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Evolution__3rd_Edition

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..<br />

Expected frequency ( piqi )<br />

(a)<br />

0.025<br />

0.020<br />

0.015<br />

0.010<br />

0.005<br />

0<br />

7<br />

44<br />

Linkage disequilibrium ( D )<br />

Figure 8.4<br />

(a) One example of the pattern of degrees of linkage<br />

disequilibrium (D) in the HLA: the linkage disequilibrium<br />

between 21 B alleles and the A 1 allele. An analogous graph can<br />

be drawn for every A allele. The A 1 B 8 haplotype occurs at a<br />

much higher than random frequency (note the gap in the<br />

x-axis). The y-axis is the expected frequency of the haplotype<br />

if the alleles were associated at random. Thus the observed<br />

Linkage disequilibrium can be<br />

caused by selection ...<br />

. . . and by linkage, ...<br />

. . . randon drift ...<br />

15<br />

40<br />

35<br />

5<br />

27<br />

CHAPTER 8 / Two-locus and Multilocus Population Genetics 205<br />

8<br />

13 X<br />

0.02<br />

14<br />

22 21<br />

39<br />

0<br />

–0.015 –0.010 –0.005 0 0.005 0.010 0.070 0 1,000 2,000 3,000<br />

38<br />

45 41<br />

18<br />

17<br />

47 37<br />

Linkage disequilibriun<br />

0.08<br />

0.06<br />

0.04<br />

(b)<br />

Distance between loci (kilobases)<br />

frequency of a haplotype is the y-axis value plus (or minus) its<br />

x-axis value. (b) The linkage disequilibrium between eight HLA<br />

loci: more closely linked loci show higher linkage disequilibrium;<br />

the y-axis is a kind of average linkage disequilibrium for the<br />

multiple alleles (see Hedrick et al. (1991) for the exact<br />

measure). Figure 8.3 is a map of the loci, and compare with<br />

Figure 8.2 for the effect of recombination. Redrawn, by<br />

permission of the publisher, from Hedrick et al. (1991).<br />

causing the linkage disequilibrium? In Papilio and in at least some of the HLA associations,<br />

it is probably due to selection. If selection favors individuals with particular<br />

combinations of alleles, then it produces linkage disequilibrium. But selection is not<br />

the only possible cause for linkage disequilibrium, and a full study of a real case must<br />

examine three other factors.<br />

The first factor is linkage. For linked loci, a number of generations are required for<br />

recombination to do its randomizing work (see Figure 8.2). Loosely linked loci will not<br />

show linkage disequilibrium for long. However, as the rate of recombination between<br />

two loci decreases the amount of time that alleles can be non-randomaly associated<br />

between them goes up. This may be one reason why, in the human HLA system, the<br />

average linkage disequilibrium is larger between more closely linked loci (Figure 8.4b).<br />

For tightly linked loci, some linkage disequilibrium can persist indefinitely.<br />

A second factor that can cause linkage disequilibrium is random drift. Random processes<br />

have the interesting property of being able to cause persistent, not just transitory,<br />

linkage disequilibrium. If random sampling produces by chance an excess of a haplotype<br />

in a generation, linkage disequilibrium will have arisen. This is true for all four<br />

haplotypes: random sampling that produces an excess of any of them will disturb the<br />

state of linkage equilibrium. Any haplotype could be “favored” by chance, so the disequilibrium<br />

is equally likely to have D > 0 or D < 0. As a population approaches linkage<br />

equilibrium, all random fluctuations in haplotype frequencies will tend to be away<br />

from the linkage equilibrium values. If a population is well away from the point of

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