Linkage Disequilibrium - Definition

Definition

Consider the haplotypes for two loci A and B with two alleles each—a two-locus, two-allele model. Then the following table defines the frequencies of each combination:

Note that these are relative frequencies. One can use the above frequencies to determine the frequency of each of the alleles:

If the two loci and the alleles are independent from each other, then one can express the observation as " is found and is found". The table above lists the frequencies for, and for, hence the frequency of is, and according to the rules of elementary statistics .

The deviation of the observed frequency of a haplotype from the expected is a quantity called the linkage disequilibrium and is commonly denoted by a capital D:

In the genetic literature the phrase "two alleles are in LD" usually means that D ≠ 0. Contrariwise, "linkage equilibrium" means D = 0.

The following table illustrates the relationship between the haplotype frequencies and allele frequencies and D.

is easy to calculate with, but has the disadvantage of depending on the frequencies of the alleles. This is evident since frequencies are between 0 and 1. If any locus has an allele frequency 0 or 1 no disequilibrium can be observed. When the allelic frequencies are 0.5, the disequilibrium is maximal. Lewontin suggested normalising D by dividing it by the theoretical maximum for the observed allele frequencies.

Thus:

where

Another measure of LD which is an alternative to is the correlation coefficient between pairs of loci, expressed as

.

This is also adjusted to the loci having different allele frequencies.

In summary, linkage disequilibrium reflects the difference between the expected haplotype frequencies under the assumption of independence, and observed haplotype frequencies. A value of 0 for indicates that the examined loci are in fact independent of one another, while a value of 1 demonstrates complete dependency.