THE GENETiCAl THEoRy of NATuRAl SElECTioN 111
genetic variation as measured by p(1 – p) equals 0. The opposite situation is when
variation is maximized, which happens when p = (1 – p) = 0.5 (FIGURE 5.8).
The key conclusion is this: the rate of evolution is proportional to the strength of
selection and the amount of genetic variation. In the absence of either of those two
ingredients, there is no evolution by selection.
Knowing Δp tells us what the population will look like in the next generation.
The frequency of A 2 in the next generation is equal to its current frequency plus
the evolutionary change. Using pʹ to represent the frequency of A 2 at the start of
generation 2,
pʹ = p + Δp (5.4)Now let’s look further into the future. We can take the frequency of A 2 at the
start of generation 2 and substitute that number for p on the right side of Equations
5.3 and 5.4 to find the allele frequency at the start of generation 3. Repeating that
process lets us trace the trajectories of the allele frequency through time (see Figure
5.7). The trajectories are S-shaped. They change slowly when p is near 0 or near 1,
and most rapidly when p is near 0.5. Although the strength of selection is constant,
the genetic variation is not: variation is small when either allele is rare, and large
when the alleles are about equally frequent (see Figure 5.8).
When a beneficial allele spreads by selection, the final outcome is that it
becomes fixed. That is, it reaches a frequency of 1, and the other allele is elimi-
nated. The conclusion is that positive selection ultimately eliminates genetic varia-
tion. That means other evolutionary factors must be responsible for maintaining all
the genetic variation that we see in nature. Mutation is one, and we will see shortly
that there are also others.
A beneficial allele spreads through a population more quickly if it is more
strongly selected. There is a simple rule of thumb that gives the time needed for an
allele to spread most of the way through the population when heterozygotes have
intermediate fitness. A beneficial allele will increase in frequency from 10 percent
to 90 percent in roughly 4/s generations (FIGURE 5.9). For example, if A 2 increasesFutuyma Kirkpatrick Evolution, 4e
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Evolution4e_05.08.ai Date 02-15-2017(A) p = 0.05 (B) p = 0.5 (C) p = 0.95A 1 A 1A 1 A 1A 1 A 1
A A^1 A^1
1 A 1A 1 A 1A 1 A 1
A 1 A 1A 1 A 1A 1 A 1A 1 A 1A 1 A 1A 1 A 1A 1 A 1A 1 A 1A 1 A 1
A 1 A 1
A 1 A 1A 1 A 1A 1 A 1A 1 A 1A 1 A 1A 1 A 1A 1 A 2A 1 A 2A 1 A 2A 1 A 2A 1 A 2A 1 A 2
A 1 A 2A 1 A 2A 1 A 2A 1 A 2
A 1 A 2A 1 A 2A 1 A 2A 1 A 2A 2 A 2
A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A 2A 2 A (^2) A
2 A 2
A 2 A (^2) A 2 A 2
A 2 A 2
A 2 A 2
FIGURE 5.8 The amount of genetic
variation at a locus depends on the allele
frequencies. Genetic variation is greatest
when allele frequencies are intermediate.
There is little variation when the fre-
quency p of allele A 2 is near 0 or near 1.
Variation is maximized when p = 0.5.
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