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Hardy Weinberg equilibrum  (equations and conditions)

The Hardy-Weinberg equilibrium is the statement that allele frequencies in a population remain constant over time, in the absence of forces to change them. Its name derives from Godfrey Hardy, an English mathematician, and Wilhelm Weinberg, a German physician, who independently formulated it in the early twentieth century. The statement and the set of assumptions and mathematical tools that accompany it are used by population geneticists to analyze the occurrence of, and reasons for, changes in allele frequency. Evolution in a population is often defined as a change in allele frequency over time. The Hardy-Weinberg equilibrium, therefore, can be used to test whether evolution is occurring in populations.

Basic Concepts

A population is a set of interbreeding individuals all belonging to the same species. In most sexually reproducing species, including humans, each organism contains two copies of virtually every gene—one inherited from each parent. Any particular gene may occur in slightly different forms, called alleles. An organism with two identical alleles is called homozygous for that gene, and one with two different alleles is called heterozygous. During the formation of gametes, the two alleles separate into different gametes. Mating unites egg and sperm, so that the offspring obtains two alleles for each gene.

The two alleles for a gene typically have different effects on the phenotype, or characteristics, of the organism. For many genes, one allele will control the phenotype if it is present in either one or two copies; this allele, which is often represented by a single, uppercase letter—B, for example—is said to be dominant. The other allele will only exert a visible effect if the dominant allele is not present; it is said to be recessive and is often represented by a lowercase letter—b, for example. The genotype of an organism specifies both alleles for a particular gene and is often symbolized by pairs of letters, such as BB, Bb, or bb, with each letter representing an allele.

It is important to understand that "dominant" does not mean an allele is more common in the population—lethal dominant alleles are very rare, for instance. Nor does dominant necessarily mean an allele will spread through the population. Likewise, "recessive" does not necessarily mean an allele will become less common. Indeed, the Hardy-Weinberg equilibrium shows conditions under which allele frequencies remain unaltered over generations.

The principle is based off the following table:

Assumptions of the Hardy-Weinberg Model

Before examining the mathematical model underlying the Hardy-Weinberg equilibrium, let us look at the assumptions under which it operates:

1. Organisms reproduce sexually.
2. Mating is random.
3. Population size is very large.
4. Migration in or out is negligible.
5. Mutation does not occur.
6. Natural selection does not act on the alleles under consideration.

While the list appears to be so restrictive that no population can meet its requirements, in fact many do, to a very good first approximation. Even more to the point, variation from the Hardy-Weinberg equilibrium tells a population geneticist that one or more of these assumptions is not being met, thereby providing a clue about the forces at work within the population. Perhaps surprisingly, populations need not be very big to meet the conditions above—populations with as few as one thousand to two thousand individuals can do so.

Biographies: Hardy, or Godfrey Harold Hardy:

Godfrey Harold Hardy was one of the foremost mathematicians in England during the early part of the twentieth century. He was primarily a pure mathematician, specializing in branches of mathematics that study the behavior of numbers (such as number theory and analysis). He also made important contributions to areas of applied mathematics, and is known for formulating the Hardy-Weinberg law of population genetics. He taught at both Cambridge and Oxford and published over three hundred-fifty research papers, either alone or in collaboration with other mathematicians--most notably John Edensor Littlewood and S. I. Ramanujan.

Weinberg, or Wilhelm Weinberg:

Weinberg was born in Stuttgart and studied medicine at Tübingen and Munich, receiving an M.D. in 1886. He returned to Stuttgart in 1889, where he remained running a large practice as a gynecologist and obstetrician until he retired to Tübingen a few years before his death in 1937. Much of his academic life he spent studying genetics especially focusing on applying the laws of inheritance to populations.^[3]

Additional contributions by Weinberg to statistical genetics included the first estimate of the rate of twinning - Realizing that identical twins would have to be same-sex, while dizygotic twins could be either same or opposite sex, Weinberg derived the formula for estimating the frequency of monozygotic and dizygotic twins from the ratio of same sex and opposite twins to the total of maternities.^[2] Weinberg also estimated that the heritability of twinning itself was close to zero.

Hardy, Weinberg, and the population geneticists who followed them came to understand that evolution will not occur in a population if seven conditions are met:

These conditions are the absence of the things that can cause evolution.  In other words, if no mechanisms of evolution are acting on a population, evolution will not occur--the gene pool frequencies will remain unchanged.  However, since it is highly unlikely that any of these seven conditions, let alone all of them, will happen in the real world, evolution is the inevitable result.

http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/H/Hardy_Weinberg.html

^This website gives a great example as to how the Hardy Weinberg Equilibrum works.