Evolution__3rd_Edition

..
Expected frequency ( piqi )
(a)
0.025
0.020
0.015
0.010
0.005
0
7
44
Linkage disequilibrium ( D )
Figure 8.4
(a) One example of the pattern of degrees of linkage
disequilibrium (D) in the HLA: the linkage disequilibrium
between 21 B alleles and the A 1 allele. An analogous graph can
be drawn for every A allele. The A 1 B 8 haplotype occurs at a
much higher than random frequency (note the gap in the
x-axis). The y-axis is the expected frequency of the haplotype
if the alleles were associated at random. Thus the observed
Linkage disequilibrium can be
caused by selection ...
. . . and by linkage, ...
. . . randon drift ...
15
40
35
5
27
CHAPTER 8 / Two-locus and Multilocus Population Genetics 205
8
13 X
0.02
14
22 21
39
0
–0.015 –0.010 –0.005 0 0.005 0.010 0.070 0 1,000 2,000 3,000
38
45 41
18
17
47 37
Linkage disequilibriun
0.08
0.06
0.04
(b)
Distance between loci (kilobases)
frequency of a haplotype is the y-axis value plus (or minus) its
x-axis value. (b) The linkage disequilibrium between eight HLA
loci: more closely linked loci show higher linkage disequilibrium;
the y-axis is a kind of average linkage disequilibrium for the
multiple alleles (see Hedrick et al. (1991) for the exact
measure). Figure 8.3 is a map of the loci, and compare with
Figure 8.2 for the effect of recombination. Redrawn, by
permission of the publisher, from Hedrick et al. (1991).
causing the linkage disequilibrium? In Papilio and in at least some of the HLA associations,
it is probably due to selection. If selection favors individuals with particular
combinations of alleles, then it produces linkage disequilibrium. But selection is not
the only possible cause for linkage disequilibrium, and a full study of a real case must
examine three other factors.
The first factor is linkage. For linked loci, a number of generations are required for
recombination to do its randomizing work (see Figure 8.2). Loosely linked loci will not
show linkage disequilibrium for long. However, as the rate of recombination between
two loci decreases the amount of time that alleles can be non-randomaly associated
between them goes up. This may be one reason why, in the human HLA system, the
average linkage disequilibrium is larger between more closely linked loci (Figure 8.4b).
For tightly linked loci, some linkage disequilibrium can persist indefinitely.
A second factor that can cause linkage disequilibrium is random drift. Random processes
have the interesting property of being able to cause persistent, not just transitory,
linkage disequilibrium. If random sampling produces by chance an excess of a haplotype
in a generation, linkage disequilibrium will have arisen. This is true for all four
haplotypes: random sampling that produces an excess of any of them will disturb the
state of linkage equilibrium. Any haplotype could be “favored” by chance, so the disequilibrium
is equally likely to have D > 0 or D < 0. As a population approaches linkage
equilibrium, all random fluctuations in haplotype frequencies will tend to be away
from the linkage equilibrium values. If a population is well away from the point of