Evolution__3rd_Edition

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Adaptive topographies can be used
to think about abstract evolutionary
questions
Figure 8.8
Fitness surface for two loci.
(a) A combination of the
patterns in Figures 8.7a and
b: there is a heterozygous
advantage at locus A and one
allele has a higher fitness
than the other at locus B.
(b) A two-locus fitness surface
with two peaks.
CHAPTER 8 / Two-locus and Multilocus Population Genetics 215
fitness is highest at the equilibrium gene frequency given by the standard equation
(Section 5.12.1, p. 123). Mean fitness declines either side of the equilibrium gene frequency,
where more of the unfavorable homozygotes will be dying each generation
than at the equilibrium (Figure 8.7b). The graph is also called a fitness surface.
In these two cases, natural selection carries the population to the gene frequency
where mean fitness is at a maximum. With one favorable allele, the maximum mean
fitness is where the allele is fixed a and natural selection will act to fix the allele. With
heterozygous advantage, the maximum mean fitness is where the smallest number of
homozygotes are dying each generation a and natural selection drives the population
to an equilibrium where the amount of homozygote death is minimized.
A question of interest in theoretical population genetics is whether natural selection
always drives the population to the state at which the mean fitness is the maximum
possible. Frequency-dependent selection (Section 5.13, p. 127) is a case in which natural
selection may not act to maximize mean fitness. When a polymorphism is maintained
by frequency-dependent selection, the fitness of each genotype is highest when it is
rare. But when a genotype is rare, natural selection acts to increase its frequency,
making it less rare. The effect of selection can then be to reduce mean fitness.
If natural selection does not always maximize mean fitness, that opens up a further a
and still unanswered a theoretical question of whether natural selection does act to
maximize some other function, but we shall not pursue that question here. Whatever
the answer to it, natural selection does still maximize simple mean fitness in many
cases. For many purposes, we can safely think of natural selection as a hill-climbing
process, by analogy with the hills in the adaptive topography (Figure 8.7).
Now consider a second locus. Selection can be going on here too, and the fitness
surface for the two loci might look like Figure 8.8. Figure 8.8a shows a simple case in
which one locus has heterozygous advantage and the other has a single favored allele.
The idea of an adaptive topography can be extended to as many loci as interact to determine
an organism’s fitness, but further loci have to be imagined, rather than drawn, on
two-dimensional paper.
Mean fitness
(a) (b)
0 10 1
allele of Frequency
Frequency of A allele
B Mean fitness
0 1 0
1
allele of Frequency
Frequency of A allele
B