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Understanding Hardy Weinberg Equilibrium in Biology

May 2, 2025

Lecture Notes: Math in Biology - Hardy Weinberg Equilibrium

Introduction

  • Misconception: No math in biology.
  • Math is integral in biology (e.g., chi squares, osmotic pressure, gel electrophoresis)
  • Key topic: Hardy Weinberg Equilibrium (HWE)
    • Named after a mathematician and physician.
    • States that allele and genotype frequencies remain constant unless evolutionary forces act upon them.

Population and Variation

  • Population: Organisms of the same species that can breed and have fertile offspring.
  • Variation: Differences among individuals in a population.

Hardy Weinberg Equilibrium Assumptions

  • No evolutionary force: Necessary for HWE.
  • 5 Assumptions for HWE:
    1. No selection: Traits don't affect reproductive fitness.
    2. No mutation: Genes are inherited without mutation.
    3. No migration: No movement in or out of the population.
    4. Large population: To minimize genetic drift.
    5. Random mating: No selective choice in mating.

Importance of Hardy Weinberg Equilibrium

  • Provides a baseline for comparing evolving populations.
  • Useful for understanding the impact of evolutionary forces.

Hardy Weinberg Equations

  • Allele Frequency Equation:
    [ p + q = 1 ]
    • ( p ): Dominant allele frequency
    • ( q ): Recessive allele frequency
  • Genotype Frequency Equation: [ p^2 + 2pq + q^2 = 1 ]
    • ( p^2 ): Homozygous dominant frequency (GG)
    • ( 2pq ): Heterozygous frequency (Gg)
    • ( q^2 ): Homozygous recessive frequency (gg)

Example Problem

  1. New population: 500 frogs (375 dark green, 125 light green)
  2. Determine genotype frequencies:
    • Dark green can be GG or Gg.
    • Light green (gg): 125/500 = 0.25 (gg frequency)
  3. Calculate ( q ):
    • ( q^2 = 0.25 ) ( \Rightarrow ) ( q = \sqrt{0.25} = 0.5 )
  4. Calculate ( p ):
    • ( p + q = 1 ) ( \Rightarrow ) ( p = 0.5 )
  5. Calculate all genotype frequencies:
    • ( p^2 = 0.25 ) (GG frequency)
    • ( 2pq = 0.5 ) (Gg frequency)
    • ( q^2 = 0.25 ) (gg frequency)

Tips for Solving Hardy Weinberg Problems

  1. Use a calculator: Precision may require calculations.
  2. Verify results: Ensure calculated values sum to 1.
  3. Avoid assumptions: Use known info (e.g., recessive traits like light green gg frogs).
  4. Practice: Work on problems to increase proficiency.

Conclusion

  • Hardy Weinberg provides a comparison base for evolutionary studies.
  • Encouragement to practice and apply this mathematical concept in biology.

Note: Remember, the Hardy Weinberg Equilibrium is often not met in real-life populations but serves as a crucial theoretical model.

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