Evolution__3rd_Edition

124 PART 2 / Evolutionary Genetics
We construct a model of gene
frequencies with heterozygous
advantage
Sickle cell anemia illustrates the
theory
the frequency of a is increasing, and vice versa. Only when the chance is the same for
both will the gene frequencies be stable.
What is the chance that an A gene will be carried by an individual who will die without
reproducing? An A gene is either (with chance q) in a heterozygote and survives or
(with chance p) in an AA homozygote and has a chance s of dying. Its total chance of
dying is therefore ps. An a gene similarly is either (with chance p) in a heterozygote and
survives or (with chance q) in an aa homozygote and has chance t of dying: its chance of
death is qt. At the equilibrium,
Chance of death of an A gene = chance of death of an a gene
p*s = q*t (5.10)
Substitute p*s = (1 − p*)t
and rearrange p* = t/(s + t) (5.11)
Similarly if we substitute q = (1 − p), q* = s/(s + t). Now we have derived the equilibrial
gene frequencies when both homozygotes have lower fitness than the heterozygote.
The equilibrium has all three genotypes present, even though the homozygotes are
inferior and are selected against. They continue to exist because it is impossible to
eliminate them. Matings among heterozygotes generate homozygotes. The exact gene
frequency at equilibrium depends on the relative selection against the two homozygotes.
If, for instance, AA and aa have equal fitness, then s = t and p = 1 /2 at equilibrium.
If AA is relatively more unfit than aa then s > t and p < 1 /2; there are fewer of the
more strongly selected against genotypes.
When heterozygotes are fitter than the homozygotes, therefore, natural selection
will maintain a polymorphism. The result was first proved by Fisher in 1922 and
independently by Haldane. We shall come later to consider in more detail why genetic
variability exists in natural populations, and heterozygous advantage will be one of
several controversial explanations to be tested.
5.12.2 Sickle cell anemia is a polymorphism with
heterozygous advantage
Sickle cell anemia is the classic example of a polymorphism maintained by heterozygous
advantage. It is a nearly lethal condition in humans, responsible for about
100,000 deaths a year. It is caused by a genetic variant of α-hemoglobin. If we symbolize
the normal hemoglobin allele by A and the sickle cell hemoglobin by S, then people
who suffer from sickle cell anemia are SS. Hemoglobin S causes the red blood cells to
become curved and distorted (sickle shaped); they can then block capillaries and cause
severe anemia if the blocked capillary is in the brain. About 80% of SS individuals die
before reproducing. With such apparently strong selection against hemoglobin S it was
a puzzle why it persisted at quite high frequencies (10% or even more) in some human
populations.
If we compare a map of the incidence of malaria with a map of the gene frequency
(Figure 5.9), we see that they are strikingly similar. Perhaps hemoglobin S provides
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