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Biology

Hardy-Weinberg Principle

The Hardy-Weinberg Principle predicts allelic frequencies for a population that is not evolving.

When considering two alleles at a locus, like a red and brown coat allele in a squirrel population, the sum of the frequencies of each of the alleles represented by the letters p and q will equal one since there are only two alleles.

Additionally, the frequencies of each of the specific genotypes can be calculated. The frequency of red and brown coated individuals in the population, both of the homozygous types, will equal the square of the allelic frequency, or p squared and q squared. Since homozygous individuals have two of the same alleles.

Heterozygous individuals with red brown coats can arise two ways. If the egg provides the red allele and sperm the brown or vice versa. Therefore the frequency of the heterozygous individuals is two times the product of the allelic frequencies, Two times p times q.

The sum of all of these genotypic frequencies will be one. This principle is only true under specific, non-evolving conditions. There must be no selection, mating is random, and there is no selection for particular genotypes. There must be no gene flow from outside the population, and no mutations inside the population. Last, the population size must be very large because in small populations random events can substantially change allelic frequencies.

Diploid organisms have two alleles of each gene, one from each parent, in their somatic cells. Therefore, each individual contributes two alleles to the gene pool of the population. The gene pool of a population is the sum of every allele of all genes within that population and has some degree of variation. Genetic variation is typically expressed as a relative frequency, which is the percentage of the total population that has a given allele, genotype or phenotype.

In the early 20^{th} century, scientists wondered why the frequency of some rarely-observed dominant traits did not increase in randomly-mating populations with each generation. For example, why does the dominant polydactyly trait (*E*, extra fingers and/or toes) not become more common than the usual number of digits (*e*) in many animal species? In 1908, this phenomenon of unchanged genetic variation across generations was independently demonstrated by a German physician, Wilhelm Weinberg, and a British Mathematician, G. H. Hardy. The principle later became known as Hardy-Weinberg equilibrium.

The Hardy-Weinberg equation (*p*^{2} + 2*pq* + *q*^{2} = 1) elegantly relates allele frequencies to genotype frequencies. For instance, in a population with polydactyly cases, the gene pool contains *E* and *e* alleles with relative frequencies of *p* and *q*, respectively. Since the relative frequency of an allele is a proportion of the total population, *p* and *q* add up to 1 (*p* + *q* = 1).

The genotype of individuals in this population is either *EE*, *Ee*, or *ee*. Hence, the proportion of individuals with the *EE* genotype is *p* × *p*, or *p*^{2}, and the proportion of individuals with the *ee *genotype is *q* × *q*, or *q*^{2}. The proportion of heterozygotes (*Ee*) is 2*pq *(*p* × *q* and *q* × *p*) since there are two possible crosses that produce the heterozygous genotype (i.e., the dominant allele can come from either parent). Similar to allele frequencies, genotype frequencies also add up to 1; therefore, *p*^{2} + 2*pq* + *q*^{2} = 1, which is known as the Hardy-Weinberg equation.

Hardy-Weinberg equilibrium states that, under certain conditions, allele frequencies in a population will remain constant over time. Such populations meet five conditions: infinite population size, random mating of individuals, and an absence of genetic mutations, natural selection, and gene flow. Since evolution can simply be defined as the change in allele frequencies in a gene pool, a population that fits Hardy-Weinberg criteria does not evolve. Most natural populations violate at least one of these assumptions and therefore are seldom in equilibrium. Nevertheless, the Hardy-Weinberg principle is a useful starting point or null model for the study of evolution, and can also be applied to population genetics studies to determine genetic associations and detect genotyping errors.

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Douhovnikoff, Vladimir, and Matthew Leventhal. “The Use of Hardy–Weinberg Equilibrium in Clonal Plant Systems.” *Ecology and Evolution* 6, no. 4 (January 25, 2016): 1173–80. [Source]

Salanti, Georgia, Georgia Amountza, Evangelia E. Ntzani, and John P. A. Ioannidis. “Hardy–Weinberg Equilibrium in Genetic Association Studies: An Empirical Evaluation of Reporting, Deviations, and Power.” *European Journal of Human Genetics* 13, no. 7 (July 2005): 840–48. [Source]

Hosking, Louise, Sheena Lumsden, Karen Lewis, Astrid Yeo, Linda McCarthy, Aruna Bansal, John Riley, Ian Purvis, and Chun-Fang Xu. “Detection of Genotyping Errors by Hardy–Weinberg Equilibrium Testing.” *European Journal of Human Genetics* 12, no. 5 (May 2004): 395–99. [Source]

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