hardy-weinberg equations

The Hardy-Weinberg principle is a fundamental concept in population genetics that describes the conditions under which allele and genotype frequencies in a population will remain constant from generation to generation. These conditions are rarely met in nature, but the Hardy-Weinberg principle provides a valuable null hypothesis for detecting evolutionary changes.

Hardy-Weinberg Conditions

1. No mutation: The rate of mutation must be negligible.
2. Random mating: Individuals must mate randomly, without any preference for certain genotypes.
3. No gene flow: There should be no migration of individuals into or out of the population.
4. No genetic drift: The population must be large enough to avoid random changes in allele frequencies.
5. No selection: All genotypes must have equal survival and reproductive rates.

Hardy-Weinberg Equations

• The Hardy-Weinberg equations are used to calculate the expected allele and genotype frequencies in a population under equilibrium conditions.

• There are two primary equations:

  1. Equation 1: Allele Frequencies

     • p + q = 1

     • Where:

       • p represents the frequency of the dominant allele in the population.
       • q represents the frequency of the recessive allele in the population.

  2. Equation 2: Genotype Frequencies

     • p^2 + 2pq + q^2 = 1

     • Where:

       • p^2 represents the frequency of the homozygous dominant genotype.
       • 2pq represents the frequency of the heterozygous genotype.
       • q^2 represents the frequency of the homozygous recessive genotype.

Applying the Equations

1. Problem Solving:

   • To solve Hardy-Weinberg problems, start by identifying the information given in the problem.

   • Typically, you will be given the frequency of one of the genotypes (e.g., the frequency of the homozygous recessive genotype).

   • Use this information to calculate the allele frequencies (p and q), and then use these frequencies to calculate the frequencies of the other genotypes.

2. Example:

   • In a population of butterflies, the frequency of the homozygous recessive genotype (aa) is 0.16. What is the frequency of the dominant allele (A)?

     1. Given: q^2 = 0.16
     2. Solve for q: q = \sqrt{0.16} = 0.4
     3. Solve for p: p = 1 - q = 1 - 0.4 = 0.6

   • Therefore, the frequency of the dominant allele (A) is 0.6.

Deviations from Hardy-Weinberg Equilibrium

• Deviations from Hardy