Evolution, 4th Edition

Futuyma Kirkpatrick Evolution, 4e

Sinauer Associates

Troutt Visual Services

Evolution4e_05.19.ai Date 12-13-2016

20 40 60 80 100

0.2

0.4

0.6

0.8

1.0

0

Generation

Frequency of

A

2

(A) Positive

w 11 w 12 w 22

Fitness

20 40 60 80 100

0.2

0.4

0.6

0.8

1.0

0

Generation

Frequency of

A

2

(B) Overdominance

w 11 w 12 w 22

Fitness

20 40 60 80 100

0.2

0.4

0.6

0.8

1.0

0

Generation

Frequency of

A

2

(C) Underdominance

w 11 w 12 w 22

Fitness

FIGURE 5.19 Allele frequency trajectories under

three kinds of selection. In each case, trajectories

are shown for three different starting frequencies

of the A 2 allele. (A) Positive selection favors allele

A 2 , which spreads to fixation from any starting

frequency. In this example, A 2 increases fitness by

s = 0.05, and the relative fitnesses are w 11 = 1,

w 12 = 1.05, and w 22 = 1.1. (B) With overdominance,

the A 1 A 2 heterozygote has highest fitness. Starting

at any allele frequency, A 2 evolves to a polymor-

phic equilibrium. Selection preserves genetic

variation. In this example, the relative fitnesses

are w 11 = 0.9, w 12 = 1, and w 22 = 0.8, and the final

frequency of allele A 2 is 0.33 (dashed line). (C) With

underdominance, the A 1 A 2 heterozygote has the

lowest fitness. Populations evolve to different final

allele frequencies depending on where they start.

In this example, the relative fitnesses are w 11 = 1.1,

w 12 = 1, and w 22 = 1.2. If allele A 2 starts at a fre-

quency below 0.33 (dashed line), it is lost, but if it

starts above that frequency it spreads to fixation.

to use the heterozygote as the fitness reference. Estimates for the relative survival

of the three genotypes in Nigeria (a country in equatorial West Africa) are:

Genotype AA AS SS

Relative survival 0.88 1 0.14

Although these data are now 40 years old, recent research shows that malaria con-

tinues to cause strong selection on the β-hemoglobin locus [14].

This is the most famous example of overdominance, which occurs when the

heterozygote has higher fitness than both homozygotes. (Another example comes

from the Soay sheep discussed earlier; see Figure 5.13.) Overdominance leads to

a kind of evolutionary outcome that we have not yet discussed. The population

evolves to a stable polymorphic equilibrium, which means that both alleles are

maintained. Given the relative fitnesses of the AA and SS homozygotes (and again

using the AS heterozygote as the fitness reference), a mathematical model like that

in Box 5A tells us that any population that has genetic variation will evolve to the

same final allele frequency (FIGURE 5.19). Ultimately the population reaches an

equilibrium at which the frequency of the S allele is

(5.7)

This formula holds for any values of wAA and wSS that lie between 0 and 1.

p

1 – wAA

ˆ=

2 – wAA – wSS

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