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2023年美國大學生數學建模競賽（MCM/ICM）A題賽題公布

Category: 國際競賽, 數模國際競賽, 翰林嚴選 Date: 2023年2月17日下午5:41

萬眾矚目的2023年度美賽終于正式開賽了！每年的這個時候，很多參賽團隊都會涌入官網查看題目，結果不少團隊就會被卡住，只能一遍又一遍地刷新網頁，為了幫大家節省時間和精力，避免在官網“無限”刷新卻擠不進去的尷尬，小編為大家帶來2023年美國大學生數學建模學術活動（MCM/ICM）A題賽題。

中文賽題 A：飽經旱災的植物群落

背景

不同植物物種對應激有不同的反應方式。例如，草原對干旱非常敏感。干旱發生的頻率和嚴重程度各不相同。眾多觀察結果表明，不同物種的存在數量在植物群落面對連續幾代的干旱循環時發揮了重要作用。在一些只有一種植物物種的群落中，接下來的幾代植物并沒有像多種物種的群落中的個體那樣適應干旱條件。這些觀察結果引發了許多問題。例如，植物群落中最少需要多少個物種才能從這種局部生物多樣性中獲益？隨著物種數量的增加，這種現象如何擴展？這對植物群落的長期生存能力意味著什么？

要求

考慮干旱適應性與植物群落中物種數量的關系，您的任務是探索和更好地理解這一現象。具體而言，您應該：

開發一個數學模型，預測植物群落在暴露于各種不規則的天氣周期中的變化情況，包括降水應該充足的干旱時期。該模型應考慮干旱周期中不同物種之間的相互作用。探索您可以從模型中得出的有關植物群落與更大環境之間長期相互作用的結論。考慮以下問題：
- 植物群落所需的不同植物物種數量是多少，并且隨著物種數量的增加會發生什么？
- 植物群落中物種類型對您的結果有什么影響？
- 未來天氣周期中更頻繁和更廣泛發生干旱的影響是什么？如果干旱不那么頻繁，那么物種數量對整體種群的影響是否相同？
其他因素，如污染和棲息地減少，如何影響您的結論？
您的模型表明應該采取什么措施確保植物群落的長期生存能力，以及對更大環境的影響是什么？

你的PDF解決方案總頁數不得超過25頁，包括：

一頁摘要。
目錄。
完整的解決方案。
參考文獻清單。

注意：MCM比賽有25頁的限制。你的所有提交內容都計入這25頁的限制（摘要，目錄，報告，參考文獻清單以及任何附錄）。你必須引用報告中使用的想法、圖片和其他材料的來源。

詞匯表

生物多樣性：指世界或特定棲息地或生態系統中生命的多樣性。

Problem A: Drought-Stricken Plant Communities

Background

Different species of plants react to stresses in different ways. For example, grasslands are quite sensitive to drought. Droughts occur at varying frequencies and varying levels of severity. Numerous observations suggest that the number of different species present plays a role in how a plant community adapts when exposed to cycles of drought over successive generations. In some communities with only one species of plant, the generations that follow are not as well adapted to drought conditions as the individual plants in communities with four or more species. These observations raise many questions. For example, what is the minimal number of species necessary for a plant community to benefit from this type of localized biodiversity? How does this phenomenon scale as the number of species increases? What does this imply for the long-term survivability of a plant community?

Requirement

Considering the relationship of drought adaptability with respect to the number of species in a plant community, your task is to explore and better understand this phenomenon. Specifically, you should:

Develop a mathematical model to predict how a plant community changes over time as it is exposed to various irregular weather cycles. Include times of drought when precipitation should be abundant. The model should account for interactions between different species during cycles of drought.
Explore what conclusions you can draw from your model with respect to the long-term interactions of a community of plants and the larger environment. Consider the following questions:
- How many different plant species are required for the community to benefit and what happens as the number of species grows?
- How do the types of species in the community impact your results?
- What are the impact of a greater frequency and wider variation of the occurrence of droughts in future weather cycles? If droughts are less frequent, does the number of species have the same impact on the overall population?
How do other factors such as pollution and habitat reduction impact your conclusions?
What does your model indicate should be done to ensure the long-term viability of a plant community and what are the impacts on the larger environment?

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

One-page Summary Sheet.
Table of Contents.
Your complete solution.
Reference List. Note: The MCM Contest has a 25-page limit. All aspects of your submission count toward the 25-page limit (Summary Sheet, Table of Contents, Report, Reference List, and any Appendices). You must cite the sources for your ideas, images, and any other materials used in your report.