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4: Genetically Variable Traits Change in Response to Selection
with different genotypes, allowing individuals with certain
genotypes to produce more offspring than others. Natural
selection is one of the most important of the forces that
brings about evolutionary change and can be summarized as
Observation 1 Many more individuals are produced
each generation than are capable of surviving long
enough to reproduce.
Observation 2 There is much phenotypic variation
within natural populations.
Observation 3 Some phenotypic variation is heritable.
In the terminology of quantitative genetics, some of
the phenotypic variation in these characteristics is due
to genetic variation, and these characteristics have
Logical consequence Individuals with certain
characters (called adaptive traits) survive and
reproduce better than others. Because the adaptive
traits are heritable, offspring will tend to resemble
their parents with regard to these traits, and there will
be more individuals with these adaptive traits in the
next generation. Thus, adaptive traits will tend to
increase in the population through time.
In this way, organisms become genetically suited to their
environments; as environments change, groups of organisms
change in ways that make them better able to survive and
For thousands of years, humans have practiced a form
of selection by promoting the reproduction of organisms
with traits perceived as desirable. This form of selection is
artificial selection, and it has produced the domestic plants
and animals that make modern agriculture possible.
Predicting the Response to Selection
When a quantitative characteristic is subjected to natural or
artificial selection, it will frequently change with the passage of
time, provided that there is genetic variation for that characteristic in the population. Suppose that a dairy farmer breeds
only those cows in his herd that have the highest milk production. If there is genetic variation in milk production, the mean
milk production in the offspring of the selected cows should
be higher than the mean milk production of the original herd.
This increased production is due to the fact that the selected
cows possess more genes for high milk production than does
the average cow, and these genes are passed on to the offspring.
The offspring of the selected cows possess a higher proportion
of genes for greater milk yield and therefore produce more
milk than the average cow in the initial herd.
The extent to which a characteristic subjected to selection changes in one generation is termed the response to
selection. Suppose that the average cow in a dairy herd produces 80 liters of milk per week. A farmer selects for
increased milk production by breeding the highest milk producers, and the progeny of these selected cows produce 100
liters of milk per week on average. The response to selection
is calculated by subtracting the mean phenotype of the original population (80 liters) from the mean phenotype of the
offspring (100 liters), obtaining a response to selection of
100 Ϫ 80 ϭ 20 liters per week.
The response to selection is determined primarily by
two factors. First, it is affected by the narrow-sense heritability, which largely determines the degree of resemblance
between parents and offspring. When the narrow-sense heritability is high, offspring will tend to resemble their parents;
conversely, when the narrow-sense heritability is low, there
will be little resemblance between parents and offspring.
The second factor that determines the response to selection is how much selection there is. If the farmer is very
stringent in the choice of parents and breeds only the highest milk producers in the herd (say, the top 2 cows), then all
the offspring will receive genes for high-quality milk production. If the farmer is less selective and breeds the top 20 milk
producers in the herd, then the offspring will not carry as
many superior genes for high milk production, and they will
not, on average, produce as much milk as the offspring of the
top 2 producers. The response to selection depends on the
phenotypic difference of the individuals that are selected as
parents; this phenotypic difference is measured by the selection differential, defined as the difference between the mean
phenotype of the selected parents and the mean phenotype
of the original population. If the average milk production of
the original herd is 80 liters and the farmer breeds cows with
an average milk production of 120 liters, then the selection
differential is 120 Ϫ 80 ϭ 40 liters.
The response to selection (R) depends on the narrowsense heritability (h2) and the selection differential (S):
R ϭ h2 ϫ S
This equation can be used to predict the magnitude of
change in a characteristic when a given selection differential
is applied. G. A. Clayton and his colleagues estimated the
response to selection that would take place in abdominal
bristle number of Drosophila melanogaster. Using several
different methods, they first estimated the narrow-sense
heritability of abdominal bristle number in one population
of fruit flies to be 0.52. The mean number of bristles in the
original population was 35.3. They selected individual flies
with a mean bristle number of 40.6 and intercrossed them
to produce the next generation. The selection differential
was 40.6 Ϫ 35.3 ϭ 5.3; so they predicted a response to selection to be
R ϭ 0.52 ϫ 5.3 ϭ 2.8
The response to selection of 2.8 is the expected increase in
the characteristic of the offspring above the mean of the
original population. They therefore expected the average
high- and low-oil-content strains revealed that at least 20
loci take part in determining oil content.
high oil content
The response to selection is influenced by narrow-sense heritability
and the selection differential.
✔ Concept Check 3
The narrow-sense heritability for a trait is 0.4 and the selection
differential is 0.5. What is the predicted response to selection?
Limits to Selection Response
low oil content
16.14 In a long-term response-to-selection experiment,
selection for oil content in corn increased oil content in one
line to about 20%, whereas oil content was almost
eliminated in another line.
number of abdominal bristles in the offspring of their
selected flies to be 35.3 ϩ 2.8 ϭ 38.1. Indeed, they found an
average bristle number of 37.9 in these flies.
Rearranging Equation 16.10 provides another way to
calculate the narrow-sense heritability:
In this way, h2 can be calculated by conducting a responseto-selection experiment. First, the selection differential is
obtained by subtracting the population mean from the mean
of selected parents. The selected parents are then interbred,
and the mean phenotype of their offspring is measured. The
difference between the mean of the offspring and that of the
initial population is the response to selection, which can be
used with the selection differential to estimate the heritability. Heritability determined by a response-to-selection
experiment is usually termed the realized heritability. If certain assumptions are met, the realized heritability is identical with the narrow-sense heritability.
One of the longest selection experiments is a study of oil
and protein content in corn seeds (Figure 16.14). This experiment began at the University of Illinois on 163 ears of corn
with an oil content ranging from 4% to 6%. Corn plants having high oil content and those having low oil content were
selected and interbred. Response to selection for increased
oil content (the upper line in Figure 16.14) reached about
20%, whereas response to selection for decreased oil content
reached a lower limit near zero. Genetic analyses of the
When a characteristic has been selected for many generations, the response eventually levels off and the characteristic no longer responds to selection (Figure 16.15). A
potential reason for this leveling off is that the genetic variation in the population may be exhausted; at some point, all
individuals in the population have become homozygous for
alleles that encode the selected trait. When there is no more
additive genetic variation, heritability equals zero and there
can be no further response to selection.
The response to selection may level off even while some
genetic variation remains in the population, however,
because natural selection opposes further change in the
characteristic. Response to selection for small body size in
mice, for example, eventually levels off because the smallest
animals are sterile and cannot pass on their genes for small
body size. In this case, artificial selection for small size is
opposed by natural selection for fertility, and the population
can no longer respond to the artificial selection.
Mean number of bristles
Percentage of oil content
16.15 The response of a population to selection often levels
off at some point in time. In a response-to-selection experiment
for increased number of bristles on the abdomen of female fruit flies,
the number of bristles increased steadily for about 20 generations and
then leveled off.
• Quantitative genetics focuses on the inheritance of complex
characteristics whose phenotypes vary continuously. For many
quantitative characteristics, the relation between genotype and
phenotype is complex because many genes and environmental
factors influence a characteristic.
The individual genes that influence a polygenic characteristic
follow the same Mendelian principles that govern
discontinuous characteristics, but, because many genes
participate, the expected ratios of phenotypes are obscured.
A frequency distribution, in which the phenotypes are
represented on one axis and the number of individuals
possessing each phenotype is represented on the other, is
a convenient means of summarizing phenotypes found in
a group of individuals.
• The mean and variance provide key information about a
distribution: the mean gives the central location of the
distribution, and the variance provides information about
how the phenotype varies within a group.
Phenotypic variance in a characteristic can be divided into
components that are due to additive genetic variance,
dominance genetic variance, genic interaction variance,
environmental variance, and genetic–environmental
• Broad-sense heritability is the proportion of the phenotypic
variance due to genetic variance; narrow-sense heritability is
the proportion of the phenotypic variance due to additive
Heritability provides information only about the degree to
which variation in a characteristic results from genetic
differences. Heritability is based on the variances present
within a group of individuals, and an individual does not
have heritability. Heritability of a characteristic varies among
populations and among environments. Even if heritability for
a characteristic is high, the characteristic may still be altered
by changes in the environment. Heritabilities provide no
information about the nature of population differences in
• Quantitative trait loci are chromosome segments containing
genes that control polygenic characteristics. QTLs can be
mapped by examining the association between the inheritance
of a quantitative characteristic and the inheritance of genetic
The amount that a quantitative characteristic changes in a
single generation when subjected to selection (the response
to selection) is directly related to the selection differential
and narrow-sense heritability.
quantitative genetics (p. 407)
quantitative trait locus (QTL) (p. 407)
meristic characteristic (p. 410)
threshold characteristic (p. 410)
frequency distribution (p. 413)
normal distribution (p. 414)
mean (p. 414)
variance (p. 415)
heritability (p. 415)
phenotypic variance (p. 416)
genetic variance (p. 416)
environmental variance (p. 416)
variance (p. 416)
additive genetic variance (p. 417)
dominance genetic variance (p. 417)
genic interaction variance (p. 417)
broad-sense heritability (p. 417)
narrow-sense heritability (p. 418)
natural selection (p. 421)
artificial selection (p. 422)
response to selection (p. 422)
selection differential (p. 422)
realized heritability (p. 423)
Answers to Concept Checks
2. The heritability indicates that about 40% of the differences in
blood pressure among African Americans in Detroit are due to
additive genetic differences. It neither provides information
about the heritability of blood pressure in other groups of people
nor indicates anything about the nature of differences in blood
pressure between African Americans in Detroit and people in
1. Seed weight in a particular plant species is determined by pairs
of alleles at two loci (aϩaϪ and bϩbϪ) that are additive and equal
in their effects. Plants with genotype aϪaϪ bϪbϪ have seeds that
average 1 g in weight, whereas plants with genotype aϩaϩ bϩbϩ
have seeds that average 3.4 g in weight. A plant with genotype
aϪaϪ bϪbϪ is crossed with a plant of genotype aϩaϩ bϩbϩ.
a. What is the predicted weight of seeds from the F1
progeny of this cross?
b. If the F1 plants are intercrossed, what are the expected
seed weights and proportions of the F2 plants?
aϪaϪ bϪbϪ ϫ aϩaϩ bϩbϩ
Ϫ Ϫ Ϫ Ϫ
a a b b
4 ϫ 4 ϭ 16
2 * 14 = 18
4 * 12 = 18
Average seed weight
1 g ϩ (0 ϫ 0.6 g) ϭ 1 g
8 ϭ 416
1 g ϩ (1 ϫ 0.6 g) ϭ 1.6 g
4 * 14 = 116
16 ϩ 14 ϭ 616
1 g ϩ (2 ϫ 0.6 g) ϭ 2.2 g
4 * 12 = 18
2 * 14 = 18
8 ϭ 416
1 g ϩ (3 ϫ 0.6 g) ϭ 2.8 g
1 g ϩ (4 ϫ 0.6 g) ϭ 3.4 g
4 * 14 = 116
2 * 12 = 14
4 ϫ 14 ϭ 116
The difference in average seed weight of the two parental
genotypes is 3.4 g Ϫ 1 g ϭ 2.4 g. These two genotypes differ in
four genes; so, if the genes have equal and additive effects, each
gene difference contributes an additional 2.4 g/4 ϭ 0.6 g of
weight to the 1-g weight of a plant (aϪaϪ bϪbϪ), which has
none of the contributing genes.
The cross between the two homozygous genotypes produces
the F1 and F2 progeny shown in the table at the top of this page.
a. The F1 are heterozygous at both loci (aϩaϪ bϩbϪ) and
possess two genes that contribute an additional 0.6 g each to the
1-g weight of a plant that has no contributing genes. Therefore,
the seeds of the F1 should average 1 g ϩ 2(0.6 g) ϭ 2.2 g.
b. The F2 will have the following phenotypes and proportions:
16 1 g; 416 1.6 g; 616 2.2 g; 416 2.8 g; and 116 3.4 g.
2. Phenotypic variation is analyzed for milk production in a herd
of dairy cattle and the following variance components are
Additive genetic variance (VA)
Dominance genetic variance (VD)
Genic interaction variance (VI)
Environmental variance (VE)
Genetic–environmental interaction variance (VGE)
a. What is the narrow-sense heritability of milk production?
b. What is the broad-sense heritability of milk production?
To determine the heritabilities, we first need to calculate VP
VP ϭ VA ϩ VD ϩ VI ϩ VE ϩ VGE
ϭ 0.4 ϩ 0.1 ϩ 0.2 ϩ 0.5 ϩ 0
VG ϭ VA ϩ VD ϩ VI
b. The broad-sense heritability is: H2 =
3. A farmer is raising rabbits. The average body weight in his
population of rabbits is 3 kg. The farmer selects the 10 largest
rabbits in his population, whose average body weight is 4 kg, and
interbreeds them. If the heritability of body weight in the rabbit
population is 0.7, what is the expected body weight among
offspring of the selected rabbits?
a. The narrow-sense heritability is: h2 =
The farmer has carried out a response-to-selection experiment, in
which the response to selection will equal the selection differential
times the narrow-sense heritability. The selection differential
equals the difference in average weights of the selected rabbits
and the entire population: 4 kg Ϫ 3 kg ϭ 1 kg. The narrow-sense
heritability is given as 0.7; so the expected response to selection
is: R ϭ h2 ϫ S ϭ 0.7 ϫ 1 kb ϭ 0.7 kg. This value is the increase
in weight that is expected in the offspring of the selected parents;
so the average weight of the offspring is expected to be: 3 kg ϩ
0.7 kg ϭ 3.7 kg.
*1. How does a quantitative characteristic differ from a
2. Briefly explain why the relation between genotype and
phenotype is frequently complex for quantitative
*3. Why do polygenic characteristics have many phenotypes?
4. What information do the mean and variance provide about
*5. List all the components that contribute to the phenotypic
variance and define each component.
*6. How do the broad-sense and narrow-sense heritabilities
7. Briefly describe common misunderstandings or
misapplications of the concept of heritability.
8. Briefly explain how genes affecting a polygenic characteristic
are located with the use of QTL mapping.
*9. How is the response to selection related to the narrow-sense
heritability and the selection differential? What information
does the response to selection provide?
10. Why does the response to selection often level off after
many generations of selection?
Application Questions and Problems
*11. Indicate whether each of the following characteristics would
be considered a discontinuous characteristic or a
quantitative characteristic. Briefly justify your answer.
a. Kernel color in a strain of wheat, in which two
codominant alleles segregating at a single locus
determine the color. Thus, there are three phenotypes
present in this strain: white, light red, and medium red.
b. Body weight in a family of Labrador retrievers. An
autosomal recessive allele that causes dwarfism is
present in this family. Two phenotypes are recognized:
dwarf (less than 13 kg) and normal (greater than 13 kg).
c. Presence or absence of leprosy. Susceptibility to leprosy
is determined by multiple genes and numerous
d. Number of toes in guinea pigs, which is influenced by
genes at many loci.
e. Number of fingers in humans. Extra (more than five)
fingers are caused by the presence of an autosomal
*12. Assume that plant weight is determined by a pair of alleles
at each of two independently assorting loci (A and a, B and b)
that are additive in their effects. Further assume that each
allele represented by an uppercase letter contributes 4 g to
weight and that each allele represented by a lowercase letter
contributes 1 g to weight.
a. If a plant with genotype AA BB is crossed with a plant
with genotype aa bb, what weights are expected in the
b. What is the distribution of weight expected in the
*13. Assume that three loci, each with two alleles (A and a,
B and b, C and c), determine the differences in height
between two homozygous strains of a plant. These genes
are additive and equal in their effects on plant height.
One strain (aa bb cc) is 10 cm in height. The other strain
(AA BB CC) is 22 cm in height. The two strains are crossed,
and the resulting F1 are interbred to produce F2 progeny.
Give the phenotypes and the expected proportions of the
14. Seed size in a plant is a polygenic characteristic. A grower
crosses two pure-breeding varieties of the plant and
measures seed size in the F1 progeny. She then backcrosses
the F1 plants to one of the parental varieties and measures
seed size in the backcross progeny. The grower finds that
seed size in the backcross progeny has a higher variance
than does seed size in the F1 progeny. Explain why the backcross progeny are more variable.
*15. Phenotypic variation in tail length of mice has the following
Additive genetic variance (VA)
Dominance genetic variance (VD)
Genic interaction variance (VI)
Environmental variance (VE)
Genetic–environmental interaction variance (VGE) = 0.0
a. What is the narrow-sense heritability of tail length?
b. What is the broad-sense heritability of tail length?
16. The narrow-sense heritability of ear length in Reno rabbits is
0.4. The phenotypic variance (VP) is 0.8, and the
environmental variance (VE) is 0.2. What is the additive
genetic variance (VA) for ear length in these rabbits?
17. A characteristic has a narrow-sense heritability of 0.6.
a. If the dominance variance (VD) increases and all other
variance components remain the same, what will
happen to the narrow-sense heritability? Will it
increase, decrease, or remain the same? Explain.
b. What will happen to the broad-sense heritability? Explain.
c. If the environmental variance (VE) increases and all
other variance components remain the same, what will
happen to the narrow-sense heritability? Explain.
d. What will happen to the broad-sense heritability?
18. Many researchers have estimated the heritability of human
traits by comparing the correlation coefficients of
monozygotic and dizygotic twins. An assumption in using
this method is that two monozygotic twins experience
environments that are no more similar to each other than
those experienced by two dizygotic twins. How might this
assumption be violated? Give some specific examples of ways
in which the environments of two monozygotic twins might
be more similar than the environments of two dizyotic twins.
19. A genetics researcher determines that the broad-sense
heritability of height among Southwestern University
undergraduate students is 0.90. Which of the following
conclusions would be reasonable? Explain your answer.
a. Because Sally is a Southwestern University
undergraduate student, 10% of her height is
determined by nongenetic factors.
b. Ninety percent of variation in height among all
undergraduate students in the United States is due
to genetic differences.
c. Ninety percent of the height of Southwestern University
undergraduate students is determined by genes.
d. Ten percent of the variation in height among
Southwestern University undergraduate students is
determined by variation in nongenetic factors.
e. Because the heritability of height among Southwestern
Unversity students is so high, any change in the
students’ environment will have minimal effect on
20. Drosophila buzzati is a fruit fly that feeds on the rotting
fruits of cacti in Australia. Timothy Prout and Stuart Barker
calculated the heritabilities of body size, as measured by
thorax length, for a natural population of D. buzzati raised
in the wild and for a populatios of D. buzzati collected in
the wild but raised in the laboratory (T. Prout and J. S. F.
Barker. 1989. Genetics 123:803–813). They found the
Heritability of body size
0.0595 Ϯ 0.0123
0.3770 Ϯ 0.0203
Why do you think the heritability measured in the
laboratory-reared population is higher than that
measured in the natural population raised in the wild?
*21. Mr. Jones is a pig farmer. For many years, he has fed his
pigs the food left over from the local university cafeteria,
which is known to be low in protein, deficient in vitamins,
and downright untasty. However, the food is free, and his
pigs don’t complain. One day a salesman from a feed
company visits Mr. Jones. The salesman claims that his
company sells a new, high-protein, vitamin-enriched feed
that enhances weight gain in pigs. Although the food is
expensive, the salesman claims that the increased weight
gain of the pigs will more than pay for the cost of the feed,
increasing Mr. Jones’s profit. Mr. Jones responds that he
took a genetics class when he went to the university and
that he has conducted some genetic experiments on his
pigs; specifically, he has calculated the narrow-sense
heritability of weight gain for his pigs and found it to be
0.98. Mr. Jones says that this heritability value indicates that
98% of the variance in weight gain among his pigs is
determined by genetic differences, and therefore the new
pig feed can have little effect on the growth of his pigs.
He concludes that the feed would be a waste of his money.
The salesman doesn’t dispute Mr. Jones’ heritability
estimate, but he still claims that the new feed can
significantly increase weight gain in Mr. Jones’ pigs. Who
is correct and why?
22. Joe is breeding cockroaches in his dorm room. He finds
that the average wing length in his population of
cockroaches is 4 cm. He chooses six cockroaches that
have the largest wings; the average wing length among
these selected cockroaches is 10 cm. Joe interbreeds these
selected cockroaches. From earlier studies, he knows that
the narrow-sense heritability for wing length in his
population of cockroaches is 0.6.
a. Calculate the selection differential and expected
response to selection for wing length in these
b. What should be the average wing length of the progeny
of the selected cockroaches?
23. Three characteristics in beef cattle—body weight, fat
content, and tenderness—are measured, and the following
variance components are estimated:
In this population, which characteristic would respond best
to selection? Explain your reasoning.
*24. A rancher determines that the average amount of wool
produced by a sheep in her flock is 22 kg per year. In an
attempt to increase the wool production of her flock, the
rancher picks five male and five female sheep with the
greatest wool production; the average amount of wool
produced per sheep by those selected is 30 kg. She
interbreeds these selected sheep and finds that the average
wool production among the progeny of the selected sheep
is 28 kg. What is the narrow-sense heritability for wool
production among the sheep in the rancher’s flock?
25. A strawberry farmer determines that the average weight of
individual strawberries produced by plants in his garden
is 2 g. He selects the 10 plants that produce the largest
strawberries; the average weight of strawberries among
these selected plants is 6 g. He interbreeds these selected
strawberry plants. The progeny of these selected plants
produce strawberries that weigh 5 g. If the farmer were to
select plants that produce an average strawberry weight of
4 g, what would be the predicted weight of strawberries
produced by the progeny of these selected plants?
26. Pigs have been domesticated from wild boars. Would you
expect to find higher heritability for weight among domestic
pigs or among wild boars? Explain your answer.
27. Bipolar illness is a psychiatric disorder that has a strong
hereditary basis, but the exact mode of inheritance is not
known. Research has shown that siblings of patients with
bipolar illness are more likely to develop the disorder than
are siblings of unaffected persons. Findings from a recent
study demonstrated that the ratio of bipolar brothers to
bipolar sisters is higher when the patient is male than when
the patient is female. In other words, relatively more brothers
of bipolar patients also have the disease when the patient is
male than when the patient is female. What does this
observation suggest about the inheritance of bipolar illness?
28. We have explored some of the difficulties in separating the
genetic and environmental components of human
behavioral characteristics. Considering these difficulties
and what you know about calculating heritability, propose
an experimental design for accurately measuring the
heritability of musical ability.
29. A student who has just learned about quantitative genetics
says, “Heritability estimates are worthless! They don’t tell you
anything about the genes that affect a characteristic. They
don’t provide any information about the types of offspring
to expect from a cross. Heritability estimates measured in
one population can’t be used for other populations; so they
don’t even give you any general information about how
much of a characteristic is genetically determined. I can’t
see that heritabilities do anything other than make
undergraduate students sweat during tests.” How would
you respond to this statement? Is the student correct? What
good are heritabilities, and why do geneticists bother to
30. Eugene Eisen selected for increased 12-day litter weight
DATA (total weight of a litter of offspring 12 days after birth) in a
population of mice (E. J. Eisen. 1972. Genetics 72:129–142).
The 12-day litter weight of the population steadily
increased, but then leveled off after about 17 generations. At
generation 17, Eisen took one family of mice from the
selected population and reversed the selection procedure: in
this group, he selected for decreased 12-day litter size. This
group immediately responded to decreased selection; the
12-day litter weight dropped 4.8 g within one generation
and dropped 7.3 g after 5 generations. Based on the results
of the reverse selection, what is the most likely explanation
for the leveling off of 12-day litter weight in the original
of Bighorn Sheep
ocky Mountain bighorn sheep (Ovis canadensis) are
among North America’s most spectacular animals,
characterized by the male’s magnificent horns that curve
gracefully back over the ears, spiraling down and back up
beside the face. Two hundred years ago, bighorn sheep were
numerous throughout western North America, ranging
from Mexico to southern Alberta and from Colorado to
California. Meriwether Lewis and William Clark reported
numerous sightings of these beautiful animals in their expedition across the western United States from 1804 to 1806.
Before 1900, the number of bighorn sheep in North
America was about 2 million.
Unfortunately, settlement of the west by Europeans was
not kind to the bighorns. Beginning in the late 1800s, hunting, loss of habitat, competition from livestock, and diseases
carried by domestic sheep decimated the bighorns. Today,
fewer than 70,000 bighorn sheep remain, scattered across
Rocky Mountain bighorn sheep (Ovis canadensis). A population of bighorn
North America in fragmented and isolated populations.
sheep at the National Bison Range suffered the loss of genetic variation owing to
In 1922, wildlife biologists established a population of
genetic drift; the introduction of sheep from other populations dramatically
increased genetic variation and the fitness of the sheep. [Tom J. Ulrich/Visuals
bighorn sheep at the National Bison Range, an isolated tract
of 18,000 acres nestled between the mountains of northwestern Montana. In that year, 12 bighorn sheep—4 males (rams) and 8 females (ewes)—
were trapped at Banff National Park in Canada and transported to the National Bison
Range. No additional animals were introduced to this population for the next 60 years.
At first, the population of bighorns at the National Bison Range flourished, protected
there from hunting and livestock. Within 8 years, it had grown to 90 sheep but then began
to slowly decrease in size. Population size waxed and waned through the years, but the number of sheep had dropped to about 50 animals by 1985, and the population was in trouble.
The amount of genetic variation was low compared with other native populations of
bighorn sheep. The reproductive rate of both male and female sheep had dropped, and the
size and survival of the sheep were lower than in more-healthy populations. The population at the National Bison Range was suffering from genetic drift, an evolutionary force
operating in small populations that causes random changes in the gene pool and the loss
of genetic variation.
To counteract the negative effects of genetic drift, biologists added 5 new rams from
other herds in Montana and Wyoming in 1985, mimicking the effects of natural migration
among herds. Another 10 sheep were introduced between 1990 and 1994. This influx of
new genes had a dramatic effect on the genetic health of the population. Genetic variation
among individual sheep increased significantly. Outbred rams (those containing the new
genes) were more dominant, were more likely to copulate, and were more likely to produce
offspring. Outbred ewes had more than twice the annual reproductive success of inbred
females. Adult survival increased after the introduction of new genes, and, slowly, the population grew in size, reaching 69 sheep by 2003.
he bighorn sheep at the National Bison Range illustrate
an important principle of genetics: small populations
lose genetic variation with the passage of time through
genetic drift, often with catastrophic consequences for survival and reproduction. The introduction of new genetic
variation into an inbred population, called genetic rescue,
often dramatically improves the health of the population
and can better ensure its long-term survival. These effects
have important implications for wildlife management, as
well as for how organisms evolve in the natural world.
This chapter introduces population genetics, the branch
of genetics that studies the genetic makeup of groups of individuals and how a group’s genetic composition changes with
time. Population geneticists usually focus their attention on
a Mendelian population, which is a group of interbreeding,
sexually reproducing individuals that have a common set of
genes, the gene pool. A population evolves through changes
in its gene pool; therefore, population genetics is also the
study of evolution. Population geneticists study the variation
in alleles within and between groups and the evolutionary
forces responsible for shaping the patterns of genetic variation found in nature. In this chapter, we will learn how the
gene pool of a population is measured and what factors are
responsible for shaping it. At the end of the chapter, we turn
to the evolutionary changes that bring about the appearance
of new species and patterns of evolutionary change at the
17.1 Genotypic and Allelic
Frequencies Are Used to
Describe the Gene Pool
of a Population
An obvious and pervasive feature of life is variability. Consider
a group of students in a typical college class, the members of
which vary in eye color, hair color, skin pigmentation, height,
weight, facial features, blood type, and susceptibility to
numerous diseases and disorders. No two students in the class
are likely to be even remotely similar in appearance.
Humans are not unique in their extensive variability
(Figure 17.1a); almost all organisms exhibit variation in
phenotype. For instance, lady beetles are highly variable in
17.1 All organisms exhibit genetic variation. (a) Extensive variation among humans. (b) Variation in the spotting patterns of Asian
lady beetles. [Part a: Paul Warner/AP.]
Population and Evolutionary Genetics
their patterns of spots (Figure 17.1b), mice vary in body size,
snails have different numbers of stripes on their shells, and
plants vary in their susceptibility to pests. Much of this phenotypic variation is hereditary. Recognition of the extent of
phenotypic variation led Charles Darwin to the idea of evolution through natural selection. Genetic variation is the
basis of all evolution, and the extent of genetic variation
within a population affects its potential to adapt to environmental change.
In fact, even more genetic variation exists in populations
than is visible in the phenotype. Much variation exists at the
molecular level owing, in part, to the redundancy of the
genetic code, which allows different codons to specify the
same amino acid. Thus, two members of a population can
produce the same protein even if their DNA sequences are
different. DNA sequences between the genes and introns
within genes do not encode proteins; much of the variation
in these sequences probably also has little effect on the
An important, but frequently misunderstood, tool used
in population genetics is the mathematical model. Let’s take
a moment to consider what a model is and how it can be
used. A mathematical model usually describes a process as an
equation. Factors that may influence the process are represented by variables in the equation; the equation defines the
way in which the variables influence the process. Most models are simplified representations of a process because the
simultaneous consideration of all of the influencing factors
is impossible; some factors must be ignored in order to
examine the effects of others. At first, a model might consider only one factor or a few factors, but, after their effects
have been understood, the model can be improved by the
addition of more details. Importantly, even a simple model
can be a source of valuable insight into how a process is
influenced by key variables.
Before we can explore the evolutionary processes that
shape genetic variation, we must be able to describe the
genetic structure of a population. The usual way of doing so
is to enumerate the types and frequencies of genotypes and
alleles in a population.
divide by the total number of individuals in the sample (N).
For a locus with three genotypes AA, Aa, and aa, the frequency (f ) of each genotype is
f (AA) =
number of AA individuals
f (Aa) =
number of Aa individuals
f (aa) =
number of aa individuals
The sum of all the genotypic frequencies always equals 1.
Calculating Allelic Frequencies
The gene pool of a population can also be described in terms
of the allelic frequencies. There are always fewer alleles than
genotypes; so the gene pool of a population can be described
in fewer terms when the allelic frequencies are used. In a sexually reproducing population, the genotypes are only temporary assemblages of the alleles: the genotypes break down
each generation when individual alleles are passed to the
next generation through the gametes, and so the types and
numbers of alleles, rather than genotypes, have real continuity from one generation to the next and make up the gene
pool of a population.
Allelic frequencies can be calculated from (1) the numbers or (2) the frequencies of the genotypes. To calculate the
allelic frequency from the numbers of genotypes, we count
the number of copies of a particular allele present in a sample and divide by the total number of all alleles in the sample:
number of copies
of the allele
frequency of an allele =
number of copies of all
alleles at the locus
A frequency is simply a proportion or a percentage, usually
expressed as a decimal fraction. For example, if 20% of the
alleles at a particular locus in a population are A, we would
say that the frequency of the A allele in the population is
0.20. For large populations, where it is not practical to determine the genes of all individual members, a sample of the
population is usually taken and the genotypic and allelic frequencies are calculated for this sample. The genotypic and
allelic frequencies of the sample are then used to represent
the gene pool of the population.
To calculate a genotypic frequency, we simply add up
the number of individuals possessing the genotype and
For a locus with only two alleles (A and a), the frequencies of
the alleles are usually represented by the symbols p and q,
and can be calculated as follows:
p = f (A) =
Calculating Genotypic Frequencies
2nAA + nAa
2naa + nAa
q = f (a) =
where nAA, nAa, and naa represent the numbers of AA, Aa,
and aa individuals, and N represents the total number of
individuals in the sample. We divide by 2N because each
diploid individual has two alleles at a locus. The sum of the
allelic frequencies always equals 1 (p + q = 1); so, after p
has been obtained, q can be determined by subtraction:
q = 1 Ϫ p.
Alternatively, allelic frequencies can be calculated from
the genotypic frequencies. To do so, we add the frequency of
the homozygote for each allele to half the frequency of the