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# Hardy-Weinberg(哈迪-温伯格)定律与遗传漂变

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Hardy-Weinberg(哈迪-温伯格)定律与遗传漂变

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.

#### The Hardy-Weinberg Equilibrium Principle

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 Weinberg1,2. 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 p2 + 2pq + q2 = 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 p2, homozygous recessive by q2, and heterozygous by 2pq. 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 = p2 + 2pq + q2.

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.

#### Genetic Drift

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 disease3,4. 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 progression3,5-6. 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 disease4. 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.

#### References

1. Hardy, G. H. (Jul 1908). 'Mendelian Proportions in a Mixed Population' (PDF). Science. 28 (706): 49–50. doi:10.1126/science.28.706.49. ISSN 0036-8075. PMID 17779291.
2. Weinberg, W. (1908). 'Über den Nachweis der Vererbung beim Menschen'. Jahreshefte des Vereins für vaterländische Naturkunde in Württemberg. 64: 368–382.
3. Eguchi S, Matsuura M. Testing the Hardy-Weinberg equilibrium in the HLA system. Biometrics. 1990 Jun;46(2):415-26. PubMed PMID: 2364131.
4. 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.
5. 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.
6. https://hla-net.eu/tools/frequency-estimation/
7. 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