2020年美國HiMCM數學建模競賽B題中英文

中文賽題：資助生物多樣性保護

背景：數千種動植物麵臨(lin) 著可能導致其滅絕的威脅，而可以拯救它們(men) 的生物多樣性保護行動卻經常有效。當生物多樣性保護的資金有限時，資金管理者會(hui) 麵臨(lin) 困難的決(jue) 定。管理者需要決(jue) 定他們(men) 應該資助哪些項目來最好地實現他們(men) 的目標，而不僅(jin) 僅(jin) 是拯救大多數物種。如何分配這些資金非常重要，特別是如果某些保護行動的效益因項目而異，具體(ti) 項目的行動成本又不同，而這些行動的可用資金遠遠低於(yu) 支持所有擬議項目所需的資金。

每個(ge) 項目的時間線和生命周期的變化使這個(ge) 問題變得更加複雜。保護項目可能需要進行幾年或幾十年的時間，項目期間發生費用的時間點可能會(hui) 因項目範圍、位置、目標物種和責任機構的不同而有很大差異。這意味著保護項目的預算必須在項目的整個(ge) 生命周期內(nei) 提供足夠的資金。此外，由於(yu) 項目對時間和資源的需求不同，管理者需要密切監控他們(men) 的預算，以便有效地分配資金。例如，當某些項目在某些時候需要更多的資金時，他們(men) 需要確保有足夠的資金可用，並利用在同一時間資金需求的較少項目。

目標：確定如何有效地資助瀕危和受威脅物種的生物多樣性保護活動，這些保護活動的預期成本會(hui) 隨時間變化。

HiMCM案例：優(you) 先考慮佛羅裏達州（美國）的植物保護行動和資金

佛羅裏達州是植物多樣性保護的熱點地區之一，其20%的物種受到威脅。在《美國瀕危物種法》（ESA）的作用下，隻有2%的這些植物物種（約64種）得到了保護，但目前資金不足，無法保護數量有限的物種。佛羅裏達珍稀植物保護基金會(hui) （FRPCE）（見附件A）是一個(ge) 由保護管理者牽頭的信托基金，長期提供資金支持佛羅裏達稀有和瀕危植物物種的研究和保護。這項信托基金的目的是吸納足夠的捐款，以支付保護的前期費用和目前傳(chuan) 統籌款活動難以應付的長期費用。

要求：

1. 考慮到需要保護佛羅裏達州的瀕危植物物種並在未來對其進行管理，建立一個(ge) 模型，向FRPCE董事會(hui) 建議“長期和可靠”資金所需的最低籌資額。出於(yu) HiMCM問題的目的，我們(men) 將把我們(men) 的分析局限於(yu) 所附數據（附件B）中包含的48種瀕危物種。請注意，數據庫中的每一行都表示一個(ge) 物種的保護項目。

   • 確定並討論FRPCE董事會(hui) 在其保護工作和預算決(jue) 策中應考慮的相關(guan) 目標。根據這些目標，你會(hui) 用什麽(me) 方法來評估一個(ge) 提議的籌款計劃是“最好的”？

   • 列出並說明瀕危植物物種的一些一般特征。指出你將在你的決(jue) 策模型中使用的保護這些物種的因素。

   • 為(wei) FRPCE董事會(hui) 開發一個(ge) 模型或算法（或一組模型或算法），用於(yu) 確定一個(ge) 籌資時間表（不同時間點要求的資金），該計劃將最大限度地減少需要籌集的資金，但仍然獲得必要的資金來實施我們(men) 48個(ge) 物種保護項目，並在未來對其進行管理。

2. 運用你的模型，向FRPCE董事會(hui) 推薦物種保護項目的優(you) 先資助順序，以便在一段時間內(nei) 平衡可用資金與(yu) 這些項目所需的支出。討論你的建議。

3. 寫(xie) 一頁非技術性備忘錄給FRPCE董事會(hui) 解釋你的結果，並根據你的建模和分析提出建議。

你們(men) 的（PDF格式）論文頁數不能超過25頁，並且應該包括：

• 一頁摘要。
• 目錄。
• 你們完整的解題過程。
• 參考文獻。
• 一頁備忘錄。

注意：HiMCM 競賽現在有25頁的限製。你提交的論文所有部分（摘要、目錄、參考文獻和任何附錄）的總頁數必須控製在25頁以內(nei) 。

附件：

• 附件A：佛羅裏達瀕危植物保護基金會(hui)

• 附件B：HiMCM2020ProblemB_ThreatenedPlantsData.xlsx 瀕危植物數據

數據字段：

• unique_id：該物種的唯一植物標識符。

• Benefit：表示資助一個(ge) 物種預期相對保護價(jia) 值。它考慮到物種受到威脅的程度，以及采取保護措施恢複物種的容易程度。

• Taxonomic Uniqueness：衡量物種唯一性的指標；數字越大，表示越獨特。

• Feasibility of Success：如果所有的行動都得到資助，物種將免於(yu) 滅絕的可能性。

• Year "n" cost*：對於(yu) 第一行上的物種保護，該項目第“n”年的估計成本（美元）； {1, 2, 3, , 25}。

詞匯表：

• 生物多樣性：在一個(ge) 特定的時間內(nei) ，特定棲息地內(nei) 不同植物、動物和其他物種之間的多樣性或多種類的數量。

• 生物多樣性保護：保護和保存地球上多種多樣的物種、棲息地、生態係統和遺傳(chuan) 多樣性的活動。

• 瀕危物種：種群數量急劇減少，瀕臨(lin) 滅絕的物種。

• 傳(chuan) 統籌款：每年或定期進行的籌款活動，包括要求捐款以達到特定金額。

比賽組委會(hui) 感謝來自亞(ya) 利桑那州和佛羅裏達州的研究人員在設計本問題的幫助。在HiMCM比賽結束後，COMAP將在HiMCM網頁和春季聯合出版物上公布這些研究人員及其機構。

附件A：佛羅裏達瀕危植物保護基金會(hui)

佛羅裏達州擁有豐(feng) 富而獨特的自然多樣性，約占美國本土植物類群的18%。但隨著持續的威脅，瀕危物種的數量增加，該州被視為(wei) 優(you) 先保護區。根據《美國瀕危物種法》，佛羅裏達州不到5%的瀕危植物物種得到保護，隻有一小部分保護佛羅裏達植物所需的行動得到資助。由於(yu) 現有的植物保護資金不足以支持瀕危植物的研究、保護和管理，代表佛羅裏達州七個(ge) 機構的一組保護專(zhuan) 家於(yu) 2015年開始對話，發起佛羅裏達稀有植物保護基金會(hui) （FRPCE）。FRPCE是一種機製，旨在提供長期和可靠的資金，以支持佛羅裏達瀕危植物物種及其生態係統的相關(guan) 保護項目。

摘自：Negron-Ortiz, V. (2019, July 27-31). A Conservation Endowment for imperiled plants in Florida [Conference session]. Botany 2019 Conference: Sky Islands and Desert Seas, Tucson, Arizona. The Botanical Society of America。經作者許可印刷。

英文賽題：Funding Biodiversity Conservation

Background: Thousands of species of plants and animals face threats that could result in their extinction, while biodiversity conservation actions that could save them are often available. Conservation managers face difficult decisions when there is limited funding for biodiversity conservation. Managers need to decide which projects they should fund to best achieve their objectives, not the least of which is to save the most species. This is particularly important if the benefits of certain conservation actions vary across projects, the costs of these actions for specific projects differ, and the available funding for these actions is considerably less than is needed to support all proposed projects.

One issue that makes this a more difficult problem is the varying timeline and life cycle of each project. Conservation projects can take years or decades, and the schedule of when costs are incurred during the project can vary significantly depending on the project's scope, location, targeted species, and responsible agency. This means that budgets for conservation projects must provide adequate funds for the entire lifetime of the project. Additionally, managers need to closely monitor their budgets to efficiently allocate funds as demand for resources vary across projects and time. For example, they need to ensure they have adequate resources available for times when some projects require more funding, and take advantage of times when some projects require less.

Objective: Determine how to efficiently invest in biodiversity conservation activities for endangered and threatened species that take place over long time frames, and whose expected costs change over that time.

HiMCM Case: Prioritize Action and Funding for Plant Conservation in Florida (USA)Florida is one of the hotspots for plant biodiversity conservation, with 20% of its species imperiled. Only 2% of these plant species (~64) receive protection under the US Endangered Species Act (ESA), but funding is currently inadequate for protecting even this limited number of species. The Florida Rare Plant Conservation Endowment (FRPCE) (see Attachment A) is a trust fund spearheaded by conservation managers to provide funds over time to support research, protection, and conservation of rare and imperiled plant species found in Florida. This trust fund aims to generate an adequate endowment to pay for both the up-front costs of conservation and the long-term costs that are currently difficult to meet with traditional fundraising campaigns.

Requirements:

1. Given the need to recover imperiled plant species in Florida and manage them into the future, develop a model to advise the FRPCE Board of the minimum fundraising required for "long-term and reliable" funding. For the purposes of this HiMCM problem, we will limit our analysis to the 48 imperiled species included in the attached data set (Attachment B). Note that each row in the database indicates a recovery project for a species.

   • Identify and discuss relevant objectives that the FRPCE Board should consider in their conservation efforts and budgeting decisions. Using these objectives, what measures would you use to evaluate a proposed fundraising plan as being the "best?"
   • List and address some general characteristics of imperiled plant species. Indicate the factors involved in these species' protection that you will use in your decision model.
   • Develop a model or algorithm (or set of models or algorithms) for the FRPCE Board to use to determine a fundraising schedule (money required with timeline) that will minimize the funds required to be raised, yet still obtain the necessary resources to implement the recovery projects for our 48 species and manage them into the future.

2. Apply your model to recommend to the FRPCE Board a priority order of funding for the recovery projects that will manage balancing the funds available with the spending required on these projects over time. Discuss your recommendation.

3. Write a one-page non-technical memo to the FRPCE Board explaining your results, and make recommendations based on your modeling and analysis.

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

• One-page Summary Sheet.
• Table of Contents.
• Your complete solution.
• One-page Memo.
• References list.Note: The HiMCM Contest now has a 25 page limit. All aspects of your submission count toward the 25 page limit (Summary Sheet, Table of Contents, Reference List and any Appendices).

Attachments:

• Attachment A: A Conservation Endowment For Imperiled Plants In Florida

• Attachment B: HiMCM2020ProblemB_ThreatenedPlantsData.xlsx

Data Fields:

• unique_id: the unique plant identifier for that species.

• Benefit: a measure that indicates the expected relative conservation value of funding one species over another. It takes into account information about how threatened a species is and how easy it would be to perform the conservation actions to recover it.

• Taxonomic Uniqueness: a measure of the uniqueness of the species; larger number indicates greater uniqueness.

• Feasibility of Success: the probability that the species will be protected from extinction if all of the actions receive funding.

• Year "n" cost: the estimated recovery cost in US dollars for each row's species in the "nth" year of that project; {1, 2, 3, , 25}.

Glossary:

• Biodiversity: the amount of diversity or variety between different plants, animals, and other species in a given habitat at a particular time.

• Biodiversity Conservation: the practice of protecting and preserving the great variety of species, habitats, ecosystems, and genetic diversity on the planet.

• Imperiled Species: those species whose populations have decreased so dramatically that they are at risk of extinction.

• Traditional Fundraising: fundraising efforts or campaigns that occur annually or on a regular schedule that involve requests for donations to attain a specific total monetary goal.

COMAP thanks researchers from Arizona and Florida for their assistance in developing this project. Upon completion of HiMCM, COMAP will recognize these researchers and their institutions on the HiMCM webpage and in our spring Consortium publication.

Attachment A: A Conservation Endowment for imperiled plants in Florida

Florida has a rich and unique natural diversity, with about 18% of native U.S. plant taxa. But with ongoing threats, the number of imperiled species has increased and the State has been considered a conservation priority region. Less than 5% of imperiled plant species in Florida receive protection under the U.S. Endangered Species Act, and only a small portion of actions needed to recover Florida plants have been financed. Because existing plant conservation funding is inadequate to support research, protection, and management of imperiled plants, a group of conservation specialists representing seven institutions in Florida began conversations in 2015 to initiate the Florida Rare Plant Conservation Endowment (FRPCE). The FRPCE is being established as a mechanism to provide long-term and reliable funding to support conservation-related projects for Florida imperiled plant species and their ecosystems.

Excerpt from: Negron-Ortiz, V. (2019, July 27-31). A Conservation Endowment for imperiled plants in Florida [Conference session]. Botany 2019 Conference: Sky Islands and Desert Seas, Tucson, Arizona. The Botanical Society of America. Printed with permission from the author.

Glossary:

• Taxa (singular taxon): classification/taxonomic units at a given level. Plant taxonomy or classification is the science of naming organisms and placing them in a hierarchical structure, each level being given a name (e.g., kingdom, division (phylum), class, order, family, genus, species). Taxa are arranged in hierarchy from kingdom to subspecies.