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- 首页 >> OS编程 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:
Output:
2. OpenAI Ernie (Nov 5, 2023 version, Ernie 4.0)
Query1:
Output:
3. Github CoPilot (Feb 3, 2024 version)
Query1:
Output:
4. Google Bard (Feb 2, 2024 version)
Query:
Output:
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:
Output:
2. OpenAI Ernie (Nov 5, 2023 version, Ernie 4.0)
Query1:
Output:
3. Github CoPilot (Feb 3, 2024 version)
Query1:
Output:
4. Google Bard (Feb 2, 2024 version)
Query:
Output: