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Hardy-Weinberg Equilibrium

Judith Stanhope


Introduction

An understanding of evolution depends upon knowledge of population genetics. One of the more difficult concepts to understand when studying population genetics is Hardy-Weinberg Equilibrium. Since it is abstract and quantitative, students often feel threatened and quickly shy away from it. They frequently ask, 'Why do we have to know this? Of what value is it?'

Why do students need to know Hardy-Weinberg Equilibrium, and how do we, as teachers, convey the principle to them? As Thomas Merten (1992) states: 'If you have ever been asked questions such as the ones that follow, you begin to see why studying population genetics might be useful:

1. I'm confused! How can O be the most common of the blood types if it is a recessive trait?

2. If Huntington's disease is a dominant trait, shouldn't three-fourths of the population have Huntington's while one-fourth have the normal phenotype?

3. Shouldn't recessive traits be gradually ëswamped out' so they disappear from the population?

These questions reflect the common misconception that the dominant allele of a trait will always have the highest frequency in a population and the recessive allele will always have the lowest frequency. On the contrary, as G. H. Hardy stated in 1908, 'There is not the slightest foundation for the idea that a dominant trait should show a tendency to spread over a whole population, or that a recessive trait should die out.' Gene frequencies can be high or low no matter how the allele is expressed, and can change, depending on the conditions that exist. It is the changes in gene frequencies over time that result in evolution. The Hardy-Weinberg Principle provides a baseline to determine whether of not gene frequencies have changed in a population and thus whether evolution has occurred.

A brief description of the Hardy-Weinberg Principle and a series of activities follow. The activities which are listed below vary in difficulty. The teacher may pick and choose the most appropriate activity for his or her students.

  1. Establishing Hardy-Weinberg Equilibrium

  2. M & M Lab

  3. Fishy Frequencies

  4. How to Use Hardy-Weinberg to Find Gene Frequencies in a Wild Population

  5. Hardy-Weinberg Problems Tutorial

  6. Evolution and Gene Frequencies

  7. Genetics Survey Project

  8. Hardy-Weinberg Made Easy: A Seventh Way

  9. Thumb Measurement

  10. The Use of Dialogues in the Classroom

Background Information

Recall, it is at the population level that evolution occurs. A population is a group of individuals of the same species in a given area whose members can interbreed. Because the individuals of a population can interbreed, they share a common group of genes known as the gene pool. Each gene pool contains all the alleles for all the traits of all the population. For evolution to occur in real populations, some of the gene frequencies must change with time. The gene frequency of an allele is the number of times an allele for a particular trait occurs compared to the total number of alleles for that trait.

Gene frequency = the number of a specific type of allele / the total number of alleles in the gene pool

An important way of discovering why real populations change with time is to construct a model of a population that does not change. This is just what Hardy and Weinberg did. Their principle describes a hypothetical situation in which there is no change in the gene pool (frequencies of alleles), hence no evolution.

Consider a population whose gene pool contains the alleles A and a. Hardy and Weinberg assigned the letter p to the frequency of the dominant allele A and the letter q to the frequency of the recessive allele a. Since the sum of all the alleles must equal 100%, then p + q = 1. They then reasoned that all the random possible combinations of the members of a population would equal (p+q)2 or p2+ 2pq + q2. The frequencies of A and a will remain unchanged generation after generation if the following conditions are met:

1. Large population. The population must be large to minimize random sampling errors.

2. Random mating. There is no mating preference. For example an AA male does not prefer an aa female.

3. No mutation. The alleles must not change.

4. No migration. Exchange of genes between the population and another population must not occur.

5. No natural selection. Natural selection must not favor any particular individual.
Let's look at an analogy that may help the students understand Hardy-Weinberg Equilibrium. Imagine a 'swimming' pool of genes as shown in Figure 1.



Find: Frequencies of A and a. and the genotypic frequencies of AA, Aa and aa.

Solution:

f(A) = 12/30 = 0.4 = 40%

f(a) = 18/30 = 0.6 = 60%

Then, p + q = 0.4 + 0.6 = 1

and p2 + 2pq + q2 = AA + Aa + aa

= .16 + .48 + .36 = 1

As long as the conditions of Hardy-Weinberg are met, the population can increase in size and the gene frequencies of A and a will remain the same. Thus, the gene pool does not change.

Now, suppose more 'swimmers' dive in as shown in Figure 2. What will the gene and genotypic frequencies be?



Solution:

f(A) = 12/34 = .35 = 35 %

f(a) = 22/34 = .65 = 65%

f(AA) = 0.12, f(Aa) = 0.23 and f (aa) = 0.42

The results show that Hardy-Weinberg Equilibrium was not maintained. The migration of swimmers (genes) into the pool (population ) resulted in a change in the population's gene frequencies. If the migration were to stop and the other agents of evolution (i.e., mutation, natural selection and non-random mating) did not occur, then the population would maintain the new gene frequencies generation after generation. It is important to note that a fifth factor affecting gene frequencies is population size. The larger a population is, the number of changes that occur by chance alone becomes insignificant. In the analogy above, a small population was deliberately used to simplify the explanation.

References

Hardy, G.H. 1908. 'Mendelian proportions in a mixed population.' Science, vol. 28, 49-50.

Merten, Thomas R. February 1992. 'Introducing students to population genetics and the Hardy-Weinberg Principle.' The American Biology Teacher, vol 54, no. 2. pp. 103-107.




Lab: Establishing Hardy-Weinberg Equilibrium


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