Hardy-Weinberg Equilibrium Principle

Hardy-Weinberg Equilibrium Principle

• The Hardy-Weinberg Equilibrium Principle is used to show that evolution does not happen under certain conditions.
• It provides a set of testable assumptions, and if any of these assumptions are violated, the conclusions do not hold.
• It serves as a null model to test evolution against.

Assumptions of Hardy-Weinberg

• There is no selection, meaning all members contribute equally to the gene pool.
• There is no mutation, meaning no new alleles are created.
• There is no migration, meaning all alleles stay in the gene pool.
• The population size is infinitely large, meaning no random events or genetic drift occur.
• Mates are chosen randomly (panmixia).

Why Use Hardy-Weinberg?

• It allows for the prediction of genotype frequencies given allele frequencies.
• Genotypes will approximate a binomial distribution after one generation of random mating.
• If allele frequencies are known, genotype frequencies can be predicted.
• Allele and genotype frequencies will not change as long as the assumptions are met.

Dominance and Hardy-Weinberg

• A simple phenotypic example of dominance is polydactyly in cats, caused by a variant of the Pd gene.
• In a population of 100 cats, if 60 are polydactyl and 40 are normal, the genotype frequencies can be calculated using the Hardy-Weinberg Equilibrium Principle.

Numerical Example

• Using the Hardy-Weinberg Equilibrium Principle, the genotype frequencies can be calculated:
  • AA: 0.36
  • Aa: 0.48
  • aa: 0.16
• The allele frequencies in the next generation can be calculated:
  • Frequency of A: 0.6
  • Frequency of a: 0.4

General Case

• A single locus with alleles A and B has three possible diploid genotypes: AA, AB, and BB.
• The frequency of allele A is p, and the frequency of allele B is q, where p + q = 1.
• The genotype frequencies can be calculated using the Hardy-Weinberg Equilibrium Principle:
  • AA: p²
  • AB: 2pq
  • BB: q²

Conclusions

• The allele frequencies in a population will not change, generation after generation.
• If the allele frequencies in a population are given by p and q, the genotype frequencies will be given by p², 2pq, and q².
• A population in Hardy-Weinberg Equilibrium is not evolving.

Testing Hardy-Weinberg Equilibrium

• The Chi-squared test is used to determine if the Hardy-Weinberg Equilibrium holds or is broken.
• The test formula is: χ² = Σ((observed – expected)² / expected).
• The degrees of freedom is 1, and critical values can be looked up online or in a statistics textbook.