Hardy-Weinberg principle Totally Explained

Everything about Hardy-weinberg Ratio totally explained

In population genetics, the Hardy–Weinberg principle states that the genotype frequencies in a population remain constant or are in equilibrium from generation to generation unless specific disturbing influences are introduced. Those disturbing influences include non-random mating, mutations, natural selection, limited population size, random genetic drift and gene flow. Genetic equilibrium is a basic principle of population genetics.
   The Hardy-Weinberg principle is like a Punnett square for populations, instead of individuals. A Punnett square can predict the probability of offspring's genotype based on parents' genotype or the offsprings' genotype can be used to reveal the parents' genotype. Likewise, the Hardy-Weinberg principle can be used to calculate the frequency of particular alleles based on frequency of, say, an autosomal recessive disease.
   In the simplest case of a single locus with two alleles: the dominant allele is denoted A and the recessive a. Their frequencies are p and q; freq(A)=p and freq(a)=q. Based on the fact that the probabilities of all genotypes must sum to unity, we can determine useful, difficult-to-measure facts about a population. For example, a patient's child is a carrier of a recessive mutation that causes cystic fibrosis in homozygous recessive children. The parent wants to know the probability of her grandchildren inheriting the disease. In order to answer this question, the genetic counselor must know the chance that the child will reproduce with a carrier of the recessive mutation. This fact may not be known, but disease frequency is known. We know that the disease is caused by the homozygous recessive genotype; we can use the Hardy-Weinberg principle to work backward from disease occurrence to the frequency of heterozygous recessive individuals.
   This concept is also known by a variety of names: HWP, Hardy–Weinberg equilibrium, HWE, or Hardy–Weinberg law. It was named after G. H. Hardy and Wilhelm Weinberg.

Derivation

A better, but equivalent, probabilistic description for the HWP is that the alleles for the next generation for any given individual are chosen randomly and independent of each other. Consider two alleles, A and a, with frequencies p and q, respectively, in the population. The different ways to form new genotypes can be derived using a Punnett square (also known as a Prout Square), where the fraction in each is equal to the product of the row and column probabilities.

		Females
		A (p)	a (q)
Males	A (p)	AA (p²)	Aa (pq)
Males	a (q)	Aa (pq)	aa (q²)

The final three possible genotypic frequencies in the offspring become:

f(mathbf

ť :

= 0.023.,

For two alleles, the chi square goodness of fit test for Hardy-Weinberg proportions is equivalent to the test for inbreeding, F = 0.

History

Mendelian genetics were rediscovered in 1900. However, it remained somewhat controversial for several years as it wasn't then known how it could cause continuous characteristics. Udny Yule (1902) argued against Mendelism because he thought that dominant alleles would increase in the population. The American William E. Castle (1903) showed that without selection, the genotype frequencies would remain stable. Karl Pearson (1903) found one equilibrium position with values of p = q = 0.5. Reginald Punnett, unable to counter Yule's point, introduced the problem to G. H. Hardy, a British mathematician, with whom he played cricket. Hardy was a pure mathematician and held applied mathematics in some contempt; his view of biologists' use of mathematics comes across in his 1908 paper where he describes this as "very simple". ť To the Editor of Science: I'm reluctant to intrude in a discussion concerning matters of which I've no expert knowledge, and I should have expected the very simple point which I wish to make to have been familiar to biologists. However, some remarks of Mr. Udny Yule, to which Mr. R. C. Punnett has called my attention, suggest that it may still be worth making...

ť Suppose that Aa is a pair of Mendelian characters, A being dominant, and that in any given generation the number of pure dominants (AA), heterozygotes (Aa), and pure recessives (aa) are as p:2q:r. Finally, suppose that the numbers are fairly large, so that mating may be regarded as random, that the sexes are evenly distributed among the three varieties, and that all are equally fertile. A little mathematics of the multiplication-table type is enough to show that in the next generation the numbers will be as (p+q)²:2(p+q)(q+r):(q+r)², or as p₁:2q₁:r₁, say.

ť The interesting question is — in what circumstances will this distribution be the same as that in the generation before? It is easy to see that the condition for this is q² = pr. And since q₁² = p₁r₁, whatever the values of p, q, and r may be, the distribution will in any case continue unchanged after the second generation

The principle was thus known as Hardy's law in the English-speaking world until Curt Stern (1943) pointed out that it had first been formulated independently in 1908 by the German physician Wilhelm Weinberg (see Crow 1999). Others have tried to associate Castle's name with the Law because of his work in 1903, but it's only rarely seen as the Hardy-Weinberg-Castle Law.

Graphical representation

It is possible to represent the distribution of genotype frequencies for a bi-allelic locus within a population graphically using a de Finetti diagram. This uses a triangular plot (also known as trilinear, triaxial or ternary plot) to represent the distribution of the three genotype frequencies in relation to each other. Although it differs from many other such plots in that the direction of one of the axes has been reversed.
The curved line in the above diagram is the Hardy-Weinberg parabola and represents the state where alleles are in Hardy-Weinberg equilibrium.
It is possible to represent the effects of Natural Selection and its effect on allele frequency on such graphs (for example Ineichen & Batschelet 1975) The De Finetti diagram has been developed and used extensively by A.W.F. Edwards in his book Foundations of Mathematical Genetics.

References and notes

Further Information

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