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Investigating Population Diversity, Sex Ratio Dynamics, and Resource Utilization: Insights into Lamprey Species within the Multispecies Ecosystem of the Great Lakes

🌟 Project Introduction

This is our entry for the Mathematical Contest in Modeling (MCM) hosted by COMAP in February 2024. In this project, we explored the specific relationship between the population size, sex ratio and food abundance of lampreys in the Great Lakes of North America by constructing a mathematical model, and proposed a new method to control the lamprey population.

📜 Abstract

In the current ecological environment of the Great Lakes of North America, the invasive species lampreys pose a serious threat to the stability of the ecosystem. There is a close relationship between the population size and sex ratio of lampreys and ecological resources (such as food), which provides us with a new perspective to prevent and control the problem of lampreys in the Great Lakes of North America. This study explored the specific relationship between the population size, sex ratio and food abundance of lampreys by constructing three different hierarchical mathematical models.

  • Model 1: The Fourier transform method is used to analyze the temporal variation pattern of food abundance in the waters of the Great Lakes of North America, and a model based on differential equations is established through zero-sum game theory to describe the changes in the sex ratio of lampreys under changes in food abundance in the environment.
  • Model 2: Under ideal conditions (no interference from other species), the traditional Logistic population growth model is improved to explore the different effects of food abundance and population sex ratio on population growth rate.
  • Model 3: An ecosystem model of a local system of the Great Lakes is constructed to explore the population relationships between three species, lampreys, native fish and parasites, and a 25-year simulation is carried out by introducing cooperation and competition game theory.

In the summary section, through a detailed analysis of the three models, we reveal the interaction and constraint mechanism of the sex ratio and abundance of lamprey populations, and summarize the ecological impact of lampreys on the population size of other species. In the further discussion section, from the perspective of engineering control, how to control the population size of lampreys through the proportional-integral-differential compensation method is explored, and a new idea for the prevention and control of lampreys is proposed.

🛠️ Repository Contents

  • /code: Source code, including all code files used for research and simulation.

  • /references: All literature referenced and used in the research.

  • MCM-Summary_Final.pdf: Full paper, including AI Usage Report required by the competition

    • Contains detailed methods, results and discussion of the research, as well as AI Usage Report.

  • MCM-Summary-Final_Without_AI_Report.pdf: Full paper without AI Usage Report

    • Contains only detailed methods, results and discussion of the research, excluding AI Usage Report.

  • README.md: Instruction document, used to explain the structure and content of the repository.

  • README_en.md: English version of the instruction document, English translation of this file.

⚖️ Copyright

Our repository complies with the GPL 3.0 open source agreement and aims to provide resources for the academic and research communities.