mUTATIon AnD VARIATIon 85
No real population meets all of these conditions. Thus no real population is
expected to be exactly in Hardy-Weinberg equilibrium (although the discrepancy
may be very small). The Hardy-Weinberg equilibrium nevertheless plays a key role
in evolutionary biology. It is the foundation for mathematical models of evolution,
and it provides a null model for analyzing data. If a population is not in Hardy-
Weinberg equilibrium, then one of the conditions listed above has been violated.
The β-hemoglobin locus in humans has two alleles called A and S. They differ
by a single base in the sixth codon (see Figure 4.3). Here are the frequencies of the
genotypes at this locus among 654 adults from Musoma, Tanganyika (Africa), and
the frequencies expected if the population was at Hardy-Weinberg equilibrium [1a]:Genotype: AA AS SS
Number of adults: 400 249 5
Observed frequency: 0.612 0.381 0.008
Hardy-Weinberg expectation: 0.643 0.317 0.039The observed frequency of heterozygotes is higher and the frequencies of both
homozygotes are lower than what the Hardy-Weinberg equilibrium predicts. The
discrepancies are small but statistically significant. They result from differences
in survival: the AA and SS genotypes do not survive as well as the AS genotype.
This is one of the most famous examples of natural selection acting on our own
species, and we will discuss it further in the next chapter. It illustrates how the
Hardy-Weinberg equilibrium is used to investigate selection and other evolution-
ary processes.Gene mixing by recombination
The second type of genetic mixing results from recombination. This is the pro-
cess that combines in a gamete a gene copy at one locus that was inherited from
the mother with a gene copy at a second locus that was inherited from the father
(FIGURE 4.7). In eukaryotes, recombination occurs during meiosis. Loci that are
carried on different chromosomes recombine by the independent assortment of
those chromosomes. Recombination happens between loci on the same chromo-
some by crossing over, which joins together a piece of a chromosome inherited
from the mother with a piece inherited from the father.
The recombination rate, symbolized by r, is the probability that recombination
occurs between a given pair of loci (FIGURE 4.8). If the two loci are on different
chromosomes, when an individual makes a gamete there is a chance of 1/2 that
one of the chromosomes it carries will be from the mother and the other from the
father. Here r = 1/2, which is the maximum possible value for the recombination
rate. At the other extreme, DNA bases that are adjacent on a chromosome have an
extremely low chance of recombining. The smallest possible value for the recom-
bination rate is r = 0.
When an allele at one locus is found together in a population more often than
expected by chance with an allele at a second locus, we say the loci are in link-
age disequilibrium^1. The key effect of recombination is to erode linkage disequi-
librium. Recombination moves the population toward a state where there is no
statistical association between the alleles at the two loci, a situation called linkage
equilibrium. This is analogous to the Hardy-Weinberg equilibrium at a single locus,
where two alleles at the same locus are uncorrelated with each other. Unlike the(^1) The term “linkage disequilibrium” is unfortunate and confusing: genes that are not physically
linked (on the same chromosome) can be in linkage disequilibrium, while genes that are physi-
cally linked can be in linkage equilibrium.
Futuyma Kirkpatrick Evolution, 4e
Sinauer Associates
Troutt Visual Services
Evolution4e_04.07.ai Date 11-04-2016
A 1 A 1
A 2
A 1 A 2 A 1 A 2
A 2
B 2 B 2
A 2
Parents
Offspring
(1 – r)
Not recombined Recombined
r
Gametes
B 1 B 2
B 1 B 1
A 1
B 1 B 2 B 2 B 1
FIGURE 4.7 Recombination randomizes
the combinations of alleles at two loci. One
locus is shown as an oval and the other as
a diamond. These loci may be on the same
chromosome or on different chromosomes.
Two different alleles are indicated by the
different colors. The offspring makes two
kinds of gametes (sperm): those that have
not recombined the alleles inherited from
the parents (left), and those that have (right).
The recombination rate, r, is the fraction of
gametes that have recombined alleles.
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