Allele
An allele (Template:PronEng (US), Template:IPA) is a viable DNA (deoxyribonucleic acid) coding that occupies a given locus (position) on a chromosome. Usually alleles are sequences that code for a gene, but sometimes the term is used to refer to a non-gene sequence.  An individual's genotype for that gene is the set of alleles it happens to possess. In a diploid organism, one that has two copies of each chromosome, two alleles make up the individual's genotype. The word came from Greek  = "each other".
An example is the gene for blossom colour in many species of flower  a single gene controls the colour of the petals, but there may be several different versions (or alleles) of the gene. One version might result in red petals, while another might result in white petals. The resulting colour of an individual flower will depend on which two alleles it possesses for the gene and how the two interact.

# Introduction
An allele is an alternative form of a gene (in diploids, one member of a pair) that is located at a specific position on a specific chromosome.
Diploid organisms, for example, humans, have paired homologous chromosomes in their somatic cells, and these contain two copies of each gene. An organism in which the two copies of the gene are identical  that is, have the same allele  is called homozygous for that gene. An organism which has two different alleles of the gene is called heterozygous. Phenotypes (the expressed characteristics) associated with a certain allele can sometimes be dominant or recessive, but often they are neither. A dominant phenotype will be expressed when at least one allele of its associated type is present, whereas a recessive phenotype will only be expressed when both alleles are of its associated type.
However, there are exceptions to the way heterozygotes express themselves in the phenotype.  One exception is incomplete dominance (sometimes called blending inheritance) when alleles blend their traits in the phenotype.  An example of this would be seen if, when crossing Antirrhinums  flowers with incompletely dominant "red" and "white" alleles for petal color  the resulting offspring had pink petals.  Another exception is co-dominance, where both alleles are active and both traits are expressed at the same time; for example, both red and white petals in the same bloom or red and white flowers on the same plant. Codominance is also apparent in human blood types. A person with one "A" blood type allele and one "B" blood type allele would have a blood type of "AB".
A wild type allele is an allele which is considered to be "normal" for the organism in question, as opposed to a mutant allele which is usually a relatively new modification.
(Note that with the advent of neutral genetic markers, the term 'allele' is now often used to refer to DNA sequence variants in non-functional, or junk DNA. For example, allele frequency tables are often presented for genetic markers, such as the DYS markers.) Also there are many different types of alleles.

# Equations
There are two equations for the frequency of two alleles of a given gene (see Hardy-Weinberg principle).
Equation 1: p+q=1,
Equation 2: p^2+2pq+q^2=1
where p is the frequency of one allele and q is the frequency of the other allele.  Under appropriate conditions, subject to numerous limitations regarding the applicability of the Hardy-Weinberg principle, p^2 is the population fraction that is homozygous for the p allele, 2pq is the frequency of heterozygotes and q^2 is the population fraction that is homozygous for the q allele.
Natural selection can act on p and q in Equation 1, and obviously affect the frequency of alleles seen in Equation 2.
Equation 2 is a consequence of Equation 1, obtained by squaring both sides and applying the binomial theorem to the left-hand side.
Conversely, p^2+2pq+q^2=1 implies p+q=1 since p and q are positive numbers.
The following equation (commonly termed the Lee equation) can be used to calculate the number of possible genotypes in a diploid organism for a specific gene with a given number of alleles.
G=(a^2+a)/2
where a is the number of different alleles for the gene being dealt with and G is the number of possible genotypes. 
For example, the human ABO blood group gene has three alleles; A (for blood group A), B (for blood group B) and i (for blood group O). As such, (using the equation) the number of possible genotypes a human may have with respect to the ABO gene are 6 (AA, Ai, AB, BB, Bi, ii). The equation does not specify the number of possible phenotypes, however. Such an equation would be quite impossible as the number of possible phenotypes varies amongst different genes and their alleles. For example, in a diploid heterozygote some genotypes may show complete dominance, incomplete dominance etc., depending of the gene involved.

# Types
There are 4 different types of alleles.  Dominant, recessive, codominant, and incomplete dominant.  Depending on the inheritance of two alleles, a person may therefore end up having a dominant, recessive, codominant, or incomplete dominant trait.  In a single-gene trait, only two alleles determine the trait.  In a polygenic trait, more than two alleles control the trait.
An example of a dominant and a recessive trait is the (dis)possession of a widow's peak.  Those who have a widow's peak are dominant and those who do not have one are recessive.
An example of a codominant trait occurs in certain types of calves (cow's young).  Some calves are known as "blue roans" for their appearance of both blue and grey hairs.
An example of an incomplete dominant trait occurs in a pink 4-o'clock flower.  When a red flower (dominant) and a white flower (recessive) are crossed , those flowers with a heterozygous genotype for color are pink, showing the incomplete dominance of the red allele.
An example of multiple alleles is blood type. There are three alleles for blood type, A, B, and O. Because of this, people can have blood type A, B, AB, or O. AA or AO results in type A, BB or BO in type B, AB results in AB, and OO results in type O.

# Genetic Disorders
Genetic disorders are normally caused by the acquisition of two recessive alleles for a single-gene trait. Genetic disorders such as these include Albinism, Cystic Fibrosis, Galactosemia, Phenylketonuria (PKU), and Tay-Sachs Disease. In these cases the two alleles are autosomal (not sex chromosomes). Other disorders are recessive, but because they are located on the X chromosomes (of which men have only one copy), they are much more frequent in men than in women. One example of such a disorder is the Fragile X syndrome.
Some other disorders, such as Huntington's disease, are caused by the presence of a dominant allele.