Evolution__3rd_Edition

..
. . . which can sometimes be used
to estimate the mutation rate
In some cases, heterozygotes have
higher fitness than homozygotes
CHAPTER 5 / The Theory of Natural Selection 123
p = N/2, m = sN/2. If the mutation is highly deleterious, s ≈ 1 and m = N/2. The mutation
rate can be estimated as half the birth rate of the mutant type. The estimate is clearly
approximate, because it relies on a number of assumptions. In addition to the assumptions
of high s and low p, mating is supposed to be random. We usually have no means
of checking whether it is.
Chondrosdystrophic dwarfism is a dominant deleterious mutation in humans. In
one study, 10 births out of 94,075 had the gene, a frequency of 10.6 × 10 −5 . The estimate
of the mutation rate by the above method is then m = 5.3 × 10 −5 . However, it is possible
to estimate the selection coefficient, enabling a more accurate estimate of the mutation
rate. In another study, 108 chondrodystrophic dwarves produced 27 children; their
457 normal siblings produced 582 children. The relative fitness of the dwarves was
(27/108)/(582/457) = 0.196; the selection coefficient s = 0.804. Instead of assuming
s = 1, we can use s = 0.804. Then the mutation rate is sN/2 = 4.3 × 10 −5 , a rather lower
figure because with lower selection the same gene frequency can be maintained by a
lower mutation rate.
For many genes, we do not know the dominance relations of the alleles at the locus. A
similar calculation can be done for a recessive gene, but the formula is different, and it
differs again if the mutation has intermediate dominance. We can only estimate the
mutation rate from p = m/s if we know the mutation is dominant. The method is therefore
unreliable unless its assumptions have been independently verified. However, the
general idea of this section a that a balance between selection and mutation can exist
and explain genetic variation a will be used in later chapters.
5.12 Heterozygous advantage
5.12.1 Selection can maintain a polymorphism when the heterozygote
is fitter than either homozygote
We come now to an influential theory. We are going to consider the case in which the
heterozygote is fitter than both homozygotes. The fitnesses can be written:
Genotype AA Aa aa
Fitness 1 − s 1 1 − t
t, like s, is a selection coefficient and has a value between 0 and 1. What happens here?
There are three possible equilibria, but two of them are trivial. p = 1 and p = 0 are stable
equilibria, but only because there is no mutation in the model. The third equilibrium is
the interesting one; it has both genes present, and we can calculate the equilibrial gene
frequencies by a similar argument to the one outlined in the previous section. The
condition in which a population contains more than one gene is called polymorphism.
A genes and a genes are both removed by selection. The A genes are removed because
they appear in the inferior AA homozygotes and the a genes because they appear in
aa homozygotes. At the equilibrium, both genes must have the same chance of being
removed by selection. If an A gene has a higher chance of being removed than an a gene,