mUTATIon AnD VARIATIon 83
occurs at a locus or a DNA base in a population (FIGURE 4.5). Some alleles are
very rare. For example, one of the alleles that causes albinism (a condition in
which melanic skin pigments are missing) occurs at a frequency of about 0.0002 in
Europeans. Other alleles occur at much higher frequencies. A person’s blood type
depends on the alleles that affect the surface of the red blood cells. In the United
States, the frequency of the A blood type allele is about 0.4 (that is, about 40 per-
cent of chromosomes carry that allele).
How is this variation transmitted from one generation to the next? Most
eukaryotic species on Earth reproduce sexually: it takes both a mother and a father
to produce an offspring. Sex mixes the genes of the parents to produce genetic
combinations in the offspring not found in the parents. In organisms with meiosis
(such as ourselves), this mixing involves two basic genetic processes, segregation
and recombination. Organisms without meiosis, such as bacteria and viruses,
do not have segregation, but most of them still mix their genes by some form of
recombination.Gene mixing by segregation
Segregation is the selection of one of the two copies of a locus when a gamete is
made during meiosis. The fusion of an egg and sperm brings together the copy
from the mother with that from the father. A result is that the offspring can have
a genotype unlike either of its parents. A mother with genotype A 1 A 1 (homozy-
gous for the A 1 allele) and a father with genotype A 2 A 2 (homozygous for the A 2
allele) will have entirely heterozygous A 1 A 2 offspring. Segregation does not occur
in organisms that do not have meiosis, such as bacteria and viruses.
The mixing of genes caused by segregation changes the proportions of geno-
types in a population. Think of a population in which half the individuals are
A 1 A 1 homozygotes and half are A 2 A 2 homozygotes. When sperm and eggs are
produced by meiosis, half will carry the A 1 allele and half will carry the A 2 allele.
If sperm and eggs meet at random, the chance that an A 1 A 1 offspring is produced
equals the chance that an egg carrying an A 1 (= 1/2) is fertilized by a sperm that
also carries an A 1 (= 1/2). Thus the chance that an A 1 A 1 offspring is produced is
1/2 × 1/2 = 1/4. Likewise, the frequency of A 2 A 2 homozygotes in the offspring is
1/4. To find the frequency of A 1 A 2 heterozygotes in the offspring, we add up the
chance that a sperm with an A 1 fertilizes an egg with an A 2 (= 1/2 × 1/2 = 1/4) and
the chance that a sperm with an A 2 fertilizes an egg with an A 1 (= 1/2 × 1/2 = 1/4).
The frequency of A 1 A 2 offspring is therefore 1/2.
Looking at these numbers, we see that the frequency of genotypes changed
from one generation to the next. Heterozygotes are absent in the parents but make
up half of the offspring. What has not changed, however, are the frequencies of the
A 1 and A 2 alleles, which are equal to 1/2 in both generations. As a result, when the
offspring mate to produce a third generation, the frequencies of the A 1 A 1 , A 1 A 2 ,
and A 2 A 2 genotypes will again be 1/4, 1/2, and 1/4. Thus the population is at an
equilibrium: once the population reaches that state, no further change in genotype
frequencies will happen.
This example is a special case of the Hardy-Weinberg equilibrium, which tells
us the relative proportions of genotypes in a population when segregation is the
only factor that changes genotype frequencies. We just looked at the situation in
which the frequencies of the two alleles are equal to 1/2. The more general situa-
tion is illustrated in FIGURE 4.6. We now let the frequency of allele A 2 be any num-
ber between 0 and 1, and we represent that frequency by the symbol p. Since there
are only two alleles at the locus in this example, their frequencies must sum to 1,
and so the frequency of allele A 1 is (1 – p). Following the logic used in the earlier
example, we find that the chance of an A 2 A 2 offspring being produced is equal toFutuyma Kirkpatrick Evolution, 4e
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Evolution4e_04.05.ai Date 02-15-2017A 1 A 1A 1 A 1A 1 A 1A 1 A 1A 1 A 2A 1 A 2A 2 A 2A 2 A 2FIGURE 4.5 Allele frequencies and
genotype frequencies. In this population,
the frequency of the A 1 A 1 homozygote
genotype is 1/2, the frequency of the
A 1 A 2 heterozygote genotype is 1/4, and
the frequency of the A 2 A 2 homozygote
genotype is 1/4. Ten of the 16 copies of
the gene are the A 1 allele, so its allele
frequency is p = 10/16 = 0.625.04_EVOL4E_CH04.indd 83 3/23/17 8:55 AM