2024年MCM/ICM美國大學(xué)生數(shù)學(xué)建模競賽A題中英版發(fā)布

2024年美賽競賽時(shí)間為2024年2月2日早晨6點(diǎn)-2月6日早晨9點(diǎn)，2024年MCM/ICM美國大學(xué)生數(shù)學(xué)建模競賽A題中英版一起來看看。

中文賽題：資源可用性和性別比例

雖然一些動(dòng)物物種存在于常見的雄性或雌性之外，但大多數(shù)物種要么是雄性要么是雌性。盡管許多物種在出生時(shí)表現(xiàn)出1:1的性別比例，其他物種則偏離了均等的性別比例。這被稱為適應(yīng)性性別比例變化。例如，孵化美國短吻鱷蛋的巢穴溫度會(huì)影響出生時(shí)的性別比例。

七鰓鰻的角色復(fù)雜。在一些湖泊棲息地，它們被視為對生態(tài)系統(tǒng)有重大影響的寄生物，而在世界的一些地區(qū)，如斯堪的納維亞、波羅的海地區(qū)以及北美太平洋西北部的一些土著民族中，七鰓鰻也是食物來源。

海洋七鰓鰻的性別比例可以根據(jù)外部環(huán)境變化。海洋七鰓鰻在幼蟲階段的生長速度快慢決定了它們成為雄性還是雌性。這些幼蟲的生長速度受到食物可用性的影響。在食物可用性低的環(huán)境中，生長速率會(huì)降低，雄性的比例可達(dá)到大約78%。在食物更容易獲得的環(huán)境中，觀察到雄性的比例大約為56%。

我們關(guān)注的問題是性別比例及其依賴于局部條件的問題，特別是對于海洋七鰓鰻。海洋七鰓鰻生活在湖泊或海洋棲息地，并遷移到河流產(chǎn)卵。任務(wù)是檢查一個(gè)物種根據(jù)資源可用性改變其性別比例的能力的優(yōu)勢和劣勢。你的團(tuán)隊(duì)?wèi)?yīng)該開發(fā)并檢查一個(gè)模型，以提供對生態(tài)系統(tǒng)中結(jié)果交互的見解。

要檢查的問題包括以下內(nèi)容：

當(dāng)七鰓鰻的種群可以改變其性別比例時(shí)，對更大的生態(tài)系統(tǒng)有什么影響？對七鰓鰻種群有什么優(yōu)勢和劣勢？鑒于七鰓鰻的性別比例變化，對生態(tài)系統(tǒng)的穩(wěn)定性有什么影響？在七鰓鰻種群中有變化的性別比例的生態(tài)系統(tǒng)是否能為生態(tài)系統(tǒng)中的其他成員，如寄生物，提供優(yōu)勢？

你的PDF解決方案不得超過總共25頁，應(yīng)包括：

·一頁摘要。

·目錄。

·你的完整解決方案。

·參考文獻(xiàn)列表。

·AI使用報(bào)告（如果使用不計(jì)入25頁限制內(nèi)）。

注意：對于完整的MCM提交沒有具體要求的最小頁數(shù)。你可以使用最多25頁來展示你的解決方案工作和任何你想包含的額外信息（例如：繪圖、圖表、計(jì)算、表格）。接受部分解決方案。我們允許謹(jǐn)慎使用AI，如ChatGPT，盡管不必須通過AI創(chuàng)建解決方案。如果你選擇使用生成式AI，你必須遵循COMAP的AI使用政策。這將導(dǎo)致你必須在PDF解決方案文件的末尾添加一個(gè)額外的AI使用報(bào)告，且不計(jì)入你的解決方案的總頁數(shù)25頁。

術(shù)語表

七鰓鰻：七鰓鰻（有時(shí)不準(zhǔn)確地稱為七鰓鰻鰻）是一種古老的無頜魚類，屬于七鰓鰻目。成年七鰓鰻的特點(diǎn)是有齒的、漏斗狀的吸口。七鰓鰻主要生活在沿海和淡水中，且在大多數(shù)溫帶地區(qū)都能找到。

MCM/ICM免費(fèi)領(lǐng)真題請掃碼【翰林提供報(bào)名服務(wù)】

Problem A: Resource Availability and Sex Ratios

While some animal species exist outside of the usual male or female sexes, most species are substantially either male or female. Although many species exhibit a 1:1 sex ratio at birth, other species deviate from an even sex ratio. This is called adaptive sex ratio variation. For example, the temperature of the nest incubating eggs of the American alligator influences the sex ratios at birth.
The role of?lampreys?is complex. In some lake habitats, they are seen as parasites with a significant impact on the ecosystem, whereas lampreys are also a food source in some regions of the world, such as Scandinavia, the Baltics, and for some Indigenous peoples of the Pacific Northwest in North America.

The sex ratio of sea lampreys can vary based on external circumstances. Sea lampreys become male or female depending on how quickly they grow during the larval stage. These larval growth rates are influenced by the availability of food. In environments where food availability is low, growth rates will be lower, and the percentage of males can reach approximately 78% of the population. In environments where food is more readily available, the percentage of males has been observed to be approximately 56% of the population.

We focus on the question of sex ratios and their dependence on local conditions, specifically for sea lampreys. Sea lampreys live in lake or sea habitats and migrate up rivers to spawn. The task is to examine the advantages and disadvantages of the ability for a species to alter its sex ratio depending on resource availability. Your team should develop and examine a model to provide insights into the resulting interactions in an ecosystem.

Questions to examine include the following:

What is the impact on the larger ecological system when the population of lampreys can alter its sex ratio?

What are the advantages and disadvantages to the population of lampreys?

What is the impact on the stability of the ecosystem given the changes in the sex ratios of lampreys?

Can an ecosystem with variable sex ratios in the lamprey population offer advantages to others in the ecosystem, such as parasites?

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

·One-page Summary Sheet.

·Table of Contents.

·Your complete solution.

·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.

Glossary

Lampreys: Lampreys (sometimes inaccurately called lamprey eels) are an ancient lineage of jawless fish of the order Petromyzontiformes. The adult lamprey is characterized by a toothed, funnel-like sucking mouth. Lampreys live mostly in coastal and fresh waters and are found in most temperate regions.