Hardy-Weinberg Equilibrium Study Notes

Summary of Hardy-Weinberg Equilibrium and Genotype Frequency

Introduction to Genotype Frequencies

• We begin by defining allele frequencies and calculating genotype frequencies based on Hardy-Weinberg equilibrium.

1. Allele Frequency Interpretation

• Given an allele frequency for one allele (e.g., p = 0.9), we compute:
  • Homozygous dominant frequency ($p^2$):
    • p^2 = (0.9)^2 = 0.81
  • Heterozygous frequency ($2pq$):
    • 2pq = 2 imes 0.9 imes 0.1 = 0.18
  • Homozygous recessive frequency ($q^2$):
    • q^2 = (0.1)^2 = 0.01

2. Assumptions of Hardy-Weinberg Equilibrium

• Key assumptions include:
  • Random mating (diploid, sexually reproducing populations).
  • No selection (no differential survival or reproduction).
  • Infinite population size (no genetic drift).
  • No gene flow (no migration of alleles).
  • No mutation (no new genetic variations introduced).
  • Violations of these assumptions result in changes to allele frequencies and suggest evolution is occurring.

Application of Hardy-Weinberg Principle

1. Practical Example Calculation

• Given: Homozygous dominant genotype frequency is 0.73.
• To find the frequency of other genotypes:
  • p^2 = 0.73
  • Determine p: p = ext{sqrt}(0.73)
    ightarrow p ext{ (frequency of dominant allele)} ext{ approximately } 0.8544
  • Determine q: q = 1 - p = 1 - 0.8544 = 0.1456
  • Calculate homozygous recessive frequency: q^2 = (0.1456)^2 = 0.0212
  • Calculate heterozygous frequency: 2pq = 2 imes 0.8544 imes 0.1456 = 0.2492

2. Genotype Frequency vs. Allele Frequency

• Link: Frequency of the genotypes can be predicted directly from the frequency of alleles using the formulae:
  • Homozygous Dominant: p^2
  • Heterozygous: 2pq
  • Homozygous Recessive: q^2

3. Visual Representation of Genotype Frequencies

• Plotting the frequencies of homozygotes and heterozygotes against allele frequency gives a visual understanding of changes across populations:
  • As the frequency of dominant allele increases, the frequency of homozygous dominant also increases, while recessive decreases.

Chi-Square Test for Hardy-Weinberg Equilibrium

1. Statistical Testing of Genotype Frequencies

• When observed frequencies from a sample are collected (e.g., from blood groups), we must test if they conform to Hardy-Weinberg expectations:
  • Collect data from individuals to estimate genotype frequencies (e.g., from a population of 1000 individuals).
  • Use a chi-square test to compare observed and expected frequencies to see if they diverge significantly:
  • Null hypothesis: Observed numbers of each genotype conform to Hardy-Weinberg expectations.
  • Alternative hypothesis: Observed numbers do not conform.

2. Performing the Chi-Square Test

• Calculate chi-square ($ ext{χ}^2$):
  • Formula:
  • ext{χ}^2 = rac{(Oi - Ei)^2}{Ei} where (Oi) = observed counts, (E_i) = expected counts.
• Example calculation:
  • If observed genotypes yield counts of 600, 351, and 49, and expected counts are 602, 348, and 50, the chi-square statistic will be computed for each:
  • For each genotype category, calculate difference, square it, divide by expected, then sum.
• Determine p-value and critical chi-square value from tables according to degrees of freedom (df). Accept or reject the null hypothesis based on whether calculated chi-square exceeds the critical value.

3. Interpretation of Results

• If the chi-square value is low (i.e., below critical value), we accept the null hypothesis, indicating the population is likely in Hardy-Weinberg equilibrium.
• A high chi-square value leads to rejection of the null hypothesis, suggesting that other evolutionary processes are affecting allele frequencies.

Conclusion and Real-World Applications

• Hardy-Weinberg equilibrium provides a critical framework for understanding genetic variation and evolution in populations.
• The chi-square test serves as a fundamental method for evaluating these genetic models against real-world data, illuminating evolutionary forces at play in natural populations.