Linkage disequilibrium

In population genetics, linkage disequilibrium is the non-random association of alleles at different loci in a given population. Loci are said to be in linkage disequilibrium when the frequency of association of their different alleles is higher or lower than what would be expected if the loci were independent and associated randomly. In population genetics, linkage disequilibrium is the non-random association of alleles at different loci in a given population. Loci are said to be in linkage disequilibrium when the frequency of association of their different alleles is higher or lower than what would be expected if the loci were independent and associated randomly. Linkage disequilibrium is influenced by many factors, including selection, the rate of genetic recombination, mutation rate, genetic drift, the system of mating, population structure, and genetic linkage. As a result, the pattern of linkage disequilibrium in a genome is a powerful signal of the population genetic processes that are structuring it. In spite of its name, linkage disequilibrium may exist between alleles at different loci without any genetic linkage between them and independently of whether or not allele frequencies are in equilibrium (not changing with time). Furthermore, linkage disequilibrium is sometimes referred to as gametic phase disequilibrium; however, the concept also applies to asexual organisms and therefore does not depend on the presence of gametes. Suppose that among the gametes that are formed in a sexually reproducing population, allele A occurs with frequency p A {displaystyle p_{A}} at one locus (i.e. p A {displaystyle p_{A}} is the proportion of gametes with A at that locus), while at a different locus allele B occurs with frequency p B {displaystyle p_{B}} . Similarly, let p A B {displaystyle p_{AB}} be the frequency with which both A and B occur together in the same gamete (i.e. p A B {displaystyle p_{AB}} is the frequency of the AB haplotype). The association between the alleles A and B can be regarded as completely random—which is known in statistics as independence—when the occurrence of one does not affect the occurrence of the other, in which case the probability that both A and B occur together is given by the product p A p B {displaystyle p_{A}p_{B}} of the probabilities. There is said to be a linkage disequilibrium between the two alleles whenever p A B {displaystyle p_{AB}} differs from p A p B {displaystyle p_{A}p_{B}} for any reason. The level of linkage disequilibrium between A and B can be quantified by the coefficient of linkage disequilibrium D A B {displaystyle D_{AB}} , which is defined as provided that both p A {displaystyle p_{A}} and p B {displaystyle p_{B}} are greater than zero.Linkage disequilibrium corresponds to D A B ≠ 0 {displaystyle D_{AB} eq 0} . In the case D A B = 0 {displaystyle D_{AB}=0} we have p A B = p A p B {displaystyle p_{AB}=p_{A}p_{B}} and the alleles A and B are said to be in linkage equilibrium. The subscript 'AB' on D A B {displaystyle D_{AB}} emphasizes that linkage disequilibrium is a property of the pair {A, B} of alleles and not of their respective loci. Other pairs of alleles at those same two loci may have different coefficients of linkage disequilibrium. Linkage disequilibrium in asexual populations can be defined in a similar way in terms of population allele frequencies. Furthermore, it is also possible to define linkage disequilibrium among three or more alleles, however these higher-order associations are not commonly used in practice. The coefficient of linkage disequilibrium D {displaystyle D} is not always a convenient measure of linkage disequilibrium because its range of possible values depends on the frequencies of the alleles it refers to. This makes it difficult to compare the level of linkage disequilibrium between different pairs of alleles.