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# Hardy-Weinberg & Genetic Drift

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#### The Hardy-Weinberg Equilibrium Principle

#### Genetic Drift

#### References

#### Further Reading

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Scientists once wondered why dominant traits like tan-colored giraffe spots do not become more frequent with each generation and replace recessive traits like dark brown spots. In thinking about this conundrum, in 1908, independent from each other, Godfrey H. Hardy and Wilhelm Weinberg independently derived a theory, today known as the Hardy-Weinberg Principle and represented by this equation.

The principle states that in the absence of evolution, i.e. at equilibrium, the allele and genotype frequencies of a population will remain constant from one generation to the next. To understand this equation, let's go back to the giraffe example. Uppercase A represents the tan allele since it is dominant, and lowercase a is for the brown allele because it is recessive. The frequency of these two alleles in the population are designated as p and q respectively. So how do we know the allele frequency? Well, each individual has two alleles. In this example, 40% of the alleles in the gene pool are tan. Thus, the frequency of the tan allele, p, is 0.4, and the frequency of the brown allele, q, is 0.6. Note that p plus q is always equal to one.

Now let's go back to the Hardy-Weinberg equation. Each term in the equation represents one genotype frequency. The frequency of the homozygous dominant genotype is p squared, and the homozygous recessive is represented by q squared. The heterozygous genotype is two pq. The reason we multiply by two here is that there are two different ways of generating a heterozygous genotype. Combined, these all represent 100% of genotypes. Thus, a total frequency of one. Using the values for p and q from our giraffe example, we can determine the genotype distribution of the color gene alleles in our giraffe population. Therefore, as per the Hardy-Weinberg Principle, at equilibrium, 16% of the giraffe population will be homozygous dominant, 48% will be heterozygous, and 36% are homozygous recessive.

To maintain this balance, the Hardy-Weinberg Equilibrium Principle states that a population should meet five main assumptions. There should be random mating, large population size, no mutation, no selection on the gene in question, and no gene flow in or out of the population. Most natural populations violate at least one of these assumptions and so equilibrium is rare…but in spite of this, the principle is used as a null model for population genetics. By comparing these expected values to the actual genotype frequency in a population, it can be determined whether that population is in Hardy-Weinberg Equilibrium. If not, then this means that some form of evolution or change in allele frequency is taking place.

A general misconception about evolution is that it requires natural selection to occur. However, this is not always the case. Genetic drift is one mechanism by which evolution can occur without natural selection. It is defined as a change in the allele frequency of a population due to chance. To envision this, let's go back to the example of a giraffe population and imagine their alleles of tan and brown being represented by marbles of two different colors. We will assume here that each color starts out equally abundant. If we were to start a new generation out of this population, we would need to breed pairs of individuals and thus select from four alleles per pair. If we select a breeding pair at random, then we might end up with two marbles of each color. However, by chance alone, some pairings will have only one color marble, or three of one color and one of the other. These chance deviations from 50-50 over multiple pairings to create a new generation might mean that the next generation no longer has an equal mixture of each allele.

It's this variation of relative allele frequencies over time that defines genetic drift. Therefore, unlike adaptive evolution, where allele frequency changes to select for traits that are fit for the environment, like ladybugs with a greater amount of melanin surviving better in colder climates because of an improved ability to absorb heat, genetic drift represents a type of evolution that is purely due to stochastic change. For example, the random removal of a section of a population through a catastrophic event.

In this lab, you will perform computer and colored bead simulations of Hardy-Weinberg Equilibrium and genetic drift in a population, and then test what happens when assumptions of the equilibrium are violated.

Evolutionary change is interesting and important to study, but changes in populations occur over long periods of time and in huge physical spaces and are therefore very difficult to measure. In general, studying phenomena like this requires the use of mathematical models which are built using parameters that can be conveniently measured. These models are then used to make predictions about how changes to the system might affect the outcome.

For example, changes to the frequency of genetic alleles at individual loci in species are often observed over long time periods, but are not generally observable over short time periods. The use of computer models allows researchers to predict changes within a species’ gene pool using observations that have already been gathered, and allow for simulations of a potentially unlimited number of generations of the population. This would certainly not be possible within a human lifetime.

One equation used to model populations is the Hardy-Weinberg equilibrium equation. It was formulated independently in 1908 by both G. H. Hardy and Wilhelm Weinberg^{1,2}. The simple equation describes the expected allele frequency of a population that is* not* evolving. Because most real-life populations are evolving in response to the forces of natural selection, this formula acts as a useful null hypothesis. It is used to test whether or not different types of selection are, or are not, occurring. If measured allele frequencies differ from those that were predicted using the Hardy-Weinberg equation, then the gene in question is undergoing evolutionary change.

The Hardy-Weinberg equation can be represented as *p*^{2} + 2*pq* + *q*^{2} = 1 where *p* represents the frequency of the dominant allele and q represents the frequency of the recessive allele for the gene in question. Each expression in the equation represents the predicted frequency of one of the three possible diploid genotypes. Homozygous dominant frequency is represented by *p*^{2}, homozygous recessive by *q*^{2}, and heterozygous by 2*pq*. If these frequencies are summed, it adds up to 1, which makes sense since the full population had been divided into the three available categories.

It is also possible to describe the population, or gene pool, in terms of the two alleles, without regard to how they are packaged into diploid individuals. This equation is represented as *p + q = 1*, that is, the frequencies of the dominant and recessive alleles must add up to 1 within the population. Again, this makes sense, since the model includes just two allele possibilities. Notice that the frequency of genotypes in the population is just the quadratic expansion of the frequency of alleles in the population because (*p *+* q*)^{2} = *p*^{2 }+ 2*pq *+* q*^{2}.

The Hardy-Weinberg equation, like most other models, requires a series of assumptions. Usefully, if the real-life data differs from the predicted data, it is possible to hypothesize which of the starting assumptions was false. The assumptions of the Hardy-Weinberg equilibrium equations are: 1) the population is very large, 2) the population is closed, meaning that there are no individuals immigrating into or emigrating out of the population, 3) there are no mutations occurring on the gene in question, 4) individuals within the population are mating at random—individuals are not choosing their mates, 5) natural selection is not occurring. Again, keep in mind that the Hardy-Weinberg equilibrium equation is a null hypothesis. Frequently, real populations violate one or more of these assumptions. The equation is used to determine if and how evolution is happening.

In a relatively small population, a condition that violates the first Hardy-Weinberg assumption, it is possible for allele frequencies to have resulted from chance. This phenomenon is referred to as genetic drift. One version of this is referred to as the founder effect. If a small number of individuals move to an isolated location and start a new population, the specific genetics of those particular individuals will shape the future generations. This new small gene pool may have the same allele frequency as the original, but it is also possible, even likely, that it does not. Say the original population included 50% dominant alleles and 50% recessive. In the extreme, if all of the individuals in a migrating founder group are homozygous recessive, then the dominant allele has been lost completely and the recessive is now at 100%. A similar phenomenon, called the bottleneck effect, can occur if a population sustains a large drop in numbers due to a natural disaster, human intervention, or disease.

Importantly, genetic drift represents a type of evolution that is not necessarily adaptive. It does not specifically select for traits that are fit for the environment. Nonetheless, it is an important evolutionary force in shaping populations with a small number of individuals and will cause deviations from Hardy-Weinberg predictions. In populations that are larger, deviations from the predictions are more likely to mean that the population in question is undergoing evolution through natural selection. Under these circumstances, further consideration of the mechanisms causing this evolution can be explored.

Modern applications of the Hardy-Weinberg model include analysis of human and animal populations in terms of how their immune systems relate to their susceptibility to infectious disease^{3,4}. Many research groups are cataloging genes which encode specific immune system molecules, such as CCR5 and the major histocompatibility complex (MHC, known in humans as the human leukocyte antigen (HLA), and correlating this information to epidemiological studies regarding disease and its progression^{3,5-6}. From comparing these two types of data sets, patterns are emerging showing that some individuals are genetically resistant to particular infections while others are more likely to succumb to disease^{4}. Hardy and Weinberg’s model has been essential to the analysis of this data and has contributed to our understanding of how infections have shaped evolution.

- Hardy, G. H. (Jul 1908). 'Mendelian Proportions in a Mixed Population'
*(PDF). Science.*49–50. doi:10.1126/science.28.706.49. ISSN 0036-8075. PMID 17779291.**28**(706): - Weinberg, W. (1908). 'Über den Nachweis der Vererbung beim Menschen'.
*Jahreshefte des Vereins für vaterländische Naturkunde in Württemberg*.**64**: 368–382. - Eguchi S, Matsuura M. Testing the Hardy-Weinberg equilibrium in the HLA system. Biometrics. 1990 Jun;46(2):415-26. PubMed PMID: 2364131.
- Phillips KP, Cable J, Mohammed RS, et al. Immunogenetic novelty confers a selective advantage in host-pathogen coevolution.
*Proc Natl Acad Sci U S A*. 2018;115(7):1552-1557. - Lim JK, Glass WG, McDermott DH, Murphy PM CCR5: no longer a 'good for nothing' gene--chemokine control of West Nile virus infection. Trends Immunol. 2006 Jul; 27(7):308-12.
- https://hla-net.eu/tools/frequency-estimation/
- Santiago Rodriguez, Tom R. Gaunt and Ian N. M. Day. Hardy-Weinberg Equilibrium Testing of Biological Ascertainment for Mendelian Randomization Studies. American Journal of Epidemiology Advance Access published on January 6, 2009, DOI 10.1093/aje/kwn359. http://www.oege.org/software/hwe-mr-calc.html

Andrews, C. (2010) The Hardy-Weinberg Principle. Nature Education Knowledge 3(10):65 https://www.nature.com/scitable/knowledge/library/the-hardy-weinberg-principle-13235724