2024年美国大学生数学建模竞赛A题中英版_鉴于七鳃鳗性别比例的变化,对生态系统的稳定性有什么影响?

中文赛题：资源可用性和性别比例

虽然一些动物物种存在于常规的雄性或雌性之外，但大多数物种基本上是雄性或雌性。尽管许多物种在出生时表现出1:1的性别比例，但其他物种偏离了均等的性别比例。这被称为适应性性别比例变化。例如，孵化美国短吻鳄蛋的巢穴温度会影响出生时的性别比例。

七鳃鳗（lampreys）的角色复杂。在一些湖泊栖息地，它们被视为对生态系统有重大影响的寄生生物，而在世界某些地区，如斯堪的纳维亚、波罗的海地区以及北美洲太平洋西北部的一些原住民中，七鳃鳗也是食物来源。

海洋七鳃鳗的性别比例可以根据外部环境变化。海洋七鳃鳗在幼虫阶段的生长速度决定了它们成为雄性或雌性。这些幼虫的生长速率受到食物可用性的影响。在食物可用性低的环境中，生长速率会较低，雄性比例可达到种群的约78%。在食物较易获得的环境中，观察到雄性比例约为种群的56%。

我们专注于海洋七鳃鳗的性别比例及其对当地条件的依赖问题。海洋七鳃鳗生活在湖泊或海洋栖息地，并迁徙至河流产卵。任务是检查一个物种根据资源可用性改变其性别比例的优势和劣势。您的团队应该开发并检查一个模型，以提供对生态系统中结果相互作用的洞察。

需要检查的问题包括以下几点：

• 当七鳃鳗种群能改变其性别比例时，对更大生态系统的影响是什么？

• 对七鳃鳗种群的优势和劣势是什么？

• 鉴于七鳃鳗性别比例的变化，对生态系统稳定性的影响是什么？

• 一个性别比例可变的七鳃鳗种群的生态系统是否能为生态系统中的其他生物，如寄生生物，提供优势？

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术语表

七鳃鳗：七鳃鳗（有时不准确地称为鳗鱼）是一种古老的无颌鱼类，属于八目（Petromyzontiformes）。成年七鳃鳗的特征是具有齿状、漏斗状的吸吮口。七鳃鳗主要生活在沿海和淡水中，分布在大多数温带地区。

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?

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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.