HardyWeinberg Theory and Population Genetics
Evolution may be expressed as a change in gene frequency from one generation to the next in a population. Gene frequency is the frequency of an allele at a given locus in a population. Changes in gene frequency may be brought about by:
Consider an allele (A) at a given locus, with an alternate allele (a) located at the same locus. Let the proportion of the (A) allele in the population be p and the proportion of the (a) allele be q. Let us assume that this is not a multiple allelic series and that chromosomes with (A) plus all chromosomes with (a) will constitute the entire set of chromosomes in the population with respect to (A) and (a). Then: p + q = 1.
An individual in a diploid population which reproduces sexually is the result of one male gamete plus one female gamete being combined to form a zygote. If the mating is random, the proportions of genes in the gametes will determine the proportion of genotypes in the population. Therefore, genotype proportions in our simple 2 allele situation should be expressed by squaring the sum of the allele proportions in a simple binomial as follows:
What are five assumptions which must be made for genetic equilibrium to occur between successive generations?
Natural selection is one of the main factors, resulting in changes in gene proportions. Natural selection may take many different degrees from completely lethal to very slight. Ordinarily, however, natural selection is probably rather subtle in its action, being recognized as one population having a very slight reproductive advantage over another. The effects of selection are often illustrated by using an extreme example such as a completely lethal recessive. This situation represents complete selection against a certain genotype.
It is possible to calculate the effects of complete selection against the homozygous recessive genotype using a modification of the basic HardyWeinberg equation. Without going into the derivation of this formula, it may be expressed as follows:
qn = proportion of recessive allele after n generations of selection
qo = original frequency of the recessive allele
Note: This modified expression derived from the HardyWeinberg may only be used in situations where the homozygous recessive individuals do not reproduce.
 Define p.
 Define q.
 Define p^{2}; 2pq; q^{2}.
 In what ways do the above definitions differ?
Demonstration of the HardyWeinberg Equilibrium
The following exercise, if carried out and understood, will provide you with an understanding of the basic HardyWeinberg equilibrium and at the same time illustrate the effects of several kinds of selection on this equilibrium.
Set up a population (generation 0) made up of 100 diploid individuals. The genotype of any one of these individuals may be represented using two beans, in various combinations, as follows:
Genotype 
White beans 
Red beans 
homozygous dominant AA  2 
0 
heterozygous Aa  1 
1 
homozygous recessive aa  0 
2 
The population of 100 individuals will therefore be made up of 200 alleles (beans). Let the proportion of genotypes in these 100 individuals (200 beans) be 25% AA, 50% Aa and 25% aa. Make up the 200 beans in the appropriate proportions.
25 AA individuals 
50 white beans 

50 Aa individuals 
50 white beans 
50 red beans 
25 aa individual 
50 red beans 
100 Individuals 
100 white beans 
100 red beans 