Evolution, 4th Edition

110 CHAPTER 5

is beneficial. Each copy of this allele that an individual carries increases fitness by

a fraction s. This means that A 1 A 2 heterozygotes have relative fitness w 12 = (1 + s).

The A 2 A 2 genotype has the highest fitness of all, and its fitness is increased by a

factor of (1 + 2s) relative to the A 1 A 1 homozygotes. In the mouse example of Figure

5.6, the selection coefficient favoring the A 2 allele is s = 0.5: each copy of that allele

increases survival by 50 percent. That is extremely strong selection compared with

what is seen in most natural populations, where fitness effects of alleles are typi-

cally many times smaller.

The number s is called the selection coefficient. It is a natural measure of

the strength of selection that favors the beneficial allele. For the moment we are

assuming selection coefficients are constant in time and that the heterozygote’s

fitness is intermediate between the two homozygotes, but we will see shortly what

happens when those assumptions are not met. Note that selection coefficients

depend on which genotype is chosen to be the fitness reference. In the current

situation, it is most convenient to use the A 1 A 1 homozygotes as the standard, but

later in this chapter we will use other genotypes as the reference.

The rate of adaptation

We can predict the course of evolution if we know the current state of the popula-

tion and the strength of selection. We will use p to represent the frequency of the

A 2 allele, and so the frequency of the A 1 allele is 1 – p. The evolutionary change per

generation is measured by the change in the frequency of A 2 from the beginning

of the current generation to the beginning of the next. Using Δp to represent that

change, Box 5A shows that

Δp ≈ s p (1 – p) (5.3)

(Equation 5.3 is an approximation that is accurate when s is less than 0.1, which is

the case for the large majority of alleles in natural populations. The exact version

of the equation is a bit more complicated; see Box 5A.)

Equation 5.3 is beautiful in its simplicity, and it carries important messages. On

the left side is Δp, which is the rate at which the allele frequency evolves. The right

side shows that the rate is the product of two quantities. The first is the selection

coefficient s, which measures the strength of selection. When s = 0, there is no

selection acting, Δp = 0, and there is no evolution. The second quantity on the right

side of Equation 5.3 is p(1 – p), which is a natural measure of genetic variation. If

A 2 is absent from the population then p = 0, while if A 1 is absent then (1 – p) = 0.

In either case, there is no genetic variation at this locus. Consistent with that fact,

Futuyma Kirkpatrick Evolution, 4e

Sinauer Associates

Troutt Visual Services

Evolution4e_05.07.ai Date 12-29-2016

100 200 300 400 500

s = 0.05

s = 0.02

0.2 s = 0.01

0.4

0.6

0.8

1.0

0

Generation

Frequency of

A

2

FIGURE 5.7 The spread of three

beneficial mutations that have different

selection coefficients, s. Stronger selec-

tion leads to faster evolution.

05_EVOL4E_CH05.indd 110 3/23/17 9:01 AM