Lecture Notes: Math in Biology - Hardy Weinberg Equilibrium

Introduction to Math in Biology

• Common Misconception: People often think biology doesn't involve math.
• Examples of Math in Biology:
  • Chi squares
  • Osmotic pressure calculations
  • Standard curves with gel electrophoresis
  • Punnett square ratios

Hardy Weinberg Equilibrium

• Definition: A principle stating that allele and genotype frequencies in a population remain constant unless acted upon by evolutionary forces.
• Origin: Named after a mathematician and a physician.
• Population Definition: A group of the same species that can breed together to produce fertile offspring.
• Importance: Provides a mathematical baseline to compare evolving populations with those not subjected to evolutionary forces.

Assumptions for Hardy Weinberg Equilibrium

1. No Selection: No natural selection affecting reproductive fitness.
2. No Mutation: Genes are passed without mutation.
3. No Migration: No individuals move in or out of the population.
4. Large Population: Minimizes genetic drift.
5. Random Mating: Mating occurs without preference.

Equations in Hardy Weinberg Equilibrium

Allele Frequency Equation

• Formula: p + q = 1
  • p = dominant allele frequency
  • q = recessive allele frequency
  • Example: For alleles G and g, where p = 0.6 and q = 0.4.

Genotype Frequency Equation

• Formula: p² + 2pq + q² = 1
  • p² = homozygous dominant frequency (GG)
  • 2pq = heterozygous frequency (Gg)
  • q² = homozygous recessive frequency (gg)

Example Problem

• Scenario: New population of 500 frogs with 375 dark green and 125 light green.
• Steps:
  1. Select Equation: Use genotype frequency equation for individuals.
  2. Determine Known Values:
     • 125 light green frogs are gg.
     • Calculate q² = 0.25, hence q = 0.5.
  3. Calculate Unknowns:
     • Use p + q = 1 to find p = 0.5.
     • Plug into genotype equation:
       • p² = 0.25 (GG)
       • 2pq = 0.5 (Gg)
       • q² = 0.25 (gg)

Tips for Solving Hardy Weinberg Problems

1. Check Your Work: Ensure totals equal 1 in both equations.
2. Be Cautious with Assumptions: Use known values prudently.
3. Practice: Frequent practice is necessary for mastery.

Conclusion

• Hardy Weinberg Equilibrium is a critical tool for studying evolutionary forces by providing a constant baseline for allele and genotype frequencies.
• Encouragement to stay curious and keep exploring biology and math.