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.