Evolution__3rd_Edition

..
Other factors will be at work in real
examples
A disadvantageous mutation may
arise recurrently
evolution may happen that way. But things can be more complicated in nature. We
have considered selection in terms of different chances of survival from birth to adulthood;
but selection can also take place by differences in fertility, if individuals of different
genotypes a after they have survived to adulthood a produce different numbers of
offspring. The model had random mating among the genotypes: but mating may be
non-random. Moreover, the fitness of a genotype may vary in time and space, and
depend on what genotypes are present at other loci (a subject we shall deal with in
Chapter 8). Much of evolutionary change probably consists of adjustments in the
frequencies of alleles at polymorphic loci, as fitnesses fluctuate through time, rather
than the fixation of new favorable mutations.
These complexities in the real world are important, but they do not invalidate a or
trivialize a the one-locus model. For the model is intended as a model. It should be
used as an aid to understanding, not as a general theory of nature. In science, it is a good
strategy to build up an understanding of nature’s complexities by considering simple
cases first and then building on them to understand the complex whole. Simple ideas
rarely provide accurate, general theories; but they often provide powerful paradigms.
The one-locus model is concrete and easy to understand and it is a good starting point
for the science of population genetics. Indeed, population geneticists have constructed
models of all the complications listed in the previous paragraph, and those models are
all developments within the general method we have been studying.
5.11 A recurrent disadvantageous mutation will evolve
to a calculable equilibrial frequency
The model of selection at one locus revealed how a favorable mutation will spread through
a population. But what about unfavorable mutations? Natural selection will act to eliminate
any allele that decreases the fitness of its bearers, and the allele’s frequency will
decrease at a rate specified by the equations of Section 5.6; but what about a recurrent
disadvantageous mutation that keeps arising at a certain rate? Selection can never
finally eliminate the gene, because it will keep on reappearing by mutation. In this case,
we can work out the equilibrial frequency of the mutation: the equilibrium is between the
mutant gene’s creation, by recurrent mutation, and its elimination by natural selection.
To be specific, we can consider a single locus, at which there is initially one allele,
a. The gene has a tendency to mutate to a dominant allele, A. We must specify the
mutation rate and the selection coefficient (fitness) of the genotypes: define m as the
mutation rate from a to A per generation. We will ignore back mutation (though actually
this assumption does not matter). The frequency of a is q, and of A is p. Finally, we
define the fitnesses as follows:
Genotype aa Aa AA
Fitness 1 1 − s 1 − s
CHAPTER 5 / The Theory of Natural Selection 121
Evolution in this case will proceed to an equilibrial frequency of the gene A (we can
write the stable equilibrium frequency as p*). If the frequency of A is higher than the