2025年美國大學生數學建模競賽E題中英版

中文賽題：為農業騰出空間

情境

一片充滿參天大樹和多樣化野生動物的森林被清理，以騰出農(nong) 業(ye) 用地。這片曾經生機勃勃的生態係統——鳥類、昆蟲和動物的家園——不複存在，取而代之的是成排的農(nong) 作物。土地開始發生變化：曾經蘊含自然豐(feng) 富性的土壤變得貧瘠，害蟲開始侵襲作物。為(wei) 了應對這些問題，農(nong) 民使用了化學品，但這種做法破壞了土地的平衡。隨著這種轉變，原本繁榮的生態係統網絡被打破，取而代之的是基於(yu) 農(nong) 業(ye) 生態係統的新食物網。在一個(ge) 成熟的農(nong) 業(ye) 係統中，有蝙蝠、鳥類及其他物種，但要實現這一點，生態係統必須逐漸成熟。

建模與分析

世界各地都存在類似的情景。作為(wei) “成熟農(nong) 業(ye) 實踐考量小組”（COMAP）的成員，您被要求構建一個(ge) 模型，追蹤從(cong) 森林到農(nong) 場的棲息地變化過程。您的主管希望您的團隊能夠主導分析一個(ge) 被改造的森林區域如何隨著生態係統的演變及伴隨的農(nong) 業(ye) 選擇而發生變化。主管希望分析包括自然過程以及人類決(jue) 策。因此，您應從(cong) 一個(ge) 新清理的改造森林生態係統開始建模，並通過物種變化以及農(nong) 業(ye) 實踐的多種影響，追蹤模型的變化階段。您可以基於(yu) 假設構建森林到農(nong) 場的情景，也可以使用此類演變的曆史實際數據。以下是您在分析中可能需要考慮的方麵：

自然過程

• 構建當前生態係統的模型：為替代原始森林地區的新農業生態係統建立一個基礎食物網模型。包括生產者和消費者，以及農業周期和其季節性變化對係統動態的影響。考慮除草劑和殺蟲劑的影響，包括化學品使用對植物健康、昆蟲種群、蝙蝠和鳥類種群以及生態係統穩定性的影響。
• 物種的重新出現：隨著邊緣棲息地的成熟，本地物種逐漸回歸。當物種回歸時，這些物種與現有環境的相互作用會改變農業生態係統。將兩種不同的物種納入模型以確定其影響。

人類決(jue) 策

• 移除除草劑：隨著生態係統的成熟，農民可能嚐試減少對化學品的依賴。
  • 如果移除了除草劑，請報告生態係統在生產者和消費者方麵的穩定性。
  • 通過將蝙蝠引入食物網模型，使生態係統恢複平衡。將蝙蝠作為控製害蟲的食蟲動物和支持植物繁殖的傳粉者進行建模。考慮蝙蝠與昆蟲、植物及捕食者的相互作用對生態係統整體穩定性的影響。確定另一種有益物種以恢複生態平衡，並比較其影響。
• 綠色農業？分析農民考慮有機農業方法的影響。應考慮不同有機農業成分的情景，展示對生態係統整體及其各組成部分的影響。討論諸如害蟲控製、作物健康、植物繁殖、生物多樣性、長期可持續性及成本效益等方麵。

分享您的見解

• 包括一封寫給探索有機農業實踐的農民的一頁信。
• 為農民提供有關應采用哪些方法的建議，包括經濟權衡和可持續性討論。幫助農民製定策略，在成本和可持續性之間取得平衡，並討論如何倡導某些政策以激勵這種農業保護方式。

您的 PDF 解決(jue) 方案總頁數不得超過25頁，包括：

• 一頁摘要頁。
• 目錄。
• 完整解決方案。
• 一封給交通官員的信（一頁）。
• 參考文獻列表。
• AI使用報告（如果使用不計入 25 頁總限製）。

注意：完整的 MCM 提交文件沒有特定的最低頁數要求。您最多可使用 25 頁來包含您的所有解決(jue) 方案內(nei) 容及其他補充信息（例如圖紙、圖表、計算和表格）。允許提交部分解決(jue) 方案。我們(men) 允許謹慎使用 AI 工具（例如 ChatGPT），但完成本問題並不一定需要使用 AI 工具。如果您選擇使用生成式 AI 工具，必須遵循 COMAP 的 AI使用政策。此政策要求您在解決(jue) 方案文件的最後額外添加一份 AI 使用報告，不計入 25 頁的總限製。

全新 MCM/ICM：在線提交流程

本文旨在協助和指導參加 MCM/ICM 的學生和顧問。在文章中，COMAP 提供了有關(guan) 使用新在線提交頁麵的新在線提交流程的信息：

https://forms.comap.org/241335097294056

您需要團隊的控製號、顧問 ID 號和問題選擇才能完成提交。

術語表

改造森林區域：指森林被清理後用於(yu) 農(nong) 業(ye) 的土地。

食物網：食物網是生態係統中生物之間複雜的捕食關(guan) 係網絡，展示了能量和營養(yang) 如何在生態係統的不同層次間流動和相互作用。從(cong) 生產(chan) 者（植物）到多個(ge) 層次的消費者（草食動物、肉食動物和雜食動物），再到分解者（真菌、細菌），它對於(yu) 理解生態係統如何運作和維持平衡至關(guan) 重要。

• 初級生產者：植物和農作物。
• 初級消費者：以植物為食的草食動物。
• 次級消費者：以草食動物為食的肉食動物和其他捕食者。
• 三級消費者：以次級消費者為食的大型捕食者。
• 分解者：分解死亡生物並將營養物質帶回生態係統的真菌、細菌和蚯蚓。

農(nong) 業(ye) 生態係統：農(nong) 業(ye) 生態係統是複雜的，其中各種生物通過食物網相互作用，既支持生態平衡又促進作物生產(chan) 。人類幹預，如使用除草劑、殺蟲劑和化肥，通常用於(yu) 提高作物產(chan) 量，但可能帶來負麵的生態和經濟後果。蝙蝠在農(nong) 業(ye) 生態係統中發揮重要作用，提供諸如害蟲控製和授粉等生態服務，從(cong) 而促進農(nong) 業(ye) 的可持續性。

農(nong) 業(ye) 周期：農(nong) 業(ye) 周期是指農(nong) 業(ye) 生產(chan) 的各個(ge) 階段，從(cong) 種植和作物生長到收獲以及為(wei) 消費或銷售做準備。關(guan) 鍵階段包括：

• 土壤準備：通過翻耕、除草和添加肥料準備土地。土壤是作物生長的重要媒介，也是食物網的基礎。
• 種植/播種：在適宜的時間種植種子或秧苗，這取決於天氣、溫度和土壤條件。
• 生長期：作物通過光合作用生長，吸收空氣中的二氧化碳、土壤中的水和太陽能。這是食物網能量流動的一部分，植物是生產者，與草食動物發生相互作用。
• 施肥與害蟲控製：通過施肥確保作物獲得足夠的營養，並使用殺蟲劑或有機方法控製可能損害作物的害蟲。這些方法可能通過影響某些物種對自然食物網產生連鎖效應。
• 收獲：當作物成熟時被收割，暫時從食物網中移除植物。
• 後處理：作物被加工為食品、包裝並運輸至市場，連接農業周期與更廣泛的經濟活動。
• 消費：最終，作物被人類和動物消費，或轉化為其他產品。
• 分解：任何有機廢物可能會分解，將營養物質歸還土壤。

蝙蝠：作為(wei) 有益農(nong) 業(ye) 食物網的一個(ge) 例子，蝙蝠在維持健康生態係統中發揮重要作用，從(cong) 而帶來顯著的經濟利益。這包括害蟲控製、授粉和種子傳(chuan) 播、生態係統平衡、提供肥料的蝙蝠糞、生態旅遊，以及減少醫療成本。

邊緣棲息地：農(nong) 業(ye) 用地周圍的區域，作為(wei) 農(nong) 田與(yu) 周圍生態係統之間的緩衝(chong) 地帶。

Problem: Making Room for Agriculture

Situation

A forest filled with towering trees and diverse wildlife was cleared to make way for agriculture. The once-thriving ecosystem, home to birds, insects, and animals, vanished and in its place, rows of crops were planted. The land began to change – soil that once held the richness of nature became depleted, and pests began to invade the crops. To combat this, the farmers turned to chemicals, but the balance of the land was disrupted. With this shift, the intricate web of life that had flourished in the forest was broken, and a new, human-driven cycle of agriculture took its place creating a new food web based on an agricultural ecosystem. In an established agricultural system, there are bats, birds and other species but to get there, the ecosystem must mature.

Model and Analyze

In places throughout the world, scenarioses like this one occur. As a member of the Consideration of Mature Agricultural Practices (COMAP) group, you have been asked to construct a model to track habitat change from forest-to-farm. Your supervisor has given your team the lead in determining how a converted forest area can change over time as the ecosystem evolves along with accompanying agricultural choices. Your supervisor wants the analysis to include both natural processes as well as human decisions. Therefore, you should start your model of a newly cleared converted forest area ecosystem and track the model through stages of change due to the changes in species in addition to the many impacts of farming practices. You can make assumptions to build a situation of forest-to-farm, or you can use data and information from stages in a real historic sample of this kind of evolution. You may want to consider the following in your analysis:

Natural Processes

• Model the current ecosystem. Build a basic food web model for this new agricultural ecosystem which recently took the place of a heavily forested region. Include the producers and the consumers as well as the impact of the agriculture cycle and its seasonality which changes the system dynamics over time. Consider the impact of herbicides and pesticides by including the effects of chemical use on plant health, insect populations, bat and bird populations as well as the ecosystem stability.
• Incorporate the reemergence of species. Over time, the edge habitats begin to mature which brings back the species native to the area. As species return, the agricultural ecosystem changes due to the interactions of these species with the current environment. Incorporate two different species into the model to determine the impacts.

Human Decisions

• Removal of herbicide. As the ecosystem matures, farmers may attempt to remove some of the chemical dependance.
  • If the herbicide was removed, report on the stability of the ecosystem in terms of the producers and consumers.
  • Bring the ecosystem back into balance by incorporating bats into the food web model. Model bats as insectivores that control pest populations and as pollinators that support plant reproduction. Consider how bats' interactions with insects, plants, and predators influence the overall stability of the ecosystem. Identify another species that can provide benefits to bring the ecosystem back into balance and compare the impacts.
• Go green? Analyze the implications of a farmer considering organic farming methods. Consideration should be given to different scenarioses with varying components of organic farming. Demonstrate the impact on the ecosystem as a whole and to the individual components. Discuss aspects such as pest control, crop health, plant reproduction, biodiversity, long-term sustainability and cost effectiveness.

Share Your Insights：

• Include a one-page letter to a farmer who is exploring organic farming practices.
• Advise the farmer on what methods should be employed including discussions on economic trade-offs as well as sustainability. Help the farmer determine strategies that could be implemented to balance costs and sustainability and how advocating for certain policies could incentivize this type of conservation in agriculture.

Your PDF solution of no more than 25 total pages should include:

• One-page Summary Sheet.
• Table of Contents.
• Your complete solution.
• One-page letter to the transportation officials.
• References list.
• AI Use Report (If used does not count toward the 25-page limit.)

Note: There is no specific required minimum page length for a complete MCM submission. You may use up to 25 total pages for all your solution work and any additional information you want to include (for example: drawings, diagrams, calculations, tables). Partial solutions are accepted. We permit the careful use of AI such as ChatGPT, although it is not necessary to create a solution to this problem. If you choose to utilize a generative AI, you must follow the COMAP AI use policy. This will result in an additional AI use report that you must add to the end of your PDF solution file and does not count toward the 25 total page limit for your solution.

NEW MCM/ICM: Online Submission Process

The purpose of this article is to assist and guide students and advisors participating in MCM/ICM. In the article, COMAP, provides information about the new online submission process using the new online submission page:

https://forms.comap.org/241335097294056

You will need your team's control number, advisor id number and your problem choice to complete your submission.

Glossary

Converted Forest Area: An area where a forest was cleared so the land could be used for agriculture.

Food Web: A food web is a complex network of feeding relationships between organisms in an ecosystem. It depicts how energy and nutrients flow and interact through different levels of the ecosystem from producers (plants) to many levels of consumers (herbivores, carnivores, and omnivores) and then decomposers (fungi, bacteria). It is critical to understanding how ecosystems function and maintain balance.

• Primary producers: Plants and crops.
• Primary consumers: Herbivores that feed on plants.
• Secondary consumers: Insectivores and other predators that consume herbivores.
• Tertiary consumers: Larger predators that feed on secondary consumers.
• Decomposers: Fungi, bacteria and earthworms that break down the dead and bring nutrients back into the ecosystem.

Agricultural Ecosystem: Agricultural ecosystems are complex, with various species interacting in food webs that support both ecological balance and crop production. Human interventions such as the use of herbicides, pesticides, and fertilizers are commonly employed to increase crop yields, but these can have negative ecological and economic consequences. Bats provide valuable ecosystem services, such as pest control and pollination, which contribute to agricultural sustainability.

Agriculture Cycle: The agriculture cycle refers to the stages of agricultural production from planting and growing crops to harvesting and preparing them for consumption or sale. Key stages are:

• Preparation of Soil: Farmers prepare the land by tilling, removing weeds, and adding fertilizers. The soil is critical as it serves as the medium in which crops grow and supports the food web.
• Planting/Seeding: Farmers plant seeds or seedlings at the appropriate time for the crops to grow. This is dependent on weather, temperature and soil conditions.
• Growth Phase: Crops grow through photosynthesis as they take in carbon dioxide from the air, water from the soil, and energy from the sun. This is part of the energy flow in the food web as the plants are the producers and the herbivores may interact with them.
• Fertilization and Pest Control: Fertilizers can be applied to ensure crops have enough nutrients to grow. Pesticides or organic methods may be used to control pests that can damage crops. These methods may impact the natural food webs by affecting certain species, which can have cascading effects on the ecosystem.
• Harvesting: When the crops reach maturity, they are harvested which removes the plants from within the food web temporarily.
• Post-Harvest Processing: Crops can be processed into food products, packaged and transported to markets which connects the agricultural cycle with the broader economy.
• Consumption: Finally, the crops are consumed by humans and animals or converted into other products.
• Decomposition: Any organic waste may decompose, returning nutrients to the soil.

Bats: As an example of a species beneficial to agricultural food webs, we introduce the importance of bats. They play a critical role in maintaining healthy ecosystems, which in turn provides significant economic benefits. This includes pest control, pollination and seed dispersal, ecosystem balance, guano as fertilizer, ecotourism, as well as reduced health care cost.Edge Habitats: The habitats in the area around a field used for agriculture that serves as a buffer between the field and the surrounding ecosystem(s).