Hardy Weinberg Equilibrium Lecture Notes

Introduction

• Many assume biology is devoid of math, but math is integral to several biological concepts.
• Key examples include:
  • Chi squares
  • Osmotic pressure calculations
  • Standard curves with gel electrophoresis
  • Punnett square ratios
• One fascinating topic combining biology and math is the Hardy Weinberg Equilibrium.

Hardy Weinberg Equilibrium

• Named after a mathematician and a physician.
• States that allele and genotype frequencies in a population remain constant in the absence of evolutionary forces.
• Population: A group of organisms of the same species capable of breeding and producing fertile offspring.
• Assumptions for Equilibrium:
  1. No natural selection.
  2. No mutations.
  3. No migration (immigration or emigration).
  4. Large population size.
  5. Random mating.

Real-World Application

• Hardy Weinberg Equilibrium rarely occurs in nature due to environmental factors affecting populations.
• It serves as a mathematical baseline for comparing evolving populations with those unaffected by evolutionary forces.

Key Equations

Allele Frequencies

• Equation: p + q = 1
  • p: Dominant allele frequency
  • q: Recessive allele frequency
• Example: If 60% of alleles are G (p=0.6), then 40% are g (q=0.4).

Genotype Frequencies

• Equation: p² + 2pq + q² = 1
  • p²: Homozygous dominant frequency (GG)
  • 2pq: Heterozygous frequency (Gg)
  • q²: Homozygous recessive frequency (gg)
• Example Calculation:
  • p² = 0.36, 2pq = 0.48, q² = 0.16

Example Problem

• New frog population: 500 total, 375 dark green, 125 light green.
• Steps:
  1. Use the genotype equation (p² + 2pq + q² = 1).
  2. Calculate light green (gg) frequency: q² = 0.25 (since 125/500 = 0.25).
  3. Solve for q: q = √0.25 = 0.5.
  4. Find p: p = 1 - q = 0.5.
  5. Calculate genotype frequencies:
     • p² (GG) = 0.25
     • 2pq (Gg) = 0.5
     • q² (gg) already known = 0.25

Tips for Solving Hardy Weinberg Problems

1. Use a calculator for complex numbers.
2. Verify calculations ensure they sum to 1 for both equations.
3. Avoid assumptions about genotype without clear data.
4. Practice extensively to become familiar with the concepts and calculations involved.

Conclusion

• Hardy Weinberg Equilibrium provides a critical framework for understanding evolutionary forces.
• Practice and understanding of these principles are crucial for biologists exploring evolutionary dynamics.
• Final Reminder: Stay curious and continue to explore the fascinating intersection of math and biology.