32.2
Hardy-Weinberg Principle
The Hardy–Weinberg Principle states that in a large, randomly mating population, allele frequencies stay the same over time if the population is not evolving.
When a gene has two alleles at one locus, such as red and brown coat alleles in squirrels, their frequencies—represented by p and q—add up to one.
We can calculate the frequency of each genotype. The frequency of homozygous red and homozygous brown individuals is the square of the allele frequency—p² and q²—which gives the probability of inheriting the same allele from both parents.
Heterozygous individuals with red-brown coats can form in two ways: the egg can carry the red allele and the sperm the brown allele, or the egg can carry the brown allele and the sperm the red allele. So, the frequency of heterozygous individuals equals two times the product of the allele frequencies, or 2pq.
Together, these genotype frequencies sum to one. This principle is true only under specific, non-evolving conditions.
There must be no natural selection, and mating must be random with no preference for particular genotypes. There must be no gene flow from outside the population and no mutations within the population.
Finally, the population must be very large because random events can strongly change allele frequencies in small populations.
Although no real-world population can satisfy all of these conditions, the principle still offers a useful model for population analysis.
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 20th 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.
Hardy-Weinberg Equation
The Hardy-Weinberg equation (p2 + 2pq + q2 = 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 p2, and the proportion of individuals with the ee genotype is q × q, or q2. The proportion of heterozygotes (Ee) is 2pq (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, p2 + 2pq + q2 = 1, which is known as the Hardy-Weinberg equation.
Hardy-Weinberg Conditions
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.
The Hardy–Weinberg Principle states that in a large, randomly mating population, allele frequencies stay the same over time if the population is not evolving.
When a gene has two alleles at one locus, such as red and brown coat alleles in squirrels, their frequencies—represented by p and q—add up to one.
We can calculate the frequency of each genotype. The frequency of homozygous red and homozygous brown individuals is the square of the allele frequency—p² and q²—which gives the probability of inheriting the same allele from both parents.
Heterozygous individuals with red-brown coats can form in two ways: the egg can carry the red allele and the sperm the brown allele, or the egg can carry the brown allele and the sperm the red allele. So, the frequency of heterozygous individuals equals two times the product of the allele frequencies, or 2pq.
Together, these genotype frequencies sum to one. This principle is true only under specific, non-evolving conditions.
There must be no natural selection, and mating must be random with no preference for particular genotypes. There must be no gene flow from outside the population and no mutations within the population.
Finally, the population must be very large because random events can strongly change allele frequencies in small populations.
Although no real-world population can satisfy all of these conditions, the principle still offers a useful model for population analysis.
From Chapter 32:
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32.2 : Hardy-Weinberg Principle
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