Evolution__3rd_Edition

100 PART 2 / Evolutionary Genetics
Genotype frequency
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Gene frequency of a
The result is the Hardy–Weinberg
equilibrium
AA aa
Aa
The frequency of genotype AA after one generation of random mating is equal to the
square of the frequency of the A gene. Analogous arguments show that the frequencies
of Aa and aa are 2pq and q 2 . The Hardy–Weinberg frequencies are then:
Genotype AA : Aa : aa
Frequency p 2 : 2pq : q 2
Figure 5.2
Hardy–Weinberg frequencies of genotypes AA, Aa, and aa in
relation to the frequency of the gene a (q).
Figure 5.2 shows the proportions of the three different genotypes at different frequencies
of the gene a; heterozygotes are most frequent when the gene frequency is 0.5.
The Hardy–Weinberg genotype frequencies are reached after a single generation of
random mating from any initial genotype frequencies. Imagine, for example, two populations
with the same gene frequency but different genotype frequencies. One population
has 750 AA, 0 Aa, and 250 aa; the other has 500 AA, 500 Aa, and 0 aa. p = 0.75 and
q = 0.25 in both. After one generation of random mating, the genotype frequencies in
both will become 563 AA, 375 Aa, and 62 aa if the population size remains 1,000.
(Fractions of an individual have been rounded to make the numbers add to 1,000. The
proportions are 9/16, 6/16, and 1/16.) After reaching those frequencies immediately,
in one generation, the population stays at the Hardy–Weinberg equilibrium for as long
as the population size is large, there is no selection, and mating is random.
As we saw in Section 5.1, it is not in general possible to calculate the genotype
frequencies in a generation if you only know the gene frequencies. We can now see that
it is possible to calculate, from gene frequencies alone, what the genotype frequencies
will be in the next generation, provided that mating is random, there is no selection,
and the population is large. If the gene frequencies in this generation are p and q, in the
next generation the genotype will have Hardy–Weinberg frequencies.
The proof of the Hardy–Weinberg theorem we have worked through was longwinded.
We worked though it all in order to illustrate the general model of population
genetics in its simplest case. However, for the particular case of the Hardy–Weinberg
equilibrium, a more elegant proof can be given in terms of gametes.
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