Evolution, 4th Edition

86 CHAPTER 4

Hardy-Weinberg equilibrium, linkage equilibrium takes more than one generation

to reach. How long it takes depends on the rate of recombination between the loci.

Less recombination (smaller r) means the genes at a pair of loci mix more slowly, so

linkage equilibrium between them takes longer to reach.

We can be more specific about linkage disequilibrium by introducing a way to

measure it. Consider two loci, one with alleles A 1 and A 2 , the other with alleles B 1

and B 2. We will use PAB to represent the frequency of gametes carrying both the A 2

and the B 2 alleles, pA to represent the frequency of gametes with the A 2 allele (no

matter which B allele they have), and pB to represent the frequency of gametes with

the B 2 allele (no matter which A allele they have). The measure of linkage disequi-

librium is symbolized by D, and is defined as

D = PAB – pA pB (4.1)

(The term pA pB simply means pA times pB.) The population is in linkage equilib-

rium when D = 0. If alleles A 2 and B 2 appear together more often than expected

by chance, then D is positive. If A 2 and B 2 occur less often than expected, then D

is negative.

FIGURE 4.9 compares three populations of gametes. Although the allele frequen-

cies are the same in all three (pA = pB = 1/2), the populations clearly differ. The dif-

ferences reflect the effects of linkage disequilibrium. When D is positive, knowing

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Chromosome 1 Chromosome 2

r = 0.03

r = 0.4

r = 0.5

FIGURE 4.8 The recombination rates between three pairs of loci. A pair of loci that are

close together on the same chromosome have a low recombination rate (here, r = 0.03). A

pair that is far apart on the same chromosome has a high recombination rate that approach-

es 0.5 (here, r = 0.4). A pair of loci on different chromosomes has the maximum possible

recombination rate, r = 0.5.

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Note: I kept the coloring same as in gure 04.07

(A) D = 1/4 (B) D = –1/4 (C) D = 0

A 1 A 1 A 1 A 1 A 1 A 1

A 2 A 2 A 2 A 2 A 2 A 2 A 2 A 2 A 2 A 2 A 2 A 2

A 1 A 1 A 1 A 1

b

A 1 A 1

B 1 B 1 B 2

B 1 B 1 B 1 B 1 B 1 B 1

B 1 B 1 B 1 B 1 B 2 B 2 B 2 B 2

B 2 B 2 B 2 B 2 B 2 B 2

B 2

FIGURE 4.9 Three populations of eight gametes that have the same allele frequen-

cies (pA = pB = 1/2) but have different values of linkage disequilibrium. Linkage dis-

equilibrium is defined the same way regardless of whether the two loci are on the

same chromosome or on different chromosomes. (A) When the disequilibrium, D,

between alleles A 2 and B 2 is positive, those alleles are found together more often than

if they were associated at random. When D is at its maximum possible value (D = 1/4),

a gamete that carries allele A 2 always carries allele B 2. (B) When disequilibrium is at its

smallest possible value (D = –1/4), a gamete that carries allele A 2 always carries allele B 1.

(C) When a population is at linkage equilibrium (D = 0), there is no association between

alleles at the two loci. If a sperm carries allele A 2 , the chance that it also carries allele B 2

is simply the frequency of B 2 in the population.

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