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An allele is any one of a number of viable DNA codings of the same gene (sometimes the term refers to a non-gene sequence) occupying a given locus (position) on a chromosome. An individual's genotype for that gene will be the set of alleles it happens to possess. In an organism which has two copies of each of its chromosomes (a diploid organism), two alleles make up the individual's genotype.
An example is the gene for blossom color in many species of flower -- a single gene controls the color of the petals, but there may be several different versions of the gene. One version might result in red petals, while another might result in white petals. The color of an individual flower will depend on which two alleles it possesses for this color gene, and how the two interact.
Organisms that are diploid such as 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 said to be homozygous for that gene. An organism which has two different alleles of the gene is said to be 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 only 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".
(Note that with the advent of the study of genetic markers, the term allele is often now used to refer to DNA codings in junk DNA. For example, the term allele frequency tables are often presented for genetic markers, such as the DYS markers.)
There are two simple equations for the frequency of two alleles of a given gene (see Hardy-Weinberg principle):
Equation 1:$ p^2+2pq+q^2=1 $
Equation 2: $ p+q=1 $
Where p is the frequency of one allele and q is the frequency of the other allele. p2 is the population fraction that is homozygous for the p allele, 2pq is the frequency of heterozygotes and q2 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. It should be noted that the second equation can be derived from the first (or vice versa) since $ p^2+2pq+q^2=1 $ implies $ (p+q)^2=1 $ and p and q are positive numbers.
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