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5.2: Hardy-Weinberg Theorem

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    Why is balance important?

    To these individuals, the importance of maintaining balance is obvious. If balance, or equilibrium, is maintained within a population's genes, can evolution occur? No. But maintaining this type of balance today is difficult.

    The Hardy-Weinberg Theorem

    Godfrey Hardy was an English mathematician. Wilhelm Weinberg was a German doctor. Each worked alone to come up with the founding principle of population genetics. Today, that principle is called the Hardy-Weinberg theorem. It shows that allele frequencies do not change in a population if certain conditions are met. Such a population is said to be in Hardy-Weinberg equilibrium. The conditions for equilibrium are:

    1. No new mutations are occurring. Therefore, no new alleles are being created.
    2. There is no migration. In other words, no one is moving into or out of the population.
    3. The population is very large.
    4. Mating is at random in the population. This means that individuals do not choose mates based on genotype.
    5. There is no natural selection. Thus, all members of the population have an equal chance of reproducing and passing their genes to the next generation.

    When all these conditions are met, allele frequencies stay the same. Genotype frequencies also remain constant. In addition, genotype frequencies can be expressed in terms of allele frequencies, as the Table below shows. For a further explanation of this theorem, see Solving Hardy Weinberg Problems at

    Hardy and Weinberg used mathematics to describe an equilibrium population (p = frequency of A, q = frequency of a, so p + q = 1): p2 + 2pq + q2 = 1. Using the genotype frequencies shown in Table below, if p = 0.4, what is the frequency of the AA genotype?

    Genotype Genotype Frequency
    AA p2
    Aa 2pq
    aa q2

    A video explanation of the Hardy-Weinberg model can be viewed at (14:57).


    • The Hardy-Weinberg theorem states that, if a population meets certain conditions, it will be in equilibrium.
    • In an equilibrium population, allele and genotype frequencies do not change over time.
    • The conditions that must be met are no mutation, no migration, very large population size, random mating, and no natural selection.

    Explore More

    Use this resource to answer the questions that follow.

    • Hardy-Weinberg Equilibrium Model at
    1. This resource states that evolution will not occur in a population if seven conditions are met. What are these seven conditions?
    2. If there is no evolution, what happened to gene frequencies?
    3. What are p and q?
    4. How is p determined?
    5. p + q = _____
    6. p2 + 2pq + q2 = _____


    1. Describe a Hardy-Weinberg equilibrium population. What conditions must it meet to remain in equilibrium?
    2. Assume that a population is in Hardy-Weinberg equilibrium for a particular gene with two alleles, A and a. The frequency of A is p, and the frequency of a is q. Because these are the only two alleles for this gene, p + q = 1.0. If the frequency of homozygous recessive individuals (aa) is 0.04, what is the value of q? What is the value of p?
    3. Use the values of p and q from question 2 to calculate the frequency of the heterozygote genotype (Aa).

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