Evolution, 4th Edition

84 CHAPTER 4

the probability that a sperm carries the A 2 allele times the probability that an egg

also carries the A 2 allele, or p^2. Likewise, the frequency of A 1 A 1 offspring is (1 – p)^2 ,

and the frequency of A 1 A 2 offspring is 2p(1 – p).

Putting those results together gives us the Hardy-Weinberg proportions:

Genotype: A 1 A 1 A 1 A 2 A 2 A 2

Frequency: (1 – p)^2          2 p(1 – p) p^2

An example with p = 0.7 is shown in Figure 4.6.

The key conditions for the Hardy-Weinberg equilibrium are:

• An infinite population size


• No natural selection


• No mutation


• No movement between populations


• Random mating

Futuyma Kirkpatrick Evolution, 4e

Sinauer Associates

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Evolution4e_04.06.ai Date 11-07-2016 01-12-17

Frequency

A 1 A 1 A 1 A 2 A 2 A 2

0.50

0.75

(A) Adults

0

0.25

Frequency

A 1 A 1 A 1 A 2 A 2 A 2

0.09

0.42

0.50 0.49

0.75

0.09 0.21

0.21

0.3

0.7

A 1

0.3

A 1

0.7

A 2

Sperm

Eggs

A 2 0.49

(D) Offspring

0

0.25

Frequency

A 1 A 2

0.50

0.75

(B) Gametes

(C)

0

0.25

0.3

0.7

0.3

0.7

FIGURE 4.6 Hardy-Weinberg equilibrium results from the random union of gam-

etes. (A) In this example, 30% of the adults are A 1 A 1 homozygotes and 70% are A 2 A 2

homozygotes. The frequency of allele A 2 is p = 0.7 and the frequency of allele A 1 is

1 – p = 0.3. The population is not in Hardy-Weinberg equilibrium: there are too few

heterozygotes. (B) The frequencies of the alleles in the sperm and eggs are the same

as in the adults. (C) The numbers inside the box are the frequencies of genotypes in

the offspring that are formed by random fertilization between sperm and eggs. (D)

The genotype frequencies among the offspring are found by adding up the cells

inside the box: the frequency of A 1 A 1 homozygotes is (1 – p)^2 = 0.09, the frequency of

A 1 A 2 heterozygotes is 2 p(1 – p) = 0.42, and the frequency of A 2 A 2 homozygotes is p^2 =

0.49. The genotype frequencies are different than they were in the parents (compare

panels A and D), and are now in Hardy-Weinberg equilibrium. The allele frequencies,

however, have not changed.

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