Evolutionary Medicine

CONTENTS OF CURRICULUM UNIT 24.05.06

  1. Unit Guide
  1. Introduction
  2. Background Information
  3. Fundamental Concepts
  4. Target Audience
  5. Rationale
  6. Unit Objectives
  7. Teaching Strategies
  8. Teaching Implementation
  9. Classroom Activities
  10. Assessments
  11. Appendix
  12. References

Using Algebra to Explore Population Genetics in Lactose Tolerance

Jose Ulises Reveles Ramirez

Published September 2024

Tools for this Unit:

Teaching Implementation

Week 1: Introduction to Population Genetics and Lactose Tolerance

  • Lesson 1: Introduction to Lactose Tolerance
    • Overview of lactose tolerance
      1. Start with a brief introduction to lactose intolerance and lactose tolerance.
      2. Explain that lactose intolerance is the inability to digest lactose, a sugar in milk, due to the lack of lactase enzyme.
      3. Introduce the concept of lactase persistence, where the lactase enzyme continues to be produced into adulthood due to a genetic mutation.
    • Discuss the historical development of dairy farming and its impact on human genetics.
      1. Video as an Introduction. Show a short video explaining lactose intolerance and the genetic basis of lactase persistence. Suggested video: "The Evolution of Lactose Tolerance" by biointeractive.org (Howard Hughes Medical Institute 2015).
      2. Review of the main concepts exposed in the video
      3. Present the history of dairy farming, starting from its origins in the Neolithic period.
      4. Explain how dairy farming provided a selective advantage to individuals with lactase persistence, leading to the spread of this genetic trait.
      5. Discuss the interplay between genetic evolution and cultural practices, focusing on how they influence each other over time. For example, in regions like Northern Europe and among certain African and Middle Eastern populations, genetic traits such as lactose tolerance have evolved in response to cultural practices like dairy farming. While genetic evolution occurs through mutations and natural selection, cultural evolution involves changes in societal practices and behaviors. Understanding this coevolution highlights how genetic and cultural factors can shape populations together, even though they operate through different mechanisms.
    • Class Discussion
      1. Discuss the video and ask students to share personal experiences with lactose intolerance.
      2. Discuss why some populations have higher rates of lactase persistence than others.
    • Interactive Timeline Activity
      1. Divide students into small groups and provide each group with materials to create a timeline of the development of dairy farming and the spread of lactase persistence.
      2. Have each group present their timeline to the class.
    • Q&A and Reflection
      1. Open the floor for questions and reflections on the lesson.
      2. Assign a short reflective essay on how the historical development of dairy farming influenced human genetics.
  • Lesson 2: Basics of Population Genetics
    • An introduction to the fundamental concepts of mutation, selection, and genetic variation.

      Introduction to the Fundamental Concepts

      1. Lecture on Mutation, Selection, and Genetic Variation
      2. Define mutation as changes in the DNA sequence that can lead to genetic variation.
      3. Explain natural selection and how certain traits become more common in a population due to their advantage in survival and reproduction.
      4. Discuss genetic variation and its importance in the adaptability and resilience of populations.

      Interactive Demonstration

      1. Use a simple demonstration, such as a coin flip or a digital simulation, to show how mutations occur randomly.
      2. Discuss how some mutations can be beneficial, neutral, or harmful.

      Group Activity

      1. Divide students into small groups and give each group a set of problems related to population genetics.
      2. Problems include calculating allele frequencies, understanding Hardy-Weinberg equilibrium, and exploring genetic drift.
      3. Provide graph paper and calculators for solving the problems.

      Class Discussion

      1. Have each group present solutions to the problems and discuss their findings with the class.
      2. Highlight critical points about how mutation, selection, and genetic variation drive evolution and population genetics.

      Case Study Analysis

      1. Present a case study on lactose tolerance and its evolution in different populations.
      2. Discuss the case study with the class and relate it to the concepts learned in the lesson.

      Wrap-Up and Homework Assignment

      1. Summarize the key points from the lesson.
      2. Assign a homework problem on population genetics, including questions on mutation rates, selection coefficients, and genetic variation.
      3. Encourage students to use online resources and textbooks to complete their assignments.

Week 2: Algebraic Modeling of Genetic Data. We will explore how selection coefficients and mutation rates influence population genetics.

  • Lesson 3: Algebraic Expressions and Equations for selection coefficients and mutation rates.
    • Linear Selection Models
    • In some cases, the effect of natural selection on allele frequencies can be approximated linearly over short periods if the selection coefficient  is small and the allene’s frequency is not close to 0 or 1.

    • Linear Modeling of Selection Coefficients and Their Impact on Fitness
    • We can model the frequency of the lactase persistence allele (L) in the population at time t (measured in generations) using the following linear equation 1:

      equation

      Where:

      is the initial frequency of the lactase persistence allele,

      ΔL, the change in the allele persistence. It is approximated by L0s.

      s is the selection coefficient,

      t is the number of generations

    • Linear models for mutation rates and selection coefficients
    • We can model the lactase persistence allele (L) frequency in the population at time t (measured in generations) to calculate mutation rates using real-world data and the effect of genes' mutations. The linear model incorporating both the selection coefficient (s) and the mutation rate (u) over short periods for the frequency of an allele over time (t) is given by Equation 2:

      equation

      Where:

      is the initial frequency of the lactase persistence allele,

      s is the selection coefficient,

      u is the mutation rate, and

      t is the number of generations

Week 3: Algebraic Modeling of Genetic Data. We will explore how critical factors of genetic drifting change the frequency of alleles within a population's gene pool over time.

  • Lesson 4: Algebraic Expressions and Equations for the critical factors in genetic drifting.
    • Linear Models for Genetic Drift and Allele Frequency and Randomness

      We can model the frequency changes of the lactase persistence allele (L) in a population over time due to genetic drift, a process driven by random fluctuations rather than selection. The linear model for genetic drift incorporates the random changes in allele frequency over generations (t). The expected change in frequency is influenced by the population size (N) and the initial allele frequency (L0). The formula to represent the effect of genetic drift over time (t) is Equation 3:

      equation

      Where:

      • L0 is the initial frequency of the lactase persistence allele,
      • ΔL is the random change in allele frequency per generation,
      • N is the effective population size, and
      • t is the number of generations,
    • Linear Models for Genetic Drift and Population Size
    • The expected change in frequency is influenced by the population size (N) and the initial allele frequency (L0) and can be modeled using Equation 3, particularly comparing different population sizes.

    • Linear Model for Genetic Drifting and the Bottleneck Effect
    • The linear model for the bottleneck effect describes how allele frequencies change over generations following a bottleneck event, such as a natural disaster. The model considers the reduced population size (N) and the initial frequency of an allele (L0) before the bottleneck, and Equation 3 gives the expected allele frequency change over time (t).

    • Linear Model for Genetic Drifting and the Founder Effect
    • The linear model for the founder effect describes how allele frequencies change in the new population over generations. The model considers the founder population's initial allele frequency (L0) and the reduced population size (N). Equation 3 gives the expected allele frequency change over time (t).

Week 4: Algebraic Modeling of Genetic Data. We will explore how the combination of critical factors changes the frequency of alleles within a population's gene pool over time.

  • Linear Model, including selection coefficients and randomness

    The linear model that incorporates the selection coefficient (s) and the random effects of genetic drift (ΔL) over generations (t) describes how the frequency of an allele changes over time due to both natural selection and random drift and is given by Equation 4:

    equation

    Where:

    • L0 is the initial frequency of the lactase persistence allele,
    • s is the selection coefficient
    • ΔL is the random change in allele frequency per generation.
    • N is the effective population size, and
    • t is the number of generations.
  • Linear Model including selection coefficient, mutation rates, and the bottleneck effect.
  • To describe the change in allele frequencies due to selection, mutation, and the reduced population size following a bottleneck event. Equation 5 is structured to show the combined effects over time several generations t:

    equation

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