验,数模中最常见的是稳定性检验,实际上这里的稳定性检验和前面的灵敏度分析非常类似,等会大家看到例子就明白了。

在美赛的写作中,写的最多的就是灵敏度分析(Sensitivity Analysis),因此这里我们的标题就直接取得是灵敏度分析;如果你既要写灵敏度分析,又要写误差分析(Error Analysis),那么你可以把标题改成: Sensitivity Analysis and Error Analysis
在美赛的写作中,写的最多的就是灵敏度分析(Sensitivity Analysis),因此这里我们的标题就直接取得是灵敏度分析;如果你既要写灵敏度分析,又要写误差分析(Error Analysis),那么你可以把标题改成: Sensitivity Analysis and Error Analysis

Model Evaluation and Further Discussion
模型评估进一步讨论

注:本部分的标题需要根据你的内容进行调整,例如:如果你没有写进一步讨论的话,就直接把标题写成模型的评价(优缺点一定要写

Strengths
优势

这里写论文或者模型的优点

Weaknesses
地震

这里写缺点:缺点写的个数一般要比优点少

Further Discussion
进一步讨论

进行进一步的讨论,这里可以写模型的改进和拓展:

模型的改进:主要是针对模型中缺点有哪些可以改进的地方;
模型的改进:主要是针对模型中缺点有哪些可以改进的地方;

模型的拓展:将原题的要求进行扩展,进一步讨论模型的实用性和可行性。

8. Letter of Advice
8. 建议书

Dear Esteemed Farmers,
尊敬的农民们:

We are researchers related to the study of environmental protection. In order to better preserve the forests while enjoying a high yield of crops, please allow me to introduce our proposal on behalf of the team. We have recently conducted an all-sided research aimed at bettering both the environment and the yield of crops. Our findings showcase a strategic blueprint that highlights not only the sustainability of the nature but also the prosperity of your life. Our proposed plan comprises innovative preservation techniques and farming-centric initiatives drafted to safeguard the environment your economic interest.
我们是与环境保护研究相关的研究人员。为了更好地保护森林,同时享受高产的农作物,请允许我代表团队介绍我们的提案。我们最近进行了一项全面的研究,旨在改善环境和农作物产量。我们的研究结果展示了一个战略蓝图,不仅突出了自然的可持续性,还突出了您生活的繁荣。我们提出的计划包括创新的保护技术和以农业为中心的举措,旨在保护环境、您的经济利益。

There are a few organic farming practices that you can use. Firstly, you can use crop rotation that is a fundamental practice where different crops are grown in the same area in sequential seasons. It helps in reducing pest and disease incidence, and improving overall soil health. Secondly, you can adopt companion planting. Certain plants can be grown together to deter pests, improve pollination, and enhance overall crop health. Moreover, you can adopt Integrated Pest Management, which involves using a combination of biological, mechanical, and cultural methods to control pests. In these ways, the use of pesticides and herbicides is reduced. These ways can also lower fuel and labor costs in the long run. Organic practices, such as manual weeding and composting, may require more labor compared to conventional farming, which means higher labor costs. In the transition phase, yields might be lower due to the absence of synthetic inputs and the time taken for soil health to improve. However, over time, organic farming can lead to more resilient and productive systems. Organic certification can be expensive and time-consuming. However, it opens up access to premium markets and higher prices for organic produce. Organic farming is economic and sustainable for yourselves and for the nature on the long run.
您可以使用一些有机农业实践。首先,您可以使用作物轮作,这是一种基本做法,即在连续的季节中在同一地区种植不同的作物。它有助于减少病虫害的发生率,并改善整体土壤健康状况。其次,您可以采用伴生种植。某些植物可以一起种植以阻止害虫、改善授粉并增强作物的整体健康状况。此外,您可以采用综合害虫管理,其中包括结合使用生物、机械和培养方法来控制害虫。通过这些方式,减少了杀虫剂和除草剂的使用。从长远来看,这些方法还可以降低燃料和劳动力成本。与传统农业相比,人工除草和堆肥等有机做法可能需要更多的劳动力,这意味着更高的劳动力成本。在过渡阶段,由于缺乏合成原料和改善土壤健康所需的时间,产量可能会降低。然而,随着时间的推移,有机农业可以带来更具弹性和生产力的系统。有机认证可能既昂贵又耗时。然而,它为有机农产品打开了进入优质市场和更高价格的机会。从长远来看,有机农业对您自己和自然都是经济和可持续的。

I'd like to introduce some strategies to balance costs and sustainability. You can not only diversify crops and income sources by growing a variety of crops. It can reduce reliance on a single cash crop. Moreover, you can learn about the latest organic farming techniques and sustainable practices, which can help optimize your operations and reduce costs in the long run. It is also recommended to look for community and cooperative support. You can set up or join local farming cooperatives or networks to obtain shared resources and knowledge, as well as bulk purchasing power for inputs like seeds and compost. There are policies we advocate for to incentivize sustainable agriculture. Governments can advocate for policies that provide financial support for organic transition, such as subsidies for organic inputs, and cover crop seeds. Market access programs can support initiatives that help organic farmers access local and international markets, such as community-supported agriculture programs, and export opportunities. We invite you to support our plan, ensuring that not only can you live in harmony with nature but also you can harvest a better yield for countless years to come.
我想介绍一些平衡成本和可持续性的策略。您不仅可以通过种植各种作物来实现作物和收入来源的多样化。它可以减少对单一经济作物的依赖。此外,您可以了解最新的有机农业技术和可持续实践,从长远来看,这可以帮助您优化运营并降低成本。还建议寻找社区和合作支持。您可以建立或加入当地的农业合作社或网络,以获得共享资源和知识,以及种子和堆肥等投入品的批量购买力。我们倡导一些政策来激励可持续农业。政府可以倡导为有机转型提供财政支持的政策,例如对有机投入品的补贴,并覆盖作物种子。市场准入计划可以支持帮助有机农民进入当地和国际市场的举措,例如社区支持的农业计划和出口机会。我们邀请您支持我们的计划,确保您不仅可以与自然和谐相处,而且可以在未来无数年收获更好的产量。

Sincerely, Team #2425059
诚挚的,团队 #2425059

References
引用

参考文献至少五六篇,引用中文文献记得翻译成英文。

在正文对应部分也设置序号

引用格式一定要正确,建议从检索网站直接导出,下图以知网为例

10 Report on Use of AI
10 AI 使用报告

1. OpenAI ChatGPT (Jan 10, 2024 version, ChatGPT-4o)
1. OpenAI ChatGPT(2024 年 1 月 10 日版,ChatGPT-4o)

Query: Help find essay on global deep forest destruction
查询:帮助查找关于全球深层森林破坏的论文

Output:
输出:

To explore global forest destruction, you can utilize the interactive map provided by Global Forest Watch. This platform offers detailed data on tree cover loss, gain, and other forest-related metrics worldwide. You can access it here: https://www.globalforestwatch.org/map/
要探索全球森林破坏,您可以使用 Global Forest Watch 提供的交互式地图。该平台提供有关全球树木覆盖损失、增加和其他森林相关指标的详细数据。您可以在此处访问它:https://www.globalforestwatch.org/map/

2. OpenAI ChatGPT (Jan 10, 2024 version, ChatGPT-4o)
2. OpenAI ChatGPT(2024 年 1 月 10 日版,ChatGPT-4o)

For touching up our papers in English
用于润色我们的英文论文

3. DeepSeek (Jan 20, 2025 version DeepSeek-R1)
3. DeepSeek(2025 年 1 月 20 日版 DeepSeek-R1)

Query: What tools can be used to create beautiful mind maps
查询:可以使用哪些工具创建漂亮的思维导图

Output:
输出:

PPT/Keynote: suitable for quick implementation of basic matrix and color fills.
PPT/Keynote:适合快速实现基本的矩阵和颜色填充。

Adobe Illustrator: fine tuning of icons, arrows and gradient effects.
Adobe Illustrator:微调图标、箭头和渐变效果。

FigJam: online collaborative design with modular drag and drop and annotation support.
FigJam:在线协同设计,支持模块化拖放和注释。

4. Github CoPilot (Jan 24, 2025 version)
4. Github CoPilot(2025 年 1 月 24 日版)

Auto-completions for code used in preparing our models.
用于准备模型的代码的自动补全。

5. Perplexity(Jan 23,2025 version)
5. 困惑(2025 年 1 月 23 日版)

Query: Help find essay on global deep forest destruction
查询:帮助查找关于全球深层森林破坏的论文

Output:
输出:

Causes of Deforestation
森林砍伐的原因

Agricultural Expansion: The need for more land to grow crops and raise livestock is a primary driver of deforestation. Vast areas of forests are cleared to make way for agricultural activities, particularly for commodities like palm oil, soybeans, and beef.
农业扩张:需要更多的土地来种植农作物和饲养牲畜是森林砍伐的主要驱动力。大面积的森林被砍伐,为农业活动让路,特别是棕榈油、大豆和牛肉等商品。

Logging: Both legal and illegal logging contribute to forest loss. Timber is harvested for construction, paper products, and fuel, often leading to unsustainable practices that degrade forest ecosystems.
伐木:合法和非法伐木都会导致森林损失。采伐木材用于建筑、纸制品和燃料,这通常会导致不可持续的做法,使森林生态系统退化。

Urbanization: As populations grow, urban areas expand, necessitating the clearing of forests for housing and infrastructure. This leads to habitat destruction and increased pressure on remaining forested areas.
城市化:随着人口的增长,城市地区扩大,需要砍伐森林用于住房和基础设施。这导致栖息地破坏,并增加了对剩余森林地区的压力。

Climate Change: Changes in climate can exacerbate deforestation through phenomena like acid rain and increased temperatures that affect tree health and growth.
气候变化:气候变化会通过酸雨和温度升高等影响树木健康和生长的现象加剧森林砍伐。

Effects of Deforestation
森林砍伐的影响

Loss of Biodiversity: Forests are home to a vast array of species. Deforestation leads to habitat destruction, putting many species at risk of extinction.
生物多样性的丧失:森林是大量物种的家园。森林砍伐导致栖息地破坏,使许多物种面临灭绝的风险。

Climate Impact: Trees play a crucial role in carbon sequestration. When forests are cut down, the carbon stored in trees is released back into the atmosphere, contributing to global warming. Deforestation is responsible for approximately 20% of global greenhouse gas emissions.
气候影响:树木在碳封存中起着至关重要的作用。当森林被砍伐时,树木中储存的碳被释放回大气中,导致全球变暖。森林砍伐约占全球温室气体排放量的 20%。

Soil Erosion: The removal of trees destabilizes soil, leading to erosion and decreased soil fertility. This can result in landslides and flooding, further disrupting ecosystems.
土壤侵蚀:树木的移除会破坏土壤的稳定性,导致土壤侵蚀和土壤肥力下降。这可能导致山体滑坡和洪水,进一步破坏生态系统