Hardy-Weinberg Principle

In our articles on Genetics and Inheritance, we looked at the basic principles of how genes are passed on from generation to generation. Here, we’ll discuss what a gene pool is and explain how to calculate the frequency of an allele based on the Hardy Weinberg equation.

What is the Hardy-Weinberg principle?

The Hardy-Weinberg principle, named after English mathematician G. H. Hardy and German doctor Wilhelm Weinburg, can calculate the frequency of an allele in a population at equilibrium. It is a null model in genetics. According to the Hardy-Weinberg principle, at equilibrium, the allele frequencies of a gene within a population will not differ from one generation to the next. Unless an allele leads to a phenotype with a significant advantage or disadvantage over other alleles, its frequency in a population is unlikely to change. A population in Hardy-Weinburg equilibrium is not evolving means it is described as ‘stable’.

As we will see below, the Hardy-Weinberg principle provides us with a mathematical equation to calculate the expected frequency of an allele in a population.

${\mathrm{P}}^2+2\mathrm{PQ}+{\mathrm{Q}}^2=1$

What are the assumptions of the Hardy-Weinberg principle?

Imagine a population of diploid organisms that reproduce sexually. Let’s assume that there is no overlap between generations and that the frequencies of all alleles are equal in males and females.

There are five conditions for Hardy-Weinberg equilibrium. These are:

1. There is no selection: all alleles are equally likely to be passed on to the next generation.
2. No mutations arise.
3. There is no migration: the population is isolated.
4. The population size is infinitely large.
5. Mating is random.

What is the Hardy-Weinberg equation?

${\mathrm{P}}^2+2\mathrm{PQ}+{\mathrm{Q}}^2=1.0$

Where p² = BB, 2pq = Bb, and b² = aa.

• Consider gene B. It has the dominant allele B and recessive allele b.
• Let the probability of allele B = p and allele b = q.
• There are only two alleles, so the probability of one plus the other must be 1.0/ Thus, p+q = 1.0

If you are told that the frequency of a dominant allele in a population is 70%, you have been given p directly, p = 0.7. Therefore q = 0.3, as p + q = 1.0

In the article on Inheritance, we learned that there are only four possible arrangements of these two alleles. It follows that all together, the probability of all four will equal 1.0.

How can we calculate the probability of a genotype in a population?

Now that we have the Hardy-Weinberg equation, we can calculate the frequency of an allele in a population.

Suppose that blondeness is the result of recessive allele b, and only one in 10 people display this phenotype. What is the probability that an individual in this population is a heterozygote?

1. Since this trait is recessive, it will only appear in individuals with the genotype bb.

2. Only 1 in 10 individuals have this phenotype; the probability of bb is $q^2$ = 0.10.

3. q is the square root of 0.10. q = 0.3162.

4. p + q = 1.0. Therefore, p = 1.0 - q = 1.0 - 0.3162 = 0.6838.

5. The probability of heterozygotes is 2pq. 2pq = 0. 4324