mUTATIon AnD VARIATIon 87
that a gamete carries allele A 2 tells us that it is more likely to carry allele B 2
than expected by chance. When D is negative, a gamete that carries allele A 2 is
less likely to carry allele B 2. Last, when a population is in linkage equilibrium
(D = 0), knowing that a gamete carries allele A 2 tells us nothing about which
allele it carries at locus B. Linkage disequilibrium is therefore a statistic that
measures a property of the population. It has the same meaning whether the
two loci are on the same chromosome or on different chromosomes.
The most important role that recombination plays in evolution is through its
effects on D. If Mendelian inheritance is the only factor at work, the value of D in
the next generation is decreased by a proportion r from its value in the current
generation. Thus recombination causes the population to evolve toward linkage
equilibrium with D = 0. It does so quickly if r is large (near 1/2) and slowly if r
is small (near 0). The evolution of D with three different values of r is shown in
FIGURE 4.10. On average, there is less recombination between pairs of DNA
bases on a chromosome when they are closer to each other than when pairs are
farther apart. For that reason, D tends to be higher between pairs that are closer
(FIGURE 4.11). In real populations, linkage equilibrium is never reached exactly
because other factors besides recombination are at work (though in many cases
D is very close to 0). Nevertheless, linkage equilibrium is a valuable reference
just as the Hardy-Weinberg equilibrium is: departures from D = 0 can be used
to detect those other factors.
Linkage disequilibrium can be produced by natural selection. Epistasis is the situ-
ation in which the effect of an allele at one locus depends on the allele at a second
locus. If some combinations of alleles have high fitness, selection will generate link-
age disequilibrium between them. The primrose (Primula vulgaris) has an interest-
ing mechanism to avoid fertilizing itself. Populations of this plant have mixtures of
individuals with flowers that have the “pin” and the “thrum” phenotypes (FIGURE
4.12). In pin plants, the anthers (which produce pollen) are low in the flower, while
the stigma (which receives pollen) is high. In thrum plants, this arrangement is
reversed. Because the anthers and style are separated in both pin and thrum plants,
pollen is rarely transferred between the anthers and stigma of the same flower. The
height of the anthers is determined by one locus, and the height of the stigma by
another. These loci are in linkage disequilibrium: the allele for low anthers is most
often with the allele for a high stigma, as is the allele for high anthers with the allele
for a low stigma. Plants with the “wrong” combination of alleles have a stigma and
anthers close to each other. They self-fertilize, which produces offspring that survive
poorly. Natural selection therefore maintains the linkage disequilibrium.
A second important cause of linkage disequilibrium is the mixing of popu-
lations that have different allele frequencies. This situation is conspicuous in
countries that have people with ancestries from different geographical regions.
For example, the shape of the eyes and the curliness of the hair are determined
by different loci. In places that have people of both Asian and African ancestry,
seeing the texture of a person’s hair tells you what the shape of their eyes is
likely to be.
Linkage disequilibrium is important because it affects how genes evolve.
In the next chapter we will see that selection on one locus can cause a secondFutuyma Kirkpatrick Evolution, 4e
Sinauer Associates
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Evolution4e_04.10.ai Date 11-03-2016 01-12-17Linkage disequilibrium,D0 2 4 6r = 0.5r = 0.1r = 0.018 10
Generation0.250.200.150.100.05FIGURE 4.10 Recombination causes link-
age disequilibrium to decrease. The value
of D declines toward 0 rapidly when the re-
combination rate is large (r = 0.5), and slowly
when it is small (r = 0.01).Futuyma Kirkpatrick Evolution, 4e
Sinauer Associates
Troutt Visual Services
Evolution4e_04.11.ai Date 11-03-2016 01-13-17Position (kb)0 A B C 500
Position (kb)0500BACFIGURE 4.11 Linkage disequilibrium tends to be higher between pairs of DNA
bases that are very close to each other on a chromosome. Shown is a region of 500
thousand base pairs (kb) of a chromosome sampled from 89 humans in eastern
Asia. The x-axis and y-axis are positions along the chromosome. Three sites on the
chromosome are labeled. Sites A and B are relatively close (50 kb), and they have
high linkage disequilibrium (indicated by red). Sites B and C are farther apart (250
kb), and they have low linkage disequilibrium (indicated by white). Based on [25a].04_EVOL4E_CH04.indd 87 3/23/17 8:55 AM