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Equations

Equations

There are two equations for the frequency of two alleles of a given gene (see Hardy-Weinberg principle):

  • p+q=1, \,
  • 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, 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 genotypes 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, p2 + 2pq + q2 = 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= \frac{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 O (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, AO, AB, BB, BO, OO). 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 traits may show complete dominance, incomplete dominance etc., depending of the gene involved. Genetic disorders

Genetic disorders are normally caused if an individual carries two alleles associated with a recessive, 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 also 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 dominant and it is sufficient to carry only one allele associated with the disorder to be affected.

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