Hardy-Weinberg Equilibrium

The Hardy-Weinberg equilibrium model tries to explain why genotype frequencies may remain constant within a population. Hardy-Weinberg equilibrium in its simplest form is based on the existence of two alleles at a single genetic locus. These are generally called p and q. If we make the assumption that the population is large (effectively infinite), mating is random and that there is no difference in fitness between the genotypes, given sufficient time the genotype frequencies will be:

Genotype      pp     pq      qq
Frequency     p2     2pq     q2

This should (assuming the above assumptions are true) be stable - although the genotype frequencies may be different to the starting point, the allele frequencies should be the same as before. Equilibrium has therefore been reached. Sadly for the Hardy-Weinberg equilibrium model, the above assumptions are rarely true. In most cases, genetic equilibrium is reached by strong selection pressure in opposite directions stabalising the population.

The Hardy-Weinberg Model was put forth to explain why the recessive genes in a population would not be pushed out by the dominant genes. While it does not give an accurate representation of how gene flow works in real population (it doesn't take into account selective breeding, the founder effect, emigration and immigration, random genetic drift, etc.), it can be used to figure out the gene frequencies in a population at a specific time.

I have a hard time doing these, and I know that I could not do one of these with only the information given here in the previous WUs. So here's more information and a demonstration.

The Hardy-Weinberg Equations
These apply only to a two allelic system.
p = dominant allele
q = recessive allele
p + q = 1 (or 100% of the alleles)
p² + 2pq + q² = 1

So... Say you have a sample of 100 people. 36% have mid-digital hair. You know that mid-digital hair is caused by a dominant gene. This means that the 64% of the population that doesn't have mid-digital hair has two recessive alleles (qq). Lets plug that in.

q² (qq) = .64 (64%)
Therefore, q = .8 (the square root of q = the square root of .64)
Remember that p + q = 1
So, p + .8 = 1
Therefore, p = .2
p² = .04 (4%)
Remember, p² + 2pq + q² = 1
So, .04 + 2pq + .64 = 1
Therefore, 2pq = .32 (this is the number of heterozygous individuals)

And what, pray tell, does this mean? Well...
The allele or gene frequency: 80% for p, 20% for q.
Genotype frequencies: pq = 32%, pp = 4%, qq = 64%
Phenotype frequencies: well, this is what we started with. M-D hair 36%, no M-D hair 64%. We just add pq and pp together, since p is dominant, both will be expressed the same.

The proportions of alternate forms of a gene (alleles) in a large population will not change from generation to generation, unless they are influenced by mutation, selection, emigration, or immigration of individuals from other populations. If these conditions have no effect and if mating is random, the proportions of genotypes in the population will also remain the same after one generation.

It is important to recognize that this principle states the conditions under which evolution will not occur. Deviations from the above situation indicate that evolution is occuring as a result of Natural Selection or other factors.

Theoretically, any population can be described by the equation p2 + 2pq + q2 = 1 where p is the frequency of one allele and q is the frequency of the other. To get the gene frequencies, take the individual # of each respective allele and divide it by the total # of alleles (both types) in the population. If these frequencies are calculated for two consecutive generations and they appear to be changing significantly, evolution is occuring (a change of up to 0.05 is considered equilibrium).

The Hardy-Weinburg model demonstrates in a rigorous quantitative fashion that in a system of particulate inheritance, there is no loss of genetic variation over time. This was a problem of the blending inheritance model, in which genetic variation decayed at a constant rate. It is ironic that the mathematician Hardy couldn't stand applied mathematics, and became immortalised in the biological literature for a painfully trivial mathematical demonstration.

This genetics law states that the frequency of a given genotype will reach equilibrium in a randomly mating population and will stay constant over many generations in the absence of selection pressures.

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From the BioTech Dictionary at http://biotech.icmb.utexas.edu/. For further information see the BioTech homenode.