2 Linkage Disequilibrium
43
are discussed in greater detail in Chap. 5. Because a GWAS is designed to detect
significant LD between alleles that cause a complex disease and SNP markers, the
two-locus Wahlund effect can create a spurious signal of association if individuals
from different subpopulations are mixed together in the cases and controls. The
term “population stratification” is used in this context. It is difficult to completely
eliminate the effects of population stratification even if care is taken not to combine
individuals from different ethnic groups. The problem is that the actual extent of
variation among subpopulations in the frequencies of causative alleles is unknown,
and hence, it is not clear how narrowly defined a subpopulation has to be in order
to eliminate the effect of population stratification. For example, in carrying out
a GWAS in people of European ancestry, is it appropriate to include people of
both northern and southern European ancestry in the same study or not? Including
both would increase the sample size and hence increase the statistical power to
detect significant associations but at the risk of inducing spurious false-positive
associations. This trade-off is especially problematic for rarer complex diseases for
which the total number of affected individuals might be small. One resolution of
the problem is to allow for some population stratification by using overall genomic
averages of LD, called “genomic controls,” to infer the overall extent of LD created
by subtle population stratification (Devlin et al. 2001).
Gene flow among populations that have diverged can maintain LD in each
subpopulation separately. When there is gene flow, the organisms themselves do the
mixing and create LD between all pairs of loci that differ in allele frequency among
the subpopulations. Mathematical analysis shows that substantial LD between
closely linked loci can be maintained by this mechanism (Mitton et al. 1973; Nei
and Li 1973).
2.11 Conclusion
When the term linkage disequilibrium was introduced by Lewontin and Kojima
(Lewontin and Kojima 1960) in 1960, it was in the context of an abstract mathematical model developed to understand the combined effects of natural selection
and recombination in an infinitely large population at equilibrium. Extensive further
mathematical studies of LD were carried out in the 1960s and 1970s, but there was
almost no attempt to relate the theory to data because almost no information about
closely linked loci was available. This was the era during which genetic variation
was studied by detecting differences in electrophoretic mobility of proteins (Hubby
and Lewontin 1966). Polymorphic protein-coding loci that could be studied with
electrophoresis were not usually closely enough linked for LD to be detectable.
Linkage disequilibrium remained a somewhat arcane and mathematically difficult
part of population genetics, known and appreciated by only a few specialists.
That situation changed with the development of direct means of assessing
polymorphisms at the DNA sequence level—first restriction fragment length polymorphisms (RFLPs), then microsatellite loci, and finally SNPs. Instead of being
obscure, linkage disequilibrium became well-known, then fashionable, and finally
43
are discussed in greater detail in Chap. 5. Because a GWAS is designed to detect
significant LD between alleles that cause a complex disease and SNP markers, the
two-locus Wahlund effect can create a spurious signal of association if individuals
from different subpopulations are mixed together in the cases and controls. The
term “population stratification” is used in this context. It is difficult to completely
eliminate the effects of population stratification even if care is taken not to combine
individuals from different ethnic groups. The problem is that the actual extent of
variation among subpopulations in the frequencies of causative alleles is unknown,
and hence, it is not clear how narrowly defined a subpopulation has to be in order
to eliminate the effect of population stratification. For example, in carrying out
a GWAS in people of European ancestry, is it appropriate to include people of
both northern and southern European ancestry in the same study or not? Including
both would increase the sample size and hence increase the statistical power to
detect significant associations but at the risk of inducing spurious false-positive
associations. This trade-off is especially problematic for rarer complex diseases for
which the total number of affected individuals might be small. One resolution of
the problem is to allow for some population stratification by using overall genomic
averages of LD, called “genomic controls,” to infer the overall extent of LD created
by subtle population stratification (Devlin et al. 2001).
Gene flow among populations that have diverged can maintain LD in each
subpopulation separately. When there is gene flow, the organisms themselves do the
mixing and create LD between all pairs of loci that differ in allele frequency among
the subpopulations. Mathematical analysis shows that substantial LD between
closely linked loci can be maintained by this mechanism (Mitton et al. 1973; Nei
and Li 1973).
2.11 Conclusion
When the term linkage disequilibrium was introduced by Lewontin and Kojima
(Lewontin and Kojima 1960) in 1960, it was in the context of an abstract mathematical model developed to understand the combined effects of natural selection
and recombination in an infinitely large population at equilibrium. Extensive further
mathematical studies of LD were carried out in the 1960s and 1970s, but there was
almost no attempt to relate the theory to data because almost no information about
closely linked loci was available. This was the era during which genetic variation
was studied by detecting differences in electrophoretic mobility of proteins (Hubby
and Lewontin 1966). Polymorphic protein-coding loci that could be studied with
electrophoresis were not usually closely enough linked for LD to be detectable.
Linkage disequilibrium remained a somewhat arcane and mathematically difficult
part of population genetics, known and appreciated by only a few specialists.
That situation changed with the development of direct means of assessing
polymorphisms at the DNA sequence level—first restriction fragment length polymorphisms (RFLPs), then microsatellite loci, and finally SNPs. Instead of being
obscure, linkage disequilibrium became well-known, then fashionable, and finally