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日期：2024-02-07 09:40

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?

| ?2024 by COMAP, Inc. | www.comap.org | www.mathmodels.org | info@comap.org |

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.

v102023

Use of Large Language Models and Generative AI Tools in COMAP Contests

This policy is motivated by the rise of large language models (LLMs) and generative AI assisted

technologies. The policy aims to provide greater transparency and guidance to teams, advisors,

and judges. This policy applies to all aspects of student work, from research and development of

models (including code creation) to the written report. Since these emerging technologies are

quickly evolving, COMAP will refine this policy as appropriate.

Teams must be open and honest about all their uses of AI tools. The more transparent a team and

its submission are, the more likely it is that their work can be fully trusted, appreciated, and

correctly used by others. These disclosures aid in understanding the development of intellectual

work and in the proper acknowledgement of contributions. Without open and clear citations and

references of the role of AI tools, it is more likely that questionable passages and work could be

identified as plagiarism and disqualified.

Solving the problems does not require the use of AI tools, although their responsible use is

permitted. COMAP recognizes the value of LLMs and generative AI as productivity tools that

can help teams in preparing their submission; to generate initial ideas for a structure, for

example, or when summarizing, paraphrasing, language polishing etc. There are many tasks in

model development where human creativity and teamwork is essential, and where a reliance on

AI tools introduces risks. Therefore, we advise caution when using these technologies for tasks

such as model selection and building, assisting in the creation of code, interpreting data and

results of models, and drawing scientific conclusions.

It is important to note that LLMs and generative AI have limitations and are unable to replace

human creativity and critical thinking. COMAP advises teams to be aware of these risks if they

choose to use LLMs:

? Objectivity: Previously published content containing racist, sexist, or other biases can

arise in LLM-generated text, and some important viewpoints may not be represented.

? Accuracy: LLMs can ‘hallucinate’ i.e. generate false content, especially when used

outside of their domain or when dealing with complex or ambiguous topics. They can

generate content that is linguistically but not scientifically plausible, they can get facts

wrong, and they have been shown to generate citations that don’t exist. Some LLMs are

only trained on content published before a particular date and therefore present an

incomplete picture.

? Contextual understanding: LLMs cannot apply human understanding to the context of a

piece of text, especially when dealing with idiomatic expressions, sarcasm, humor, or

metaphorical language. This can lead to errors or misinterpretations in the generated

content.

? Training data: LLMs require a large amount of high-quality training data to achieve

optimal performance. In some domains or languages, however, such data may not be

readily available, thus limiting the usefulness of any output.

Guidance for teams

Teams are required to:

1. Clearly indicate the use of LLMs or other AI tools in their report, including which

model was used and for what purpose. Please use inline citations and the reference

section. Also append the Report on Use of AI (described below) after your 25-page

solution.

2. Verify the accuracy, validity, and appropriateness of the content and any citations

generated by language models and correct any errors or inconsistencies.

3. Provide citation and references, following guidance provided here. Double-check

citations to ensure they are accurate and are properly referenced.

4. Be conscious of the potential for plagiarism since LLMs may reproduce substantial text

from other sources. Check the original sources to be sure you are not plagiarizing

someone else’s work.

COMAP will take appropriate action

when we identify submissions likely prepared with

undisclosed use of such tools.

Citation and Referencing Directions

Think carefully about how to document and reference whatever tools the team may choose to

use. A variety of style guides are beginning to incorporate policies for the citation and

referencing of AI tools. Use inline citations and list all AI tools used in the reference section of

your 25-page solution.

Whether or not a team chooses to use AI tools, the main solution report is still limited to 25

pages. If a team chooses to utilize AI, following the end of your report, add a new section titled

Report on Use of AI. This new section has no page limit and will not be counted as part of the

25-page solution.

Examples (this is not exhaustive – adapt these examples to your situation):

Report on Use of AI

1. OpenAI ChatGPT (Nov 5, 2023 version, ChatGPT-4)

Query1: <insert the exact wording you input into the AI tool>

Output: <insert the complete output from the AI tool>

2. OpenAI Ernie (Nov 5, 2023 version, Ernie 4.0)

Query1: <insert the exact wording of any subsequent input into the AI tool>

Output: <insert the complete output from the second query>

3. Github CoPilot (Feb 3, 2024 version)

Query1: <insert the exact wording you input into the AI tool>

Output: <insert the complete output from the AI tool>

4. Google Bard (Feb 2, 2024 version)

Query: <insert the exact wording of your query>

Output: <insert the complete output from the AI tool>