2 Linkage Disequilibrium
41
that recombination occurred between them. When there is recombination, the gene
genealogies are no longer the same. Recombination has the effect of breaking the
gene genealogy of one of the loci and attaching somewhere else on the genealogy
of the other locus. When that occurs, the relationship between D or D and the
recombination rate is no longer simple, and the genealogical approach does not in
general lead to tractable analytic results. The similarity of the genealogies at the
two loci will be determined, in part, by the recombination rate between the two loci.
Loci separated by smaller genetic distances will have genealogies that are more
correlated with one another than loci which are farther apart.
2.8
Natural Selection and LD
If the genotypes at two linked loci affect survival and reproduction, the resulting
natural selection can increase the extent of linkage disequilibrium under some
conditions and even maintain permanent disequilibrium in the face of recombination
(Lewontin and Kojima 1960; Felsenstein 1965; Karlin and Feldman 1970). The
effect of selection on LD is weak, however, because it depends not on the selection
coefficients themselves but on the degree of epistasis, which is necessarily smaller.
To illustrate in a simple context, assume there is haploid selection on two linked
biallelic loci (A/a and B/b). Let the relative fitnesses of the four haplotypes
be w AB , w Ab , w aB , and w ab . Selection of this type will tend to increase D if
R = (w AB w ab )/(w Ab w aB ) > 1 (Felsenstein 1965). In other words, R is greater than
1 when the increase in fitness from having A and B together (w AB /w ab ) exceeds the
product of the gains from having A or B separately (w Ab /w ab and w aB /w ab ).
For diploid populations, more complicated but similar conditions have been
derived that show when selection can overcome the effects of recombination
and random mating and maintain permanent LD. Roughly speaking, permanent
LD can be maintained under restrictive conditions, namely, that there has to be
overdominance in fitness at each locus and c has to be less than a quantity that
summarizes the extent of epistasis in fitness (Karlin and Feldman 1970). It is
currently unclear whether epistasis in fitness among closely linked loci contributes
to observable patterns of LD.
2.9
Genetic Hitchhiking
Natural selection at a locus affects the frequencies of neutral alleles closely linked
to it, a process termed “genetic hitchhiking.” (Maynard Smith and Haigh 1974) The
idea is simple. As described above, when a new mutant arises, it is in complete
LD (D = 1) with alleles at linked polymorphic loci. If that mutant increases
rapidly in frequency because it confers a selective advantage to carriers, then neutral
alleles on the same chromosome will increase in frequency also. For example, if
B arises on an A-bearing chromosome and subsequently increases in frequency, A
also will increase in frequency. The result will be an excess of AB chromosomes.
41
that recombination occurred between them. When there is recombination, the gene
genealogies are no longer the same. Recombination has the effect of breaking the
gene genealogy of one of the loci and attaching somewhere else on the genealogy
of the other locus. When that occurs, the relationship between D or D and the
recombination rate is no longer simple, and the genealogical approach does not in
general lead to tractable analytic results. The similarity of the genealogies at the
two loci will be determined, in part, by the recombination rate between the two loci.
Loci separated by smaller genetic distances will have genealogies that are more
correlated with one another than loci which are farther apart.
2.8
Natural Selection and LD
If the genotypes at two linked loci affect survival and reproduction, the resulting
natural selection can increase the extent of linkage disequilibrium under some
conditions and even maintain permanent disequilibrium in the face of recombination
(Lewontin and Kojima 1960; Felsenstein 1965; Karlin and Feldman 1970). The
effect of selection on LD is weak, however, because it depends not on the selection
coefficients themselves but on the degree of epistasis, which is necessarily smaller.
To illustrate in a simple context, assume there is haploid selection on two linked
biallelic loci (A/a and B/b). Let the relative fitnesses of the four haplotypes
be w AB , w Ab , w aB , and w ab . Selection of this type will tend to increase D if
R = (w AB w ab )/(w Ab w aB ) > 1 (Felsenstein 1965). In other words, R is greater than
1 when the increase in fitness from having A and B together (w AB /w ab ) exceeds the
product of the gains from having A or B separately (w Ab /w ab and w aB /w ab ).
For diploid populations, more complicated but similar conditions have been
derived that show when selection can overcome the effects of recombination
and random mating and maintain permanent LD. Roughly speaking, permanent
LD can be maintained under restrictive conditions, namely, that there has to be
overdominance in fitness at each locus and c has to be less than a quantity that
summarizes the extent of epistasis in fitness (Karlin and Feldman 1970). It is
currently unclear whether epistasis in fitness among closely linked loci contributes
to observable patterns of LD.
2.9
Genetic Hitchhiking
Natural selection at a locus affects the frequencies of neutral alleles closely linked
to it, a process termed “genetic hitchhiking.” (Maynard Smith and Haigh 1974) The
idea is simple. As described above, when a new mutant arises, it is in complete
LD (D = 1) with alleles at linked polymorphic loci. If that mutant increases
rapidly in frequency because it confers a selective advantage to carriers, then neutral
alleles on the same chromosome will increase in frequency also. For example, if
B arises on an A-bearing chromosome and subsequently increases in frequency, A
also will increase in frequency. The result will be an excess of AB chromosomes.