7.2.3 Hardy-Weinberg

Key Assumptions for Hardy-Weinberg Equilibrium

For the principle to apply, these conditions must be met:

1. No mutations occur to alter alleles.
2. No migration—no alleles enter or leave the population.
3. The population size is large, minimising the effects of genetic drift.
4. No selection—all alleles are equally likely to be passed on.
5. Random mating occurs, with no preference for specific alleles.

Hardy-Weinberg Formulae

1. Allele Frequency Formula:

$$p + q = 1$$

Where:

• p = frequency of the dominant allele (A).
• q = frequency of the recessive allele (a).

2. Genotype Frequency Formula:

$$p^2 + 2pq + q^2 = 1$$

Where:

• p² = frequency of homozygous dominant individuals (AA).
• 2pq = frequency of heterozygous individuals (Aa).
• q² = frequency of homozygous recessive individuals (aa).

Step-by-Step Application

1. Identify q²:

• Start with the proportion of the population showing the recessive phenotype (q²).

2. Calculate q:

• Take the square root of q² to find q.

3. Find p:

• Use the equation $p + q = 1$ to calculate p.

4. Determine genotype frequencies:

• Calculate $p^2$, $2pq$, and $q^2$ to find the proportions of each genotype in the population.

Example Problem

If 16% of a population displays a recessive phenotype:

5. $q^2 = 0.16, so$ = $q = \sqrt{0.16} = 0.4$

6. $p + q = 1, so$ = $p = 1 - 0.4 = 0.6$

7. Genotype frequencies:

• $p^2 = 0.6^2 = 0.36 (36\%\ \text{are homozygous dominant)}.$
• $2pq = 2(0.6)(0.4) = 0.48 \text{(48\% are heterozygous)}.$
• $q^2 = 0.16 \text{(16\% are homozygous recessive)}$