2019年美赛题目Problem A: Game of Ecology

本题分析：

本题想要要求从实际生物角度出发，对权力游戏中龙这种虚拟生物的生态环境和生物特性进行建模，感觉属于比较开放类型的题目，重点在于参考生物的选择，龙虽然是虚拟的但是龙的生态特性可以参考目前生物圈里存在过的几种动物（包括已经灭绝的）进行建模。

题目中文翻译：

在虚构的电视连续剧“权力的游戏”中，基于一系列史诗般的幻想小说“冰与火之歌”[1]，三只龙是由“龙之母”的Daenerys Targaryen提出的。当孵化时，龙是小的，大约10公斤，一年后长到大约30-40公斤。它们在整个生命过程中都会继续增长，这取决于它们的食物条件和数量。

出于这个问题的目的，考虑这三个虚构的龙今天生活。假设上述龙的基本生物学是准确的。您将需要对龙进行一些额外的假设，其中可能包括龙可以飞行很远的距离，呼吸火焰和抗拒巨大的创伤。当您解决问题要求时，应该清楚您的假设是如何与动物的功能，大小，饮食，变化或特性的物理限制相关联的。

您的团队被分配来分析龙的特征，行为，习惯，饮食以及与环境的互动。为此，您将不得不考虑许多问题。至少要解决以下问题：龙的生态影响和要求是什么？这些龙的能量消耗是多少，它们的热量摄入量要求是多少？需要多少面积来支持三角龙？需要多大的社区来支持龙可以提供给龙的不同程度的援助？在解决这些问题时，请清楚您正在考虑哪些因素。

与迁移的其他动物一样，龙可能会以非常不同的气候前往世界不同的地区。气候条件对您的分析有多重要？例如，在干旱地区，暖温带地区和北极地区之间移动龙会对保持和生长龙所需的资源产生很大的影响吗？一旦你的龙分析完成，请写一封两页的信给“冰与火之歌”的作者George RR Martin，以提供关于如何保持故事的现实生态基础的指导，特别是关于龙的运动从干旱地区到温带地区和南极地区。

虽然您的龙分析并不直接适用于真实的物理情况，但数学建模本身会利用许多用于建模情境的现实特征。除了建模活动本身，描述和讨论虚构龙领域之外的情况，您的模型可能有助于提供信息并提供洞察力？

您的提交应包括：
1，单页摘要表，
2，两页信，
3，您的解决方案不超过20页，最多23页，包含您的摘要和信函。
注意：参考列表和任何附录不计入23页的限制，应在完成的解决方案后显示。
注意：您不应使用未经授权的图像和使用受版权法限制的材料。请注意您如何使用和引用您的想法和报告中使用的材料的来源。

参考
1.. Penguin Random House (2018). A Song of Ice and Fire Series. Retrieved from
https://www.penguinrandomhouse.com/series/SOO/a-song-of-ice-and-fire/.

英文题目：

In the fictional television series Game of Thrones, based on the series of epic fantasy novels A Song of Ice and Fire[1], three dragons are raised by Daenerys Targaryen, the “Mother of Dragons.” When hatched, the dragons are small, roughly 10 kg, and after a year grow to roughly 30-40 kg. They continue to grow throughout their life depending on the conditions and amount of food available to them.

For the purposes of this problem, consider these three fictional dragons are living today. Assume that thebasic biology of dragons described above is accurate. You will need to make some additional assumptions about dragons that might include, for example, that dragons are able to fly great distances, breath fire, andresist tremendous trauma. As you address the problem requirements, it should be clear how yourassumptions are related to the physical constraints of the functions, size, diet, changes, or thercharacteristics associated with the animals.

Your team is assigned to analyze dragon characteristics, behavior, habits, diet, and interaction with theirenvironment. To do so, you will have to consider many questions. At a minimum, address the following:What is the ecological impact and requirements of the dragons? What are the energy expenditures of thedragons, and what are their caloric intake requirements? How much area is required to support the threedragons? How large a community is necessary to support a dragon for varying levels of assistance that canbe provided to the dragons? Be clear about what factors you are considering when addressing thesequestions.

As with other animals that migrate, dragons might travel to different regions of the world with very differentclimates. How important are the climate conditions to your analysis? For example, would moving a dragonbetween an arid region, a warm temperate region, and an arctic region make a big difference in the resourcesrequired to maintain and grow a dragon?
Once your dragon analysis is complete, draft a two-page letter to the author of A Song of Ice and Fire,George R.R. Martin, to provide guidance about how to maintain the realistic ecological underpinning of thestory, especially with respect to the movement of dragons from arid regions to temperate regions and toarctic regions.

While your dragon analysis does not directly apply to a real physical situation, the mathematical modelingitself makes use of many realistic features used in modeling a situation. Aside from the modeling activitiesthemselves, describe and discuss a situation outside of the realm of fictional dragons that your modelingefforts might help inform and provide insight?

Your submission should consist of:
1、One-page Summary Sheet,
2、Two-page letter,
3、Your solution of no more than 20 pages, for a maximum of 23 pages with your summary and letter.
Note: Reference list and any appendices do not count toward the 23-page limit and should appear after your completed solution.
NOTE: You should not make use of unauthorized images and materials whose use is restricted by copyright laws. Please be careful in how you use and cite the sources for your ideas and the materials used in your report.

Reference
1. Penguin Random House (2018). A Song of Ice and Fire Series. Retrieved from
https://www.penguinrandomhouse.com/series/SOO/a-song-of-ice-and-fire/.