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Nomonyx24.07.2012 03:23

Rajini Sharma

Epistasis

6.97

Mathematically, the epistasis of the pairwise interaction can be expressed by a matrix . Each entry in the matrix represents the deviation of the phenotype (measured as the difference in length of the first branch from the second one, divided by the sum of the two lengths) from the genotype (1 or 0 for the homozygous and heterozygous allele, respectively). Thus, the phenotypic effect of one allele may be modulated by the genotype of the other allele. The epistasis is the difference between the heterozygote's phenotype and the homozygote's phenotype.

Epistasis has been defined by the matrix . In this matrix , each entry represents the deviation of the phenotype from the genotype, where the genotype is set to zero for the homozygous allele. The epistasis is the difference between the homozygote's phenotype and the heterozygote's phenotype.

For example, the epistasis is −0.03 between allele 1 and allele 3. The matrix is

where

The matrix can be generalized to a larger matrix by using the indices of the large matrix (2, 3, 4,...)

Symmetry and group permutation

Symmetries in genetics are analogous to the symmetries of physics. For example, imagine taking an individual and flipping it about a vertical axis, then reflecting it about a horizontal axis, and then rotating it through 90°, and finally taking it back to its original position. In physics, this would be the same as running the experiment from the other side. In genetics, the same effect would be accomplished by permuting the alleles of a pairwise interaction.

Permuting the alleles of the pairwise interaction modifies the epistasis of the interaction but not the phenotype. Consider an example with only three alleles and a pairwise interaction:

The first experiment would result in the phenotype (length) of the pair:

The second experiment would result in the phenotype:

The third experiment would result in the phenotype (length):

Permuting the alleles results in the following pairwise interactions:

The third experiment, in which alleles 1 and 3 have been permuted, results in a phenotype identical to that of the 0b46394aab

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