Genotype Frequencies and Hardy-Weinberg Equilibrium

Study Notes on Hardy-Weinberg Equilibrium and Genotype Frequencies

Key Concepts

• Hardy-Weinberg Principle: This principle explains how allele and genotype frequencies in a population remain constant from generation to generation in the absence of evolutionary influences.

Fundamental Equations

• Basic Equations:

  • The equations related to genotype frequencies are as follows:

  • $p + q = 1$

  • $p^2 + 2pq + q^2 = 1$

  • Where:

  • $p$ = frequency of the dominant allele

  • $q$ = frequency of the recessive allele

• Genotype Frequencies:

  • $p^2$: Frequency of homozygous dominant genotype

  • $2pq$: Frequency of heterozygous genotype

  • $q^2$: Frequency of homozygous recessive genotype

Example Calculations

• Given values:

  • Let $p = 0.4$

  • Therefore, $q = 1 - p = 1 - 0.4 = 0.6$

Genotype Frequencies Calculation

1. Calculate $q^2$:

   • $q^2 = (0.6)^2 = 0.36$

2. Calculate $2pq$:

   • $2pq = 2 imes 0.4 imes 0.6 = 0.48$

3. Calculate $p^2$:

   • $p^2 = (0.4)^2 = 0.16$

Total Frequency Check

• Check the equation:

  • $p^2 + 2pq + q^2 = 0.16 + 0.48 + 0.36 = 1$

• This confirms that the genotype frequencies are correct as they sum to 1.

Predictions in a Population

• If the population size (N) is 300 individuals:

  • Homozygous Dominant (A1A1):

  • Frequency is given by $p^2$:

    • $0.16 imes 300 = 48$

  • Heterozygous (A1A2):

  • Frequency is given by $2pq$:

    • $0.48 imes 300 = 144$

  • Homozygous Recessive (A2A2):

  • Frequency is given by $q^2$:

    • $0.36 imes 300 = 108$

Discrepancies and Influencing Factors

• Observed Values vs. Expected:

  • Expected homozygous dominant individuals: 48

  • Observed individuals: 120

Factors Affecting Deviations

1. Non-random Mating:

   • Could lead to a reduction in heterozygotes in the population over time.

2. Natural Selection:

   • Selection may favor certain genotypes over others, affecting population dynamics.

3. Gene Flow:

   • Introduction of new individuals into the population can change allele frequencies.

Additional Calculations

• For new population dynamics:

  • If $p = 0.35$ and $q = 0.65$:

  • Calculate $2pq$:

    • $2pq = 2 imes 0.35 imes 0.65 = 0.455$

  • For a population size of 330:

    • Expected number of heterozygotes = $0.455 imes 330 = 150.15$

• Rounding Rules:

  • Round genotype frequencies to three decimal places.

  • Round individual counts to the nearest whole number only at the end of the calculation process.