7.2.2

# Hardy-Weinberg Principle

Test yourself

## Using the Hardy-Weinberg Principle

The Hardy-Weinberg principle is used to predict allele frequencies in a population. The principle is a mathematical model.

### Predictions

• The Hardy-Weinberg principle predicts that allele frequencies will not change from generation to generation.
• The allele frequencies do not change because a populationâ€™s allele and genotype frequencies are inherently stable.

### Assumptions

• The Hardy-Weinberg principle only works if you make some assumptions about the population you are studying.
• The assumptions are:
• No mutations, migration or emigration.
• No selective pressure for or against a specific genotype.
• Population size is infinite.
• In real populations, these assumptions are not normally met but making assumptions is still useful because it provides a model we can compare to real population changes.

## The Hardy-Weinberg Equation

The Hardy-Weinberg equation is: p2 + 2pq + q2 = 1. The equation is used to predict the frequency of alleles, genotypes and phenotypes in a population.

### p + q = 1

• For every gene, there are two alleles present in an individual (except some genes on the X chromosome).
• If you know the frequency of one of these alleles, the equation p + q = 1 can be used to calculate the frequency of the other allele.
• p = frequency of one allele.
• q = frequency of other allele.

### p2 + 2pq + q2 = 1

• The Hardy-Weinberg is equation: p2 + 2pq + q2 = 1
• p2 = pp = homozygous dominant.
• q2 = qq = homozygous recessive.
• 2pq = heterozygous.
• The components of the equation allows us to calculate the number of individuals in a population that have each genotype.

### Predicting genotypes

• By observing the phenotypes in a population, you can identify how many individuals carry the homozygous recessive allele genotype (q2).
• Only individuals who are homozygous recessive show the recessive phenotype.
• Individuals with the dominant phenotype could be homozygous dominant or heterozygous.
• This number can be used in the Hardy-Weinberg equation to allow the frequencies other two genotypes to be estimated.

### Pea plants

• Pea plants can have yellow peas (pp or pq) or green peas (qq).
• If 0.25 of the population have green peas then q2 = 0.25.
• If q2 = 0.25, then q = 0.5.
• Using p + q = 1, p + 0.5 = 1, p = 0.5.
• 2pq = 0.50.
• p2 = 0.25.
• p = 0.5.