Evolution__3rd_Edition

..
. . . and use Mendel’s rules to
deduce the genotype frequencies in
the offspring
picking an AA and then an Aa (to produce an AA × Aa pair), for example, is PQ; the
chance of picking an AA and then an aa is PR; and so on.
The genotypic proportions in the offspring of each type of mating are given by the
Mendelian ratios for that cross. We can work out the frequency of a genotype in the
next generation by addition. We look at which matings generate the genotype, and add
the frequencies generated by all the matings. Let us work it out for the genotype AA. AA
individuals, Table 5.1 shows, come from AA × AA, AA × Aa (and Aa × AA), and Aa × Aa
matings. We can ignore all the other types of mating. AA × AA matings have frequency
P 2 and produce all AA offspring, AA × Aa and Aa × AA matings each have frequency PQ
and produce 50% AA offspring, and Aa × Aa matings have frequency Q 2 and produce
25% AA offspring. The frequency of AA in the next generation, 2 P′, is then:
P′=P 2 + 1 /2PQ + 1 /2PQ + 1 /4Q 2 (5.2)
This can be rearranged to:
P′=(P + 1 /2Q) (P + 1 /2Q)
We have seen that (P + 1 /2Q) is simply the frequency of the gene A, p. Therefore:
P′=p 2
CHAPTER 5 / The Theory of Natural Selection 99
Table 5.1
Calculations needed to derive the Hardy–Weinberg ratio for one locus and two alleles,
A and a. (Frequency of AA = P, of Aa = Q, and of aa = R.) The table shows the frequencies of
different matings if the genotypes mate randomly, and the genotype proportions among the
progeny of the different matings.
Mating type Frequency of mating Offspring genotype proportions
AA × AA P 2 1 AA
AA × Aa PQ 1 /2 AA : 1 /2 Aa
AA × aa PR 1 Aa
Aa × AA QP 1 /2 AA : 1 /2 Aa
Aa × Aa Q 2 1 /4 AA : 1 /2 Aa : 1 /4 aa
Aa × aa QR 1 /2 Aa : 1 /2 aa
aa × AA RP 1 Aa
aa × Aa RQ 1 /2 Aa : 1 /2 aa
aa × aa R 2 1 aa
2 Population geneticists conventionally symbolize the frequency of variables one generation on by writing
a prime. If P is the frequency of genotype AA in one generation, P′ is its frequency in the next; if p is the
frequency of an allele in one generation, p′ is its frequency in the next generation. We shall follow this
convention repeatedly in this book.