Lecture Notes: Hardy Weinberg Equilibrium in Biology

Overview

• Common misconception that biology does not involve math.
• Math is present in various biology concepts: chi squares, osmotic pressure calculations, standard curves, and Punnett squares.
• Introduction to Hardy Weinberg Equilibrium: a concept combining biology and math.

Hardy Weinberg Equilibrium

• Named after a mathematician and a physician.
• States that allele and genotype frequencies in a population remain constant unless influenced by evolutionary forces.
• Definition of a Population: A group of organisms of the same species that can interbreed and have fertile offspring.

Assumptions of Hardy Weinberg Equilibrium

• Five key assumptions:
  1. No Selection: No natural selection affecting reproductive fitness.
  2. No Mutation: Genes are inherited without mutation.
  3. No Migration: No individuals can enter or leave the population.
  4. Large Population: A large population size is necessary.
  5. Random Mating: Mating occurs without any selective preference.

Real-Life Application

• Hardy Weinberg Equilibrium is unrealistic in nature due to evolutionary forces.
• Utility: Provides a baseline for comparing evolving populations to those without evolutionary forces.

Mathematical Equations in Hardy Weinberg

1. Allele Frequency Equation:

   • (p + q = 1)
   • (p) = dominant allele frequency, (q) = recessive allele frequency.
   • Misconception: Dominant alleles are not always more common.

2. Genotype Frequency Equation:

   • (p^2 + 2pq + q^2 = 1)
   • (p^2) = homozygous dominant frequency, (2pq) = heterozygous frequency, (q^2) = homozygous recessive frequency.

Example Problem

• Scenario: New population of frogs with two color variations (dark green and light green).
• Information: 500 frogs total, 375 are dark green, 125 are light green.
• Steps:
  1. Equation Choice: Use the second equation for genotype frequencies.
  2. Determine Known Values: Use the recessive genotype frequency (q^2 = 0.25) for light green frogs (gg).
  3. Solve for Allele Frequencies:
     • (q = \sqrt{0.25} = 0.5)
     • (p + q = 1 \Rightarrow p = 0.5)
  4. Calculate Genotype Frequencies:
     • (p^2 = 0.25), (2pq = 0.5), (q^2 = 0.25)

Tips for Solving Hardy Weinberg Problems

1. Use a calculator when needed; round numbers appropriately.
2. Ensure calculated values sum to 1 in equations.
3. Avoid assumptions about dominant and recessive genotypes with given data.
4. Practice with various problems for proficiency.

Conclusion

• Importance of Hardy Weinberg Equilibrium as a tool for understanding evolutionary forces.
• Encouragement to continue exploring and being curious about biology and math interactions.