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44200_18_p575-610 3/17/04 1:34 PM Page 596



Notum Haltere
(rudimentary wing)

T1 T2 T3 A5-A8
A1 A4
A2 A3

(a) Segment names (b) Wild type
(c) Bithorax
Figure 18-24 Homeotic transformation of the third thoracic
segment (T3) of Drosophila into an extra second thoracic segment
(T2). (a) Diagram showing the normal thoracic and abdominal
segments; note the rudimentary wing structure (haltere)
normally derived from T3. Most of the thorax of the fly,
including the wings and the dorsal part of the thorax, comes
from T2. (b) A wild-type fly with one copy of T2 and one of T3.
(c) A bithorax triple mutant homozygote completely transforms
T3 into a second copy of T2. Note the second dorsal thorax
and second pair of wings (T2 structures) and the absence of
the halteres (T3 structures). [From E. B. Lewis, Nature 276,

1978, 565. Photographs courtesy of E. B. Lewis. Reprinted by
permission of Nature. Copyright 1978 by Macmillan Journals Ltd.]

(a) SCR (b) ANTP

(c) UBX (d) ABD-B

lab pb Dfd Scr Antp Ubx Abd-A Abd-B


Figure 18-25 Homeotic gene expression in Drosophila. Photomicrographs of embryos that
exhibit protein expression patterns encoded by homeotic genes in Drosophila. (a – d) The
anterior boundary of homeotic gene expression is ordered from SCR (most anterior) to ANTP,
UBX, and ABD-B (most posterior). (e) This order is matched by the linear arrangement of
the corresponding genes along chromosome 3. [Parts a and b from T. C. Kaufman, Indiana

University. Parts c and d from S. Celniker and E. B. Lewis, California Institute of Technology.]


44200_18_p575-610 3/17/04 1:34 PM Page 597

18.6 Refining the pattern 597

Figure 18-26 Hierarchical cascade that activates

Egg with maternally Anterior Posterior the elements forming the A – P segmentation pattern
in Drosophila. The maternally derived bcd and nos
deposited mRNA

mRNAs are located at the anterior and posterior

bcd nos poles, respectively. Early in embryogenesis, these
mRNA mRNA mRNAs are translated to produce a steep
anterior – posterior gradient of BCD transcription

factor. The posterior – anterior gradient of NOS

Gradients of proteins inhibits translation of hb-m mRNA, thereby
encoded by maternal mRNA NOS creating a shallow anterior – posterior gradient of

BCD HB-M transcription factor (shown as an arrow).

The gap genes, which are the A – P cardinal

HB-M genes, are activated in different parts of the

KNI embryo in response to the anterior – posterior

Homeotic gradients of the two factors BCD and
Gap HB-M. (The posterior band of HB-Z expression
gives rise to certain internal organs, not to
segments.) The correct number of segments is

HB-Z determined by activation of the pair-rule genes in

KR a zebra-stripe pattern in response to the gap-

gene-encoded transcription factors. The segment-

polarity genes are then activated in response to

the activities of the several pair-rule proteins,

leading to further refinement of the organization

within each segment. The correct identities of the

Pair-rule SCR segments are determined by
proteins expression of the homeotic

H RUN genes due to direct regulation

Segment- by the transcription factors
proteins encoded by the gap genes.

WG EN [After J. D. Watson, M. Gilman,
Segment Number
J. Witkowski, and M. Zoller,

ANTP UBX ABD-A ABD-B Recombinant DNA, 2d ed.

Copyright 1992 by James D.

Watson, Michael Gilman,

Jan Witkowski, and Mark Zoller.]

Segment Identity

accordingly to execute the increasingly finer subdivisions Such positive-feedback loops may operate entirely
of the embryo, establishing both segment number and within a cell. In several tissues, positive-feedback loops
segment identity (Figure 18-26). are established in which the homeodomain protein that
is expressed binds to enhancer elements in its own
18.6 Refining the pattern gene, ensuring that more of that homeodomain protein
will continue to be produced (Figure 18-27a).
The principles delineated in the preceding sections lay out
initial fates, but additional mechanisms must be in place to In other cases, the memory system requires cell-to-
ensure that all aspects of patterning are elaborated. Some cell interactions (Figure 18-27b). For example, among
of these mechanisms are considered in this section. the segment-polarity genes, adjacent cells express the
WG (wingless) and EN (engrailed) proteins. The EN
Memory systems for remembering cell fate protein is a transcription factor that activates the gene
encoding the molecule HH (hedgehog) in the same
Patterning decisions frequently need to be maintained in cells. HH is a protein-signaling molecule that is se-
a cell lineage for the lifetime of the organism. This re- creted from the cell and binds to a receptor on the
quirement is certainly true of the segment-polarity and surface of the WG-expressing cell. It thereby induces
homeotic gene expression patterns that are set up by the a signal-transduction cascade in the WG-expressing
A – P patterning system. The key is that patterning deci- cell, activating wingless gene expression and causing
sions are maintained through positive-feedback loops. more WG protein to be expressed. Similarly, WG is a

44200_18_p575-610 3/17/04 1:34 PM Page 598

598 Chapter 18 • The Genetic Basis of Development

(a) Transcription factor (b) Cell B Cell A

Signal B Receptor
for signal B

mRNA Nuclear Signal B TFA
Nascent transcript membrane TFB Signal A

Enhancer Receptor
for signal A
Figure 18-27 Two types of positive-feedback loops that maintain
the level of activity of transcription factors that determine cell fate. Signal A
(a) The transcription factor binds to an enhancer of its own gene,
maintaining its transcription. (b) Each adjacent cell sends out a
signal (different signals from each cell) that activates receptors,
signal-transduction pathways, and transcription-factor (TF)
expression in the other cell. This activation leads to a mutual
positive-feedback loop between the cells.

secreted protein that activates engrailed expression in side of the reproductive tract of the nematode C. elegans
the adjacent cell, inducing more EN protein in that cell. (Figure 18-28). One type is the ability of one cell to in-
duce a developmental commitment in only one neigh-
MESSAGE When the fate of a cell lineage has been boring cell, and the other is the ability of a cell to inhibit
established, it must be remembered. This is accomplished its immediate neighbors from adopting its fate.
by intracellular or intercellular positive-feedback loops.
Vulva development has been studied in detail
Ensuring that all fates are allocated: through the analysis of C. elegans mutants that have ei-
decisions by committee ther no vulva or more than one. Within the hypodermis
(the body wall of the worm), several cells have the po-
Ultimately, for a developmental field to mature into a tential to build certain parts of the vulva. Initially, all
functional organ or tissue, cells must be committed in these cells can adopt any of the required roles and so are
appropriate numbers and locations to the full range of called an equivalence group — in essence, a developmen-
functions that are needed. Cell-to-cell interactions en- tal field. To make an intact vulva, one of the cells must
sure that these proper allocations are made. Here, we fo- become the primary vulva cell, and two others must be-
cus on two types of interactions, both of which operate come secondary vulva cells; yet others become tertiary
in the development of the vulva, the opening to the out- cells that contribute to the surrounding hypodermis
(Figure 18-29a and b).

Pharynx Ovary Rectum
Intestine Eggs
Oviduct Oocytes Uterus Vulva

Figure 18-28 Adult Caenorhabditis elegans. Photomicrograph and drawing of an
adult hermaphrodite, showing various organs readily identified by their location. Note
the position of the vulva midway along the anterior – posterior axis of the worm.

[From J. E. Sulston and H. R. Horvitz, Developmental Biology 56, 1977, 111.]

44200_18_p575-610 3/17/04 1:34 PM Page 599

18.6 Refining the pattern 599

Figure 18-29 Production of the (a) Tissue derived from 1°, 2°, and 3° cells
C. elegans vulva by cell-to-cell
interactions. (a) The parts of the 3° Uterus 3°
vulva anatomy occupied by the Hypodermis Hypodermis
descendants of primary, secondary, 1°
and tertiary cells. (b) The primary, (b) Pedigrees of cells 2° 2°
secondary, and tertiary cell types are 1° vulva cell
distinguished by the cell-division Vulva
patterns that they undergo. (c) Early
in development, there is no signal 2° vulva cell 3° cell
from the anchor cell, and all the
cells are in the default tertiary cell lr lr N l r ap ap l Left
state. (d) Later in development, the lr lr r Right
anchor cell sends a signal that N No division
activates a receptor tyrosine kinase a Anterior
signal-transduction cascade. The p Posterior
cell nearest the anchor cell receives
the strongest signal and becomes (c) Early in development—no signal
the primary vulva cell. It then sends Anchor cell
out lateral inhibition signals to its
neighbors, preventing them from
also becoming primary vulva cells
and shunting them into the
secondary vulva cell pathway.

[Part b from R. Horvitz and P. Sternberg,

Nature 351, 1991, 357. Parts a, c,

and d after I. Greenwald, Trends in

Genetics 7, 1991, 366.]

(d) Subsequent signaling Anchor cell
Inductive signal

3° 3° 2° 1° 2° 3°

Lateral inhibitory signals

The key to allocating the different roles to these from similarly interpreting the anchor-cell signal, thus
cells is another single cell, called the anchor cell, which preventing them from also adopting the primary role.
lies underneath the cells of the equivalence group This process of lateral inhibition leads these neighboring
(Figure 18-29c). The anchor cell secretes a polypeptide cells to adopt the secondary fate. The remaining cells of
ligand that binds to a receptor tyrosine kinase (RTK) the equivalence group develop as tertiary cells and con-
present on all the cells of the equivalence group. Only tribute to the hypoderm surrounding the vulva. For each
the cell that receives the highest level of this signal (the of the three cell types into which the equivalence group
equivalence-group cell nearest the anchor cell) becomes develops, a specific constellation of activated transcrip-
a primary vulva cell. Only its signal-transduction path- tion factors typifies the state of the cell: primary, sec-
way is sufficiently triggered so that it in turn can activate ondary, or tertiary. Thus, through a series of intercellular
the transcription factors necessary to become a primary signals, a group of equivalent cells can develop into the
cell (Figure 18-29d). Thus we can say that the anchor three necessary cell types.
cell operates through an inductive interaction to commit
a cell to the primary vulva fate. MESSAGE Fate allocation can be made through a
combination of inductive and lateral inhibitory interactions
Having acquired its fate, the primary vulva cell between cells.
sends out a different signal to its immediate neighbors in
the equivalence group. That signal inhibits those cells

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600 Chapter 18 • The Genetic Basis of Development

18.7 The many parallels Perhaps the most striking finding is the similarity be-
in vertebrate and insect tween certain clusters of homeotic genes in mammals
pattern formation and Drosophila. In humans, the clusters of homeotic
genes are called Hox complexes. These clusters closely
How universal are the developmental principles uncov- resemble the insect ANT-C and BX-C homeotic gene
ered in Drosophila? Even now, the type of genetic analy- clusters, collectively called the HOM-C (homeotic gene
sis possible in Drosophila is not feasible in most other complex) (Figure 18-30). The ANT-C and BX-C clus-
organisms, at least not without a huge investment to ters, which are far apart on chromosome 3 of Drosophila,
develop comparable genetic tools and to breed and are together in one cluster in more primitive insects
maintain colonies of larger animals. However, in the past such as the flour beetle Tribolium castaneum. This indi-
two decades, recombinant DNA technology has pro- cates that there is only one homeotic gene cluster —
vided the necessary tools. One important approach is HOM-C — in insects and that, in the evolution of the
simply to use the power of DNA-DNA hybridization to Drosophila lineage, it was separated into two clusters.
fish out cognate genes from a different organism. If Moreover, as noted in Figure 18-25e, the genes of the
genomes have been sequenced, then it is a simple matter HOM-C cluster are arranged on the chromosome in an
to use the computer to find the gene in question. Some order that is colinear with their spatial pattern of ex-
of the most spectacular and unexpected parallels have pression: the genes at the left-hand end of the complex
come from comparing early fly and mouse development, are transcribed near the anterior end of the embryo;
given that the evolutionary distance between fly and rightward along the chromosome, the genes are tran-
mammal is so great. scribed progressively more toward the posterior (com-
pare Figure 18-30a and b).

(a) Directions of transcription of HOM-C genes

Insect lab pb Dfd Scr Antp Ubx abdA AbdB
homeotic ANT-C BX-C


REGIONS 1 2 3 4 5 6 7 8 9 10 11 12 13

Hox A A1 A2 A3 A4 A5 A6 A7 A9 A10 A11 A13

Mammalian Hox B B1 B2 B3 B4 B5 B6 B7 B8 B9 Figure 18-30 Comparison of the
homeobox structures and functions of the
genes Hox C C4 C5 C6 C8 C9 C10 C11 C12 C13 insect and mammalian homeotic
genes. (a) The comparative
Hox D D1 D3 D4 D8 D9 D10 D11 D12 D13 anatomy of the HOM-C (insect)
3´ and Hox (mammalian) gene
5´ clusters. The genes of the HOM-C
are shown at the top. Each of the
Directions of transcription of Hox genes four paralogous (see text) Hox
clusters maps on a different
(b) Drosophila Mouse chromosome. Genes shown in the
Anterior Head same color are most closely
related to one another in
lab Hox 1 structure and function. (b) The
pb Hox 2 expression domains and regions
Dfd Hox 4 of the Drosophila and mouse
Hox 5–8 embryos that require the various
Antp group Hox 9 HOM-C and Hox genes. The color
(Scr, Antp, Ubx, scheme parallels that in part a.
Tail Note that the order of domains in
and abd-A) the two embryos is the same.

Abd-B [After H. Lodish, D. Baltimore,

Posterior A. Berk, S. L. Zipursky, P. Matsudaira,

and J. Darnell, Molecular Cell

Biology, 3d ed. Copyright Scientific

American Books, 1995.]

44200_18_p575-610 3/17/04 1:34 PM Page 601

18.7 The many parallels in vertebrate and insect pattern formation 601

Hox C8 Hox A6 Hox A3

Anteriormost vertebra expressing: 11th 8th 1st

Organs expressing: Kidney Lung Pharynx
Gut Trachea
Figure 18-31 Photomicrographs showing the RNA expression patterns of Gut
three mouse Hox genes in the vertebral column of a sectioned 12.5-day-old mouse

embryo. Note that the anterior limit of each of the expression patterns is different.

[From S. J. Gaunt and P. B. Singh, Trends in Genetics 6, 1990, 208.]

We still do not know why the insect genes are clus- The correlations between structure and expression
tered or organized in this colinear fashion, but, regard- pattern are further strengthened by consideration of mu-
less of the roles of these features, the same structural or- tant phenotypes. In vitro mutagenesis techniques permit
ganization — clustering and colinearity — is seen for the efficient gene knockouts in the mouse. Many of the Hox
equivalent genes in mammals, which are organized into genes have now been knocked out, and the striking re-
the Hox clusters (see Figure 18-30a). The major differ- sult is that the phenotypes of the homozygous knockout
ence between flies and mammals is that there is only mice are thematically parallel to the phenotypes of ho-
one HOM-C cluster in the insect genome, whereas there mozygous null HOM-C flies. For example, the Hox-C8
are four Hox clusters, each located on a different chro- knockout causes ribs to be produced on the first lumbar
mosome, in mammals. These four Hox clusters are paral- vertebra, L1, which is ordinarily the first nonribbed
ogous, meaning that the order of genes in each cluster is vertebra behind those vertebrae-bearing ribs (Figure
very similar, as if the entire cluster had been quadrupli- 18-32). Thus, when Hox C8 is knocked out, the L1 ver-
cated in the course of vertebrate evolution. Each of the tebra is homeotically transformed into the segmental
genes near the left end of each Hox cluster is quite sim- identity of a more anterior vertebra. To use geneticists’
ilar not only to the others, but also to one of the insect jargon, Hox C8 Ϫ has caused a fate shift toward anterior.
HOM-C genes at the left end of the cluster. Similar Clearly, this Hox gene seems to control segmental fate in
relations hold throughout the clusters. Finally, and most a manner quite similar to that of the HOM-C genes, be-
notably, the Hox genes are expressed so as to define cause, for example, a null allele of the Drosophila Ubx
segments in the developing somites (the segmental units gene also causes a fate shift toward anterior in which T3
of the developing spinal column) and central nervous and A1 are transformed into T2.
system of the mouse and presumably the human em-
bryos. Each Hox gene is expressed in a continuous block How can such disparate organisms—fly, mouse, hu-
beginning at a specific anterior limit and running poste- man (and C. elegans)—have such similar gene sequences?
riorly to the end of the developing vertebral column The simplest interpretation is that the Hox and HOM-C
(Figure 18-31). The anterior limit differs for different genes are the vertebrate and insect descendants of a homeo-
Hox genes. Within each Hox cluster, the leftmost genes box gene cluster present in a common ancestor some 600
have the most anterior limits. These limits proceed million years ago. The evolutionary conservation of the
more and more posteriorly in the rightward direction in HOM-C and Hox genes is not an unusual occurrence. In-
each Hox cluster. Overall, the Hox gene clusters appear deed, as we are beginning to compare whole genomes, we
to be arranged and expressed in an order that is strik- are finding that such evolutionary and functional conser-
ingly similar to that of the insect HOM-C genes (see vation seems to be the norm rather than the exception.
Figure 18-30b). For example, 60 percent of human genes associated with
a heritable disease have related genes in Drosophila.

44200_18_p575-610 3/17/04 1:34 PM Page 602 Chapter 18 • The Genetic Basis of Development


(a) (b)

Figure 18-32 Phenotype of a homeotic mutant mouse. Mice homozygous for a targeted
knockout of the Hox C8 gene were created by using cultured embryonic stem cells.
(a) An enlargement of the thoracic and lumbar vertebrae of a homozygous Hox C8Ϫ mouse.
Note the ribs coming from L1, the first lumbar vertebra. L1 in wild-type mice had no ribs.
(b) An unexpected second phenotype of the Hox C8Ϫ knockout: the homozygous mutant
mouse on the right has clenched fingers, whereas the wild-type mouse on the left
has normal fingers. [From H. Le Mouellic, Y. Lallemand, and P. Brulet, Cell 69, 1992, 251.]

MESSAGE Developmental strategies in animals are quite possible. How does the SRY product work? It is a DNA-
ancient and highly conserved. In essence, a mammal, a binding transcription factor that acts on genes in the un-
worm, and a fly are put together with the same basic building differentiated gonad, transforming it into a testis. If there
blocks and regulatory devices. Plus ça change, plus c’est la is no SRY product (as in normal XX females), then the
même chose! undifferentiated gonad develops into an ovary. Once a
testis has developed, the genes for testosterone synthesis
18.8 The genetics of sex are activated. Testosterone (androgen) is a steroid hor-
determination in humans mone that is responsible for male secondary sexual char-
acteristics such as body shape and body hair patterns —
An important part of development is the development the male phenotype.
of sex. Most animals and many plants show sexual di-
morphism and, in most of these cases, sex determination Leaving the testis, testosterone enters the blood-
is genetically “hardwired.” We will look at humans as stream, which transports it to target cells that will pro-
an example, while noting that there is a range of deter- duce the male characteristics. The hormone is lipid solu-
mination mechanisms quite different from that which ble, and so it passes straight through the membranes of
follows. However, in human sex determination, we will its target cells and enters the cytoplasm. It binds to a
see some developmental players that by now should be proteinaceous receptor called the androgen receptor, en-
familiar — notably, a toggle switch, wide-acting transcrip- coded by a gene called AR, which resides on the X chro-
tion factors, and cell-to-cell communication. mosome. Together, the testosterone and its bound recep-
tor enter the cell’s nucleus and act as a transcription
Follow this story by referring to Figure 18-33, which factor that turns on maleness genes. The AR protein is
shows sexual development in men. It is clear that the crucial to male sex determination. If AR is deleted or
key toggle switch is the gene on the short arm of the Y null in function, then the testosterone cannot act and no
chromosome called SRY (sex regulation on the Y ). The maleness results. Recall from Chapter 2 the X-linked
presence of SRY leads to maleness, whereas its absence recessive human variant called androgen insensitivity
leads to femaleness. Its importance is witnessed by the syndrome, this syndrome results from mutation of the
observation that if SRY is deleted or has null function, AR gene.
then an XY female results, and, conversely, if SRY is
translocated to another chromosome, then XX males are Hence we see two key genes that code for transcrip-
tion factors and a range of downstream “target genes”
both in the testis (primary sex) and in somatic cells that
will undergo secondary sexual differentiation.

44200_18_p575-610 3/17/04 1:34 PM Page 603

18.9 Do the lessons of animal development apply to plants? 603

Somatic cell Figure 18-33 Gene interaction
in sex determination in the
Testosterone- 6 Genes for secondary human male. The sequence of gene
pathway sexual characteristics action is numbered, starting with
genes synthesis of the SRY protein
in the gonad.
Receptor X
4 5


Germ cell


3 Genes for secondary
sexual characteristics



1 AR Testis-




18.9 Do the lessons of animal be considerably different from those encountered in ani-
development apply to plants? mal development.

The evidence emerging from the results of comparative An active area of plant developmental genetics re-
studies of pattern formation in a variety of animals indi- search utilizes a small flowering plant called Arabidopsis
cates that many important developmental pathways are thaliana as a model genetic system (see the Model Or-
ancient inventions conserved and maintained in many, if ganism box on the next page). The most intensively stud-
not all, animal species. The life history, cell biology, and ied developmental process in Arabidopsis is flower pat-
evolutionary origins of plants would, in contrast, argue tern formation. Just as the homeotic gene cluster controls
against the appearance of these same sets of pathways in segmental identity in animal development, a series of
the regulation of plant development. Plants have very transcriptional regulators determine the fate of the four
different organ systems from those of animals, depend layers (whorls) of the flower. The outermost whorl of the
on inflexible cell walls for structural rigidity, separate flower normally develops into the sepals; the next whorl,
germ line from soma very late in development, and are the petals; the next, the stamens; and the innermost de-
very dependent on light intensity and duration to trigger velops into the carpels (Figure 18-34). Several genes have
various developmental events. Certainly, plants use hor- been identified that, when knocked out or ectopically ex-
mones to regulate gene activity, to signal locally between pressed, transform one or more of these whorls into an-
cells by as yet unknown signals, and to create cell-fate other. For example, the gene AP1 (Apetala-1) causes the
differences by means of transcription factors. The gen- homeotic transformation of the outer two whorls into
eral themes for establishing cell fates in animals are the inner two. Analogously to the homeotic mutants in
likely to be seen in plants as well, but the participating animals, the number of whorls remains the same (four),
molecules in these developmental pathways are likely to but their identities are transformed. The study of the spa-
tial expression patterns and mutant phenotypes of the

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604 Chapter 18 • The Genetic Basis of Development

MODEL ORGANISM Arabidopsis thaliana

More than any other genetic model organism dis- and biochemical pathways. Finally, the genome of
cussed in this text, Arabidopsis is a product of the ge- Arabidopsis has been sequenced, and many tools, such
nomics era. It has a genome of only 120 megabase as insertional mutagenesis, exist for overlaying the
pairs of DNA that is organized into a haploid comple- genetic and transcriptional maps of this plant.
ment of five chromosomes (the diploid number is 10).
Thus, Arabidopsis genome size and complexity com- A single Arabidopsis plant. [Dan Tenaglia,
pare to those of the fruit fly, Drosophila melanogaster.]
In contrast, the genome of corn, a genetic model or-
ganism of long standing (see the Model Organism box
in Chapter 13), is about 2500 Mb, almost the same as
human. Another feature that makes Arabidopsis at-
tractive to geneticists is its rapid life cycle: it takes
only about 6 weeks for a planted seed to produce a
new crop of seed. Arabidopsis is also very small (see
the photo), growing to less than 10 cm. Its short
stature makes it easy to grow in the laboratory in cul-
ture tubes or on petri plates, and, because it is a self-
fertilizing plant, F2 mutagenesis screens can be per-
formed in a straightforward manner. Thus, geneticists
have obtained many mutations with interesting pheno-
types that affect a variety of developmental events

Stamen se
Carpel ca

pe st


se BB BB
(a) AA AA
pe st

Petal Sepal Flower gene-
expression pattern
(a) (b)
(b) A B C Gene class
Figure 18-34 Flower development in Arabidopsis thaliana.
(a) The mature products of the four whorls of a flower. Figure 18-35 Flower-identity gene expression and the
(b) A cross-sectional diagram of the developing flower, with establishment of whorl fate. (a) The patterns of gene expression
the normal fates of the four whorls indicated. From outermost corresponding to the different whorl fates. (b) The shaded
to innermost, they are sepal (se), petal (pe), stamen (st), and regions of the cross-sectional diagrams of the developing
carpel (ca). [Photograph courtesy of Vivian F. Irish; from V. F. Irish, flower indicate the gene expression patterns for genes of the
A, B, and C classes. Refer to Figure 18-34 for the normal
“Patterning the Flower,” Developmental Biology 209, 1999, anatomy of the developing flower. [From V. F. Irish, “Patterning

211 – 222.] the Flower,” Developmental Biology 209, 1999, 211 – 222.]

various flower-identity genes has produced a model in expression of the class A and class B genes. Stamen fate is
which whorl fate is established through the combinator- established through the action of transcription factors
ial action of multiple transcription factors (Figure 18-35). produced by simultaneous expression of class B and class
Thus, sepal (outermost whorl fate) is established through C genes. Finally, carpel fate is established through the ac-
the action of transcription factors expressed by genes of tion of transcription factors expressed by class C genes.
the class A type only. Petal fate is established through the Just as the homeotic segment-identity genes in animals
action of transcription factors produced by simultaneous encode a series of structurally related (homeodomain-

44200_18_p575-610 3/24/04 10:49 AM Page 605

18.10 Genomic approaches to understanding pattern formation 605

containing) transcription factors, the flower-identity genes covering these elements, is only one approach. Many
encode a series of structurally related transcription factors genes, for one reason or another, participate in processes
called MADS transcription factors, found in all eukaryotic of interest to us but cannot be detected by mutational
kingdoms. (The word MADS is composed of the first let- inactivation. For example, we now know that many gene
ters of the names of four prototypic member genes of this functions are redundant, with more than one gene in the
family.) Thus, although different in detail, the overall genome contributing to that function. Knock out one of
strategy of differentially expressed transcription factors is the genes and the product of the other is sufficient to
one of the approaches by which plant cell fate is estab- produce a normal phenotype. How then can we identify
lished. With its combination of sophisticated genetics and these pieces of the puzzle?
genomics, findings from studies of Arabidopsis pattern
formation should reveal much about the ways in which One way is by detecting expression in interesting pat-
plants develop. terns along one of the body axes. However, the gene-by-
gene approach that a geneticist might use is quite tedious,
18.10 Genomic approaches to given that the fly genome (for example) has about 15,000
understanding pattern formation genes. Instead, with some genetic tricks, we can use tran-
scriptional profiling with expression microarrays to effi-
The key to the study of a pathway or network such as ciently screen for such mutations. Here’s a recent exam-
the formation of one of the body axes is to know all of ple. A Drosophila research group was interested in
the participating elements. Mutational analysis, though studying genes that might be positively or negatively regu-
it has proved to be very powerful as a way of first un- lated by the DL protein, the protein that is distributed in a
gradient along the D – V axis of the Drosophila embryo.
Embryos were studied from mothers who were mutant

High maternal Maternal mutants No maternal
[DL] [DL]
Low maternal

Ventral Ventral Lateral Dorsal Figure 18-36
expression expression expression Examples of early
(mesoderm) (neural and (epidermis) embryonic expression
patterns of genes
) found in a microarray
profiling experiment
searching for new DL-
regulated genes.
Maternal mutants
showing high, low, or
no DL concentrations
revealed three
different sets of
target genes with
either ventral, lateral,
or dorsal expression.

[From A. Stathopoulo,

M. Van Drenth,

A. Erives, M. Markstein,

and M. Levine, Cell

111, 2002, 694.

Copyright 2002 by

Cell Press.]

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606 Chapter 18 • The Genetic Basis of Development

for one of three different genes that resulted in embryos two-hybrid analysis has been used to make protein inter-
that had high, low, or no concentrations of DL protein. action maps that expand and refine the Drosophila body
plan networks obtained by mutational analysis.
Preparations of mRNA from each of these three
maternal genotypes were hybridized to microarrays con- This is just one of many applications of high-
taining every gene in the Drosophila genome, and hy- throughput techniques for systematically screening an
bridization patterns were compared. A total of 40 new entire genome for genes of interest that can then be in-
genes were found that were activated or repressed by tensively analyzed to help tease apart an entire develop-
the DL protein, increasing the number of known DL mental pathway. This approach does not invalidate the
target genes by 500 percent. In follow-up experiments, utility of direct mutational screens; rather it is a power-
the research group was able to show that, indeed, these ful complementary approach. Neither approach alone
genes were expressed in the early embryo in domains will identify all of the relevant genes, but, together, they
corresponding to the germ layers along the D – V axis will contribute to a much more complete picture of de-
(Figure 18-36). In another approach, high throughput velopmental processes.

KEY QUESTIONS REVISITED • Do cells participate in single or multiple decision-
making processes?
• What sequence of events produces the basic body
plan of an animal? Multiple: for example, a cell must deal with its position
on the A – P and D – V axes at the same time.
Starting with a totipotent cell, genetic mechanisms pro-
duce descendent cells with different genetic fates. These • What role does cell-to-cell communication play in
fates are progressively subdivided so that the normal building the basic body plan?
set of organs results, each with its own pattern of gene
expression. It further refines cell fate within the general broad de-
velopmental fields.
• How are polarities that give rise to the main body
axes created? • Are the pathways for building biological pattern
conserved among distant species?
Both anterior – posterior and dorsal – ventral axes are
established by gradients of molecules laid down in or Yes, to a greater or lesser degree, depending on the or-
around the egg by the organism’s mother. ganism. The HOM and Hox genes of flies and mammals
are homologous and act in similar ways to determine
• How do cells recognize their locations along the body plan. Transcription-factor gradients are at work in
developing body axes? both plants and animals. All organisms use genetic
switches of various kinds.
Position is manifest as a specific pattern of transcription
factors that activate different sets of cardinal genes that
define developmental domains.

SUMMARY tablished along each of the major body axes leads to dif-
ferential expression of transcription factors along each
A programmed set of instructions in the genome of a axis. The targets of these transcription factors are regula-
higher organism establishes the developmental fates of tory elements of cardinal genes. Typically, these cardinal
cells with respect to the major features of the basic body genes are themselves transcription factors or they are an-
plan. These instructions eventually produce a fine- other class of molecule that activates other transcription
grained mosaic of different cell types deployed in the factors. The activation of cardinal genes begins the
proper spatial pattern. process of subdividing the animal into a series of
coarsely defined developmental domains.
The zygote is totipotent, giving rise to every adult
cell type. As development proceeds, successive decisions These coarse patterns are refined by a multistep
restrict each cell and its descendants (a lineage) to its process. Cells communicate patterning information
particular fate. The first developmental decisions are among themselves by using intercellular signaling sys-
very coarse. Gradients of maternally derived regulatory tems to ensure that the developing structure (embryo,
proteins establish polarity along the major body axes. In tissue, organ) operates coherently.
all cases that have been well described, the intrinsic po-
larity of the cytoskeletal system underlies the establish- The same basic set of genes identified in Drosophila
ment of this primary positional information within the and the regulatory proteins that they encode are con-
embryo. Ultimately, the positional information that is es-

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Solved problems 607

served in mammals and appear to govern major develop- late development in plants are different from those in
mental events in many — perhaps all — higher animals. It animals, but many of the same themes are seen in plant
is fair to say that the majority of genes in the metazoan and animal development. In both plants and animals,
genome are common to most members of the animal transcription factors and signaling systems are exploited
kingdom. The take-home message is that the basic path- to create pattern. However, because of the ancient phy-
ways that underlie pattern formation are ancient and are logenetic split between plants and animals and because
exploited in many different ways to produce animals the life strategies of plants and animals are dramatically
that are superficially very different from one another. different, it is not surprising that different molecules ful-
However, there are limits to the generality of the de- fill the parallel roles.
tailed mechanisms. The underlying molecules that regu-

KEY TERMS germ layer (p. 583) microtubule (p. 578)
homeodomain protein (p. 595) pair-rule gene (p. 595)
anchor cell (p. 599) homeosis (p. 595) paralogous (p. 601)
binary fate decision (p. 578) homeotic gene complex (p. 595) pole cell (p. 582)
cardinal gene (p. 591) inductive interaction (p. 599) positional information (p. 577)
cell fate (p. 577) lateral inhibition (p. 599) segment (p. 583)
cytoskeleton (p. 578) maternal-effect gene (p. 583) totipotent (p. 578)
developmental field (p. 577) maternal expression (p. 583)
equivalence group (p. 598) microfilament (p. 578)
fate refinement (p. 578)
gap gene (p. 593)

SOLVED PROBLEMS b. Diagram the relative expression patterns of
mRNAs from the gap genes Kr and kni in blastoderm
1. The anterior determinant in the Drosophila egg is embryos derived from bcd monosomic, trisomic, and
bcd. A mother heterozygous for a bcd deletion has hexasomic mothers.
only one copy of the bcdϩ gene. With the use of
P elements to insert copies of the cloned bcdϩ Solution
gene into the genome by transformation, it is possi-
ble to produce mothers with extra copies of the a. The determination of anterior – posterior parts of the
gene. Shortly after the blastoderm has formed, the embryo is governed by a concentration gradient of BCD.
Drosophila embryo develops an indentation called The furrow develops at a critical concentration of bcd.
the cephalic furrow that is more or less perpendicu- As bcdϩ gene dosage (and, therefore, BCD concentra-
lar to the longitudinal body axis. In the progeny of tion) decreases, the furrow shifts anteriorly; as the gene
bcdϩ monosomics, this furrow is very close to the an- dosage increases, the furrow shifts posteriorly.
terior tip, lying at a position one-sixth of the distance
from the anterior to the posterior tip. In the progeny b. hb Kr kni
of standard wild-type diploids (disomic for bcdϩ), the
cephalic furrow arises more posteriorly, at a position (high bcd (intermediate (low bcd
one-fifth of the distance from the anterior to the
posterior tip of the embryo. In the progeny of bcdϩ expression) bcd expression) expression)
trisomics, it is even more posterior. As additional
gene doses are added, the cephalic furrow moves 2n Ϫ 1
more and more posteriorly, until, in the progeny of
hexasomics, the it is midway along the A – P axis of 2n
the embryo.
2n ϩ 1
a. Explain the gene-dosage effect of bcdϩ on the 2n ϩ 4
formation of the cephalic furrow in relation to
the contribution that bcd makes to A – P pattern 2. In developmental pathways, the crucial events seem to
formation. be the activation of master switches that set in mo-
tion a programmed cascade of regulatory responses.

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608 Chapter 18 • The Genetic Basis of Development

Identify the master switches and explain how they b. How would you trace the formation of different
operate in sex determination in mammals. fetal membranes?

Solution Solution

In mammalian sex determination, the master switch is a. We must have markers that enable us to distinguish
the presence or absence of the SRY gene, which is ordi- different cell lineages, which can be done with mice by
narily located on the Y chromosome. In the presence using strains that differ in chromosomal or biochemical
of the protein product of this gene, which acts as a markers. (Other ways would be to use differences in sex
DNA-binding protein, certain cells of the gonad (Leydig chromosomes of XX and XY cells or to induce chromo-
cells) synthesize androgens, male-inducing steroid hor- some loss or aberrations by irradiating embryos.)
mones. These hormones are secreted into the blood-
stream and act on target tissues to induce the transcription- When you have decided on the marker difference
factor activity of the androgen receptors. In the absence to be used, one way to approach the design is to inject
of androgen-receptor activation, development proceeds a single cell from one of two strains into embryos of
along the default pathway leading to female develop- the other strain at various developmental stages. An-
ment. The factors that activate SRY expression in the other approach is to fuse embryos of defined cell
testis are not understood. Because the master switch numbers from the two strains. In either case, you
here is the actual presence or absence of the SRY gene would inspect the embryos when the ICM and mem-
itself, it is likely that the regulatory molecules that branes are distinct and recognizable. When cell inser-
activate SRY are present in the indifferent gonad early in tion or fusion results in membranes and an ICM that
development. are exclusively made up of one cell type and never a
mosaic of the two, the two developmental fates have
3. In the embryogenesis of mammals, the inner cell mass, been set.
or ICM (the prospective fetus), quickly separates
from the cells that will serve as enclosing membranes b. Carry out the same injection or fusion experiment on
and respiratory, nutritive, and excretory channels be- early embryos. Now look for the pattern of mosaicism.
tween the mother and the fetus. Correlate the presence of cells of similar genotype in
different membranes. It should be possible to determine
a. Design experiments using mosaics in mice to the lineage of cells in each set of membranes.
determine when the two fates are decided.

PROBLEMS 8. Describe briefly the experimental way that the bi-
coid gradient in Figure 18-10a was demonstrated.
1. In what ways does the cytoskeleton resemble and 9. If you swapped the 5Ј UTRs of bicoid and nanos,
what might you predict would be the effect on their
not resemble a body skeleton? gradients?

2. In what sense is a microfilament polar? 10. For what purpose is the cephalic furrow being used
in the experiment in Figure 18-13?
3. If you were describing to a nonbiologist the trans-
port of a cargo along a microtubule, what everyday 11. In which part of the cells is the DL protein found in
analogy would be most suitable? (“It is like . . .”) the dorsal region of the Drosophila blastoderm?

4. In C. elegans, how many cell divisions of the zygote 12. What is the prerequisite for the DL protein to enter
are necessary to give rise to the cell that will become a nucleus?
the precursor to the germ line? Why this number?
13. Gooseberry, runt, knirps, and antennapedia. To a
5. A rough translation of the word syncitium is “cells Drosophila geneticist what are they? How do they
together.” Is it a good word to use to describe the differ?
Drosophila syncitium?
14. Describe the expression pattern of the Drosophila
6. Draw a graph that represents a Drosophila syncitium gene eve in the late blastoderm.
with two opposing pole-high gradients.
15. Contrast the function of homeotic genes with pair-
7. Describe the practical details of an experiment in rule genes.
which you would create and demonstrate a gradient
of a molecule in solution.

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Problems 609

16. What do geneticists mean when they say that cells Fertilized egg
“communicate”? AB P1

17. What is the difference between the cell communica- ABa ABp EMS P2
tion action of the anchor cell and that of the pri-
mary cell in the development of the C. elegans MS E
a. It is possible to move these cells around during
18. What is the “ancestor” of the Hox gene B6 in the development. When the positions of ABa and ABp
Drosophila HOM set? are physically interchanged, the cells develop ac-
cording to their new position. In other words, the
19. In the human maleness-determining system, what cell that was originally in the ABa position now
do you think regulates transcription of SRY (if any- gives rise to one body-wall muscle cell, whereas the
thing)? cell that was originally in the ABp position now
gives rise to three pharyngeal muscle cells. What
20. In Arabidopsis flowers, what would be the flower does that tell us about the developmental processes
whorls in mutants that had no B gene transcripts at controlling the fates of ABa and ABp?
b. If EMS is ablated (by heat inactivation with a
21. XYY humans are fertile males. XXX humans are laser beam aimed through a microscope lens), no AB
fertile females. What do these observations reveal descendants make muscles. What does that suggest?
about the mechanisms of sex determination and
dosage compensation? c. If P2 is ablated, all AB descendants turn into
muscle cells. What does that suggest?
22. Occasionally, there are humans who are mosaics of
XX and XY tissue. They generally exhibit a uniform (Diagram from J. Priess and N. Thomson, Cell 48, 1987,
sexual phenotype. Some of them are phenotypically 241.)
female, others male. Explain these observations in
regard to the mechanism of sex determination in 27. When an embryo is homozygous mutant for the gap
mammals. gene Kr, the fourth and fifth stripes of the pair-rule
gene ftz (counting from the anterior end) do not
23. How are the gradients of BCD and HB-M estab- form normally. When the gap gene kni is mutant,
lished during early embryogenesis in Drosophila? the fifth and sixth ftz stripes do not form normally.
What is the role of the cytoskeleton in this process? Explain these results in regard to how segment
number is established in the embryo.
24. What are the similarities between DL/CACT in
Drosophila and Rb/E2F (see Chapter 17)? 28. The Drosophila embryo has a polarity that is devel-
oped through the action of maternal genes that
25. In C. elegans vulva development, one anchor cell in are expressed in the developing egg follicle in the
the gonad interacts with six equivalence-group cells ovary. Mothers homozygous for a nanos mutation
(cells with the potential to become parts of the produce embryos that lack posterior segments. How-
vulva). The six equivalence-group cells have three ever, these embryos do not display a mirror-image
distinct phenotypic fates: primary, secondary, and anterior (bicephalic) pattern. In contrast, mothers
tertiary. The equivalence-group cell closest to the homozygous for a bicoid mutation produce embryos
anchor cell develops the primary vulva phenotype. If that not only lack anterior segments but also dis-
the anchor cell is ablated, all six equivalence-group play a mirror-image posterior (bicaudal) pattern.
lineages differentiate into the tertiary state. Explain these observations in relation to the roles of
nanos, bicoid, and hunchback in anterior – posterior
a. Set up a model to explain these results. axis formation.

b. The anchor cell and the six equivalence-group 29. For many of the mammalian Hox genes, some of
cells can be isolated and grown in vitro; design an them have been shown to be more similar to one of
experiment to test your model. the insect HOM-C genes than to the others. De-
scribe an experimental approach by using the tools
26. There are two types of muscle cell in C. elegans: of molecular biology that would enable you to
pharyngeal muscles and body-wall muscles. They demonstrate this.
can be distinguished from each other, even as single
cells. In the following diagram, letters designate par-
ticular muscle precursor cells, black triangles (᭡) are
pharyngeal muscles, and white triangles (᭝) are
body-wall muscles.

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610 Chapter 18 • The Genetic Basis of Development

CHALLENGING PROBLEMS 33. In the Drosophila embryo, the 3Ј untranslated regions
(3Ј UTRs) of the mRNAs [the regions between the
30. a. When you remove the anterior 20 percent of the translation-termination codons and the poly(A) tails]
cytoplasm of a newly formed Drosophila embryo, are responsible for localizing bcd and nos to the ante-
you can cause a bicaudal phenotype, in which there rior and posterior poles, respectively. Experiments
is a mirror-image duplication of the abdominal seg- have been done in which the 3Ј UTRs of bcd and nos
ments. In other words, from the anterior tip of the have been swapped. Suppose that we make P-element
embryo to the posterior tip, the order of segments is transformation constructs with both swaps (nos
A8-A7-A6-A5-A4-A4-A5-A6-A7-A8. Explain this mRNA with bcd 3Ј UTR and bcd mRNA with nos 3Ј
phenotype in regard to the action of the anterior UTR) and transform them into the Drosophila
and posterior determinants and how they affect gap- genome. We then make a female that is homozygous
gene expression. mutant for bcd and nos and carries both swap con-
structs. What phenotype would you expect for her
b. Females homozygous for the maternally acting embryos in regard to A – P axis development?
mutation nanos (nos) produce embryos in which the
abdominal segments are absent and in which the 34. a. If you had a mutation affecting anterior –
head and thoracic segments are broad. In regard to posterior patterning of the Drosophila embryo in
the action of the anterior and posterior determinants which every other segment of the developing mu-
and gap-gene action, explain how nos produces this tant larva was missing, would you consider it a
mutant phenotype. In your answer, explain why there mutation in a gap gene, a pair-rule gene, a segment-
is a loss of segments rather than a mirror-image polarity gene, or a segment-identity gene?
duplication of anterior segments.
b. You have cloned a piece of DNA that con-
31. The three homeodomain proteins ABD-B, ABD-A, tains four genes. How could you use the spatial-
and UBX are encoded by genes within the BX-C of expression pattern of their mRNA in a wild-type
Drosophila. In wild-type embryos, the Abd-B gene is embryo to identify which represents a candidate
expressed in the posterior abdominal segments, gene for the mutation described in part a?
Abd-A in the middle abdominal segments, and Ubx
in the anterior abdominal and posterior thoracic seg- c. Assume that you have identified the candidate
ments. When the Abd-B gene is deleted, Abd-A is gene. If you now examine the wild-type spatial-
expressed in both the middle and the posterior ab- expression pattern of its mRNA in an embryo ho-
dominal segments. When Abd-A is deleted, Ubx is mozygous mutant for the gap gene Krüppel, would you
expressed in the posterior thorax and in the anterior expect to see a normal expression pattern? Explain.
and middle abdominal segments. When Ubx is
deleted, the patterns of Abd-A and Abd-B expression 35. You have in your possession wild-type and bicoid
are unchanged from wild type. When both Abd-A mutant strains. You also have cloned cDNAs for
and Abd-B are deleted, Ubx is expressed in all seg- nanos and bicoid. These plasmids are as follows:
ments from the posterior thorax to the posterior
end of the embryo. Explain these observations, tak- plasmid 1 full-length nanos cDNA
ing into consideration the fact that the gap genes plasmid 2
control the initial expression patterns of the plasmid 3 full-length bicoid cDNA
homeotic genes.
plasmid 4 bicoid 5Ј UTR–bicoid
32. In considering the formation of the A – P and ORF–nanos 3Ј UTR
D – V axes in Drosophila, we noted that, for mu- plasmid 5
tations such as bcd, homozygous mutant mothers uni- nanos 5Ј UTR-bicoid
formly produce mutant offspring with segmentation ORF–bicoid 3Ј UTR
defects. This outcome is always true regardless of whether
the offspring themselves are bcdϩ/bcd or bcd/bcd. Some nanos 5Ј UTR-bicoid
other maternal-effect lethal mutations are different, in ORF–nanos 3Ј UTR
that the mutant phenotype can be “rescued” by intro-
ducing a wild-type allele of the gene from the father. In where UTR ϭ untranslated region and ORF ϭ open
other words, for such rescuable maternal-effect lethals, reading frame (protein-coding region).
mutϩ/mut animals are normal, whereas mut/mut animals
have the mutant defect. Rationalize the difference be- The plasmids are constructed so that you can
tween rescuable and nonrescuable maternal-effect lethal generate a synthetic mRNA corresponding to the se-
mutations. quences described in each cDNA. Describe how you
could use these mRNAs to determine that bicoid
mRNA localization is due to its 3’ UTR.

36. What Arabidopsis genotypes would have

a. only carpels?
b. no carpels?

44200_19_p611-642 3/23/04 11:10 AM Page 611




• How much genetic variation is there in
natural populations of organisms?

• What are the effects of patterns of mating
on genetic variation?

• What are the sources of the genetic
variation that is observed in populations?

• What are the processes that cause changes
in the kind and amount of genetic variation
in populations?


19.1 Variation and its modulation
19.2 Effect of sexual reproduction on variation
19.3 Sources of variation
19.4 Selection
19.5 Balanced polymorphism
19.6 Random events

Shell-color polymorphism in Liguus fascitus. [From David Hillis,
Journal of Heredity, July – August 1991.]


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612 Chapter 19 • Population Genetics

CHAPTER OVERVIEW 2. The changes in population composition due to
migration of individuals between populations.
So far in our investigation of genetics, we have been
concerned with processes that take place in individ- 3. The rate of introduction of new genetic variation
ual organisms and cells. How does the cell copy DNA, into the population by mutation, which brings in
and what causes mutations? How do the mechanisms of new alleles at loci.
segregation and recombination affect the kinds and pro-
portions of gametes produced by an individual organ- 4. The production of new combinations of characters
ism? How is the development of an organism affected by recombination, which reassorts combinations of
by the interactions between its DNA, the cell machinery alleles at different loci.
of protein synthesis, cellular metabolic processes, and
the external environment? But organisms do not live 5. The changes in population composition due to the
only as isolated individuals. They interact with one an- effect of natural selection. Different genotypes may
other in groups, populations, and there are questions have differential rates of reproduction, and
about the genetic composition of those populations that genetically different offspring may have differential
cannot be answered only from a knowledge of the basic chances of survival.
individual-level genetic processes. Why are the alleles of
the protein Factor VIII and Factor IX genes that cause a 6. The consequences of random fluctuations in the
failure of normal blood clotting, hemophilia, so rare in actual reproductive rates of different genotypes.
all human populations, whereas the allele of the hemo- Because any given individual has only a few
globin ␤ gene that causes sickle-cell anemia is very com- offspring and the total population size is limited,
mon in some parts of Africa? What changes in the fre- genetic ratios from meiosis are never exactly as
quency of sickle-anemia are to be expected in the predicted by theory in real families and real
descendants of Africans in North America as a conse- populations. This random fluctuation causes genetic
quence of the change in environment and of the inter- drift in allele frequencies from generation to
breeding between Africans and Europeans and Native generation.
Americans? What genetic changes occur in a population
of insects subject to insecticides generation after genera- 19.1 Variation and its
tion? What is the consequence of an increase or decrease modulation
in the rate of mating between close relatives? All are
questions of what determines the genetic composition of Population genetics is both an experimental and a theo-
populations and how that composition may be expected retical science. On the experimental side, it provides de-
to change in time. These questions are the domain of scriptions of the actual patterns of genetic variation
population genetics. among individuals in populations and estimates the rates
of the processes of mating, mutation, recombination,
MESSAGE Population genetics relates the processes of natural selection, and random variation in reproductive
individual heredity and development to the genetic rates. On the theoretical side, it makes predictions of
composition of populations and to changes in that composition how the genetic composition of populations can be ex-
over time and space. pected to change as a consequence of the various forces
operating on them.
The genetic composition of a population is the col-
lection of frequencies of different genotypes in the pop- Observations of variation
ulation. These frequencies are the consequence of
processes that act at the level of individual organisms to Studies of population genetics have been able to explore
increase or decrease the number of organisms of each only limited sets of characters, because of the need for a
genotype. To relate the basic individual-level genetic simple relationship between phenotypic and genotypic
processes to population genetic composition, we must variation. The relation between phenotype and genotype
investigate the following phenomena (Figure 19-1): varies in simplicity depending on the character that is
observed. At one extreme, the phenotype of interest
1. The effect of mating patterns on different genotypes may be the mRNA or polypeptide encoded by a stretch
in the population. Individuals may mate at random, of the genome. At the other extreme lie the bulk of
or they may mate preferentially with close relatives characters of interest to plant and animal breeders and
(inbreeding) or preferentially with individuals of to most evolutionists — the variations in yield, growth
similar or dissimilar genotype or phenotype rate, body shape, metabolic rate, and behavior that con-
(assortative mating). stitute the obvious differences between varieties and
species. These characters have a very complex relation
to genotype. There is no allele for being 5'8" or being
5'4" tall. Such differences, if they are a consequence of

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19.1 Variation and its modulation




Assortative mating


Genetic drift

Natural selection

Figure 19-1 Overview of the phenomena that cause genetic change in populations. We begin with
two phenotypically uniform populations, into which variation is introduced by mutation. Migration
between populations then introduces these separate mutations into both populations. Assortative
mating may occur between individuals of different phenotypes or the same phenotype.
Recombination in the offspring of these matings leads to new combinations of characters that
were previously found in different individuals. Genetic drift due to random sampling of gametes
changes the frequencies of the genotypes and causes some divergence between the two
populations in the frequencies of their genotypes and phenotypes. Natural selection then causes
the populations to diverge even more.

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614 Chapter 19 • Population Genetics

genetic variation, will be affected by several or many The simplest description of single-gene variation is
genes and by environmental variation as well. For their the list of observed proportions of genotypes in a popu-
analysis we must use the methods introduced in Chapter lation. Such proportions are called the genotype fre-
22 to say anything at all about the genotypes underlying quencies. Table 19-1 shows this frequency distribution
the phenotypic variation. But, as we shall see in Chapter for the three genotypes of the MN gene in several hu-
22, it is not possible to make very precise statements man populations. Note that there is variation between
about the genotypic variation underlying such charac- individuals in each population, because there are differ-
ters. For that reason, most of the study of experimental ent genotypes present, and there is variation in the fre-
population genetics has concentrated on characters with quencies of these genotypes from population to popula-
simple relations to the genotype. The different pheno- tion. For example, most people in the Eskimo
types for such a character can be shown to be the result population are MM, while this genotype is quite rare
of different allelic forms of a single gene. A favorite ob- among Australian Aborigines.
ject of study for human population geneticists, for exam-
ple, has been the various human blood groups. The phe- More typically, instead of the frequencies of the
notype of a blood group is the presence of particular diploid genotypes, the frequencies of the alternative al-
antigens on the surface of red blood cells and of particu- leles are used. The allele frequency is simply the propor-
lar antibodies in the blood serum. The qualitatively dis- tion of that allelic form of the gene among all the copies
tinct phenotypes of a given blood group — say, the MN of the gene in the population, where each individual
group — are encoded by alternative alleles at a single lo- diploid organism in the population is counted as con-
cus, and the phenotypes are insensitive to environmental tributing two alleles for each gene. Homozygotes for an
variations. Thus, observed variation in blood types is en- allele have two copies of that allele, whereas heterozy-
tirely the consequence of simple genetic differences. gotes have only one copy. So the frequency of an allele is
the frequency of homozygotes plus half the frequency of
The study of variation consists of two stages. The heterozygotes. Thus, if the frequency of A/A individuals
first is a description of the phenotypic variation. The sec- were, say, 0.36 and the frequency of A/a individuals
ond is a translation of these phenotypes into genetic were 0.48, the allele frequency of A would be 0.36 ϩ
terms and the description of the underlying genetic vari- 0.48/2 ϭ 0.60. Box 19-1 gives the general form of this
ation. If there is a perfect one-to-one correspondence calculation. Table 19-1 shows the values of p and q, the
between genotype and phenotype, then these two steps allele frequency of the two alleles M and N of the MN
merge into one, as in the MN blood group. If the relation blood group in the different populations.
is more complex — for example, as the result of domi-
nance, heterozygotes resemble homozygotes — it may be Simple variation can be observed within and be-
necessary to carry out experimental crosses or to observe tween populations of any species at various levels, from
pedigrees to translate phenotypes into genotypes. This is the phenotype of external morphology down to the
the case for another human blood group, the ABO sys- amino acid sequences of proteins. Indeed, genotypic
tem, for which there are two dominant alleles, IA and I B, variation can be directly characterized by sequencing
and a recessive allele, i. Individuals with type A or type DNA for the same gene or for the same regions between
B blood may be either homozygous for their respective genes from multiple individuals. Every species of organ-
alleles (IAIA or I BI B) or heterozygous for their type allele ism ever examined has revealed considerable genetic
and the recessive allele (IAi or I Bi). variation, or polymorphism, manifested at one or more
levels of observation within populations, between popu-

TABLE 19-1 Frequencies of Genotypes for Alleles at MN Blood
Group Locus in Various Human Populations

Genotype Allele frequencies

Population M/M M/N N/N p(M) q(N)

Eskimo 0.835 0.156 0.009 0.913 0.087
Australian Aborigine 0.024 0.304 0.672 0.176 0.824
Egyptian 0.278 0.489 0.233 0.523 0.477
German 0.297 0.507 0.196 0.550 0.450
Chinese 0.332 0.486 0.182 0.575 0.425
Nigerian 0.301 0.495 0.204 0.548 0.452

Source: W. C. Boyd, Genetics and the Races of Man. D. C. Heath, 1950.

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19.1 Variation and its modulation 615

BOX 19-1 Calculation of Allele Frequencies

If fA/A, fA/a, and fa/a are the frequencies of the three Therefore
genotypes at a locus with two alleles, then the fre-
quency p of the A allele and the frequency q of the a p ϩ q ϭ fA/A ϩ fa/a ϩ fA/a ϭ 1.00
allele are obtained by counting alleles. Because each
homozygote A/A consists only of A alleles, and be- and
cause half the alleles of each heterozygote A/a are A
alleles, the total frequency p of A alleles in the popu- qϭ1Ϫp
lation is calculated as
If there are more than two different allelic forms, the
p ϭ fA/A ϩ 1 fA/a ϭ frequency of A frequency for each allele is simply the frequency of its
2 homozygote plus half the sum of the frequencies for
all the heterozygotes in which it appears.
Similarly, the frequency q of the a allele is given by

q ϭ fa/a ϩ 1 fA/a ϭ frequency of a

lations, or both. A gene or a phenotypic trait is said to be guishable, however, so only 121 phenotypic classes can
polymorphic if there is more than one form of the gene be seen. Remarkably, in one study of a sample of only
or more than one phenotype for that character in a pop- 100 Europeans, 53 of the 121 possible phenotypes were
ulation. In some cases nearly the entire population is actually observed.
characterized by one form of the gene or character, with
rare exceptional individuals carrying an unusual variant. AMINO ACID SEQUENCE POLYMORPHISM Studies of
That extremely common form is called the wild type, in genetic polymorphism have been carried down to the
contrast to the rare mutants. In other cases two or more level of the polypeptides encoded by the coding regions
forms are common, and it is not possible to pick out one of the genes themselves. If there is a nonsynonymous
that is the wild type. Genetic variation that might be the codon change in a gene (say, GGU to GAU), the result is
basis for evolutionary change is ubiquitous. an amino acid substitution in the polypeptide produced
at translation (in this case, aspartic acid is substituted for
It is impossible in this text to provide an adequate glycine). Variation in amino acid sequence of a protein
picture of the immense richness of even simple genetic can be detected by sequencing the DNA that codes for
variation that exists in species. We can consider only a the protein from a large number of individuals. This is
few examples of the different kinds to gain a sense of the method that would be used if one wished to know
the genetic diversity within species. Each of these exam- exactly which amino acids in the protein sequence were
ples can be multiplied many times over in other species varying, but it is extremely time-consuming and expen-
and with other characters. sive to carry out such DNA sequencing projects for
many different protein coding genes. There is, however, a
Protein polymorphisms
TABLE 19-2 Frequencies of the Alleles IA,
IMMUNOLOGIC POLYMORPHISM A number of loci in IB, and i at the ABO Blood
vertebrates encode antigenic specificities such as the Group Locus in Various
ABO blood types. More than 40 different specificities Human Populations
for antigens on human red cells are known, and several
hundred are known in domesticated cattle. Another ma- Population IA IB i
jor polymorphism in humans is the HLA system of cel-
lular antigens, which are implicated in tissue graft com- Eskimo 0.333 0.026 0.641
patibility. Table 19-2 gives the allelic frequencies for the Sioux 0.035 0.010 0.955
ABO blood group locus in some very different human Belgian 0.257 0.058 0.684
populations. The polymorphism for the HLA system is Japanese 0.279 0.172 0.549
vastly greater. There appear to be two main loci, each Pygmy 0.227 0.219 0.554
with five distinguishable alleles. Thus, there are 52 ϭ 25
different possible gametic types, making 25 different Source: W. C. Boyd, Genetics and the Races of Man. D. C. Heath, 1950.
homozygous forms and (25)(24)/2 ϭ 300 different het-
erozygotes. Not all genotypes are phenotypically distin-

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616 Chapter 19 • Population Genetics

practical substitute for DNA sequencing that can be Allele 2
used if one is interested only in detecting variant forms Allele 1
of a protein without knowing the particular amino acid Allele 3
changes involved. This method makes use of the change Allele 2
in the physical properties of a protein when one amino
acid is substituted for another. Proteins carry a net Figure 19-2 Electrophoretic gel of the proteins encoded by
charge that is the result of the ionization of side chains homozygotes for three different alleles at the esterase-5 locus in
on five amino acids (glutamic acid, aspartic acid, argi- Drosophila pseudoobscura. Each lane is the protein from a
nine, lysine, and histidine). Amino acid substitutions different individual fly. Repeated samples of proteins encoded
may directly replace one of these charged amino acids, by the same allele are identical, but there are repeatable
or a noncharged substitution near a charged amino acid differences between alleles.
may alter the degree of ionization of the charged amino
acid, or a substitution at the joining between two ␣ he- because the presence of a protein is prima facie evidence
lices may cause a slight shift in the three-dimensional of the DNA sequence encoding the protein. Thus, it has
packing of the folded polypeptide. In all these cases, the been possible to ask what proportion of all structural
net charge on the polypeptide will be altered. genes in the genome of a species are polymorphic and
what average fraction of an individual’s genome is in
The change in net charge on the protein can be de- heterozygous state, the heterozygosity, in a population.
tected by gel electrophoresis. Figure 19-2 shows the out- Very large numbers of species have been sampled by this
come of such an electrophoretic separation. The tracks method, including bacteria, fungi, higher plants, verte-
represent variants of an esterase enzyme in Drosophila
pseudoobscura, where each track is the protein from a
different individual fly. Figure 19-3 shows a similar gel
for variant human hemoglobins. In this case, most indi-
viduals are heterozygous for a variant and normal hemo-
globin A. Table 19-3 shows the frequencies of different
alleles for three enzyme-encoding genes in D. pseudo-
obscura in several populations: a nearly monomorphic
locus (malic dehydrogenase), a moderately polymorphic
locus (␣-amylase), and a highly polymorphic locus (xan-
thine dehydrogenase).

The technique of gel electrophoresis of proteins (as
well as DNA sequencing) differs fundamentally from
other methods of genetic analysis in allowing the study
of genes that are not actually varying in a population,

Hemoglobin A

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Figure 19-3 Electrophoretic gel showing normal hemoglobin A and a number of variant
hemoglobin alleles. Each lane represents a different individual. One of the dark-staining
bands is marked as normal hemoglobin A. The other dark-staining band seen in most of the
lanes (most clearly in lanes 3 and 4) represents any of several variant hemoglobins derived
from the second allele of a heterozygote. Hemoglobin A is missing from lanes 9 and 10
because the individuals are homozygotes for a variant allele [Richard C. Lewontin.]

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19.1 Variation and its modulation 617

TABLE 19-3 Frequencies of Various Alleles at Three Enzyme-Encoding
Loci in Four Populations of Drosophila pseudoobscura

Locus (enzyme-encoding) Allele Berkeley Population Austin Bogotá
Malic dehydrogenase
␣-Amylase A 0.969 Mesa Verde 0.957 1.00
B 0.031 0.043 0.00
Xanthine dehydrogenase 0.948
A 0.030 0.052 0.000 0.00
B 0.290 0.125 1.00
C 0.680 0.000 0.875 0.00
A 0.053 0.789 0.018 0.00
B 0.074 0.036 0.00
C 0.263 0.016 0.232 0.00
D 0.600 0.073 0.661 1.00
E 0.010 0.300 0.053 0.00

Source: R. C. Lewontin, The Genetic Basis of Evolutionary Change. Columbia University Press, 1974.

brates, and invertebrates. The results are remarkably con- inversions are observed in many populations of plants,
sistent over species. About one-third of genes coding for insects, and even mammals. Figure 19-4 shows a variety
proteins are detectably polymorphic at the protein level, of inversion loops found in natural populations of
and the average heterozygosity in a population over all Drosophila pseudoobscura. Each such loop is the result of
loci sampled is about 10 percent. This means that scan- carrying two homologous chromosomes, one of which
ning the genome in virtually any species would show contains a section that is in reverse linear order with re-
that about 1 in every 10 genes in an individual is in het- spect to the other chromosome (see Chapter 15). Table
erozygous condition for genetic variations that are re- 19-4 gives the frequencies of supernumerary chromo-
flected in the amino acid sequence of the proteins, and somes and translocation heterozygotes in a population of
about one-third of all genes have two or more such al- the plant Clarkia elegans from California. The “typical”
leles segregating in any population. Thus the potential of species karyotype would be hard to identify in this plant
variation for evolution is immense. The disadvantage of in which only 56 percent of the individuals lack super-
the electrophoretic technique is that it detects variation numerary chromosomes and translocations.
only in protein-coding regions of genes and misses the
important changes in regulatory elements that underlie RESTRICTION-SITE VARIATION An inexpensive and
much of evolution of form and function. rapid way to observe overall levels of variation in DNA
sequences is to digest that DNA using restriction en-
DNA structure and sequence polymorphism zymes (see Chapter 11). There are many different re-
striction enzymes, each of which will recognize a differ-
DNA analysis makes it possible to examine variation in ent base sequence and cut the DNA at the site of that
genome structure among individuals and between sequence. The result will be two DNA fragments whose
species. There are three levels at which such studies can lengths are determined by the location of the restriction
be done. Examining variation in chromosome number site in the original uncut molecule. A restriction enzyme
and morphology provides a large-scale view of reorgani- that recognizes six-base sequences (a “six cutter”) will
zations of the genome. Studying variation in the sites recognize an appropriate sequence approximately once
recognized by restriction enzymes provides a coarse every 46 ϭ 4096 base pairs along a DNA molecule [de-
view of base-pair variation. At the finest level, methods termined from the probability that a specific base (of
of DNA sequencing allow variation to be observed base which there are four) will be found at each of the six
pair by base pair. positions]. If there is polymorphism in the population
for one of the six bases at the recognition site, then the
CHROMOSOMAL POLYMORPHISM Although the kary- enzyme will recognize and cut the DNA in one variant
otype is often regarded as a distinctive characteristic of a and not in the other (see Chapter 11). Thus there will
species, in fact, numerous species are polymorphic for be a restriction fragment length polymorphism (RFLP)
chromosome number and morphology. Extra chromo- in the population. A panel of, say, eight different six-
somes (supernumeraries), reciprocal translocations, and cutter enzymes will then sample every 4096/8 Х 500

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618 Chapter 19 • Population Genetics

Figure 19-4 Inversion polymorphism of chromosome 3 in base pairs for such polymorphisms. However, when one
natural populations of Drosophila pseudoobscura. The inversions is found, we do not know which of the six base pairs at
are named for the locality at which they were first observed. the recognition site is polymorphic.
Pairings of different gene orders show loops in the polytene
chromosomes, revealing the location of the breakpoints of the If we use enzymes that recognize four-base se-
inversions. [T. Dobzhansky, Chromosomal Races in Drosophila quences (“four cutters”), there is a recognition site every
44 ϭ 256 base pairs, so a panel of eight different en-
pseudoobscura and Drosophila persimilis. Carnegie Institution of zymes can sample about once every 256/8 ϭ 32 base
pairs along the DNA sequence. In addition to single
Washington, 47 – 144, 1944.] base-pair changes that destroy restriction-enzyme recog-
nition sites, there are insertions and deletions of
stretches of DNA that occur along the DNA strand be-
tween the locations of restriction sites, and these will
also cause restriction fragment lengths to vary.

A variety of different restriction-enzyme studies has
been performed for different regions of the X chromo-
some and the two large autosomes of Drosophila
melanogaster. These have found between 0.1 and 1.0
percent heterozygosity per nucleotide site, with an aver-
age of 0.4 percent. The result of one such study on the
xanthine dehydrogenase gene in Drosophila pseudo-
obscura is shown in Figure 19-5. The figure shows, sym-
bolically, the restriction pattern of 58 chromosomes
sampled from nature, polymorphic at 78 restriction sites
along a sequence 4.5 kb in length. Remarkably, among
the 58 patterns there are 53 different ones. (Try to find
the identical pairs.)

TANDEM REPEATS Restriction fragment surveys can
reveal another form of DNA sequence variation, which
arises from the occurrence of multiply repeated DNA
sequences. In the human genome, there are a variety of
different short DNA sequences dispersed throughout
the genome, each one of which is multiply repeated in a
row (in tandem). The number of repeats may vary from
a dozen to more than 100 in different individual
genomes. Such sequences are known as variable number
tandem repeats (VNTRs). If the restriction enzymes cut
sequences that flank either side of such a tandem array, a
fragment will be produced whose size is proportional to
the number of repeated elements. The different-sized

TABLE 19-4 Frequencies of Plants with Supernumerary Chromosomes and of Translocation
Heterozygotes in a Population of Clarkia elegans from California

No supernumeraries Translocations Supernumeraries Both translocations
or translocations 0.133 0.265 and supernumeraries

0.560 0.042

Source: H. Lewis, Evolution 5, 1951, 142 – 157.

44200_19_p611-642 3/12/04 2:34 PM Page 619 619

19.1 Variation and its modulation Figure 19-5 The result of a four-cutter
survey of 58 chromosomes, probed for the
xanthine dehydrogenase gene in
Drosophila pseudoobscura. Each line is a
chromosome (haplotype) sampled from a
natural population. Each position along
the line is a polymorphic restriction rate
along the 4.5-kb sequence studied.
Where an asterisk appears, the
haplotype differs from the majority,
either cutting where most haplotypes
are not cut or not cutting where most
haplotypes are cut. At two sites, there
is no clear majority type, so a 0 or 1 is
used to show whether the site is absent
or present.

fragments will migrate at different rates in an elec- pairs by DNA sequencing can provide information of
trophoretic gel. The individual copies of the repeated se- two kinds. First, DNA sequence variation can be studied
quence elements are too short to allow distinguishing in the protein-coding regions of genes. The sequences of
between, say, 64 and 68 repeats, but size classes that in- coding regions can be translated to reveal the exact
clude several repeat numbers (bins) can be established, amino acid sequence differences in proteins from differ-
and a population can be assayed for the frequencies of ent individuals in a population or from different species.
the different classes. Table 19-5 shows the data for two DNA sequencing is superior in precision to elec-
different VNTRs sampled in two American Indian trophoretic studies of a protein from different individu-
groups from Brazil. In one case, D14S1, the Karitiana are als, which can show that there is variation in amino acid
nearly homozygous, whereas the Surui are very variable; sequences but cannot identify how many or which
in the other case, D14S13, both populations are variable amino acids differ between individuals. So, when DNA
but with different frequency patterns. sequences were obtained for the various electrophoretic
variants of esterase-5 in Drosophila pseudoobscura (see
COMPLETE SEQUENCE VARIATION A ubiquitous form Figure 19-2), electrophoretic variants were found to dif-
of genetic variation is variation in the nucleotide at a sin- fer from one another by an average of 8 amino acids, and
gle position, called a single-nucleotide polymorphism the 20 different kinds of amino acids were involved in
(SNP). Studies of variation at the level of single base polymorphisms at about the frequency that they were

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620 Chapter 19 • Population Genetics

TABLE 19-5 Size Class Frequencies for Two Different VNTR Sequences,
D14S1 and D14S13, in the Karitiana and Surui of Brazil

D14S1 D14S13

Size class Karitiana Surui Karitiana Surui

3–4 105 41 00
4–5 0 3 3 14
5–6 0 14
6–7 0 11 12
7–8 0 2 12
8–9 3 1 8 16
9 – 10 0 3 28 9
10 – 11 0 22 0
11 – 12 0 11 18 8
12 – 13 0 2 13 18
13 – 14 0 4 13 3
Ͼ 14 0 0 02
108 0 108 78


Source: Data from J. Kidd and K. Kidd, American Journal of Physical Anthropology 81, 1992, 249.

present in the protein. Such studies also show that dif- an alternative codon for the same amino acid, whereas
ferent regions of the same protein have different 75 percent of random changes would change the amino
amounts of polymorphism. For the esterase-5 protein, acid coded. For example, a change from AAT to AAC
consisting of 545 amino acids, 7 percent of amino acid still encodes asparagine, but a change to ATT, ACT,
positions are polymorphic, but the last amino acids at AAA, AAG, AGT, TAT, CAT, or GAT, all single-base-
the carboxyl terminus of the protein are totally invariant pair changes from AAT, changes the amino acid en-
between individuals, probably because these amino acids coded. So, if mutations of base pairs are at random and
are needed for the protein to function properly. if the substitution of an amino acid made no difference
to function, we would expect a 3 : 1 ratio of amino acid
Second, DNA sequence variation can also be studied replacement to silent polymorphisms. The actual ratios
in those base pairs that do not determine or change the found in Drosophila vary from 2 : 1 to 1 : 10. Clearly,
protein sequence. Such base-pair variation can be found there is a great excess of synonymous polymorphism,
in DNA in 5Ј flanking sequences that may be regulatory. showing that most amino acid changes make a differ-
The importance of studying variation in regulatory se- ence to function and therefore are subject to natural se-
quences cannot be overemphasized. It has been sug- lection. It should not be assumed, however, that silent
gested that most of the evolution of shape, physiology, sites in coding sequences are entirely free from con-
and behavior rests on changes in regulatory sequences. If straints. Different alternative triplet codings for the
that is true, then much of the sequence variation in cod- same amino acid may differ in speed and accuracy of
ing regions and in the amino acid sequences for which transcription, and the mRNA corresponding to different
they code is beside the point. There is also variation in alternative triplets may have different accuracy and
introns, in nontranscribed DNA 3Ј to the gene, and in speed of translation because of limitations on the pool
those nucleotide positions in codons (usually third posi- of tRNAs available. Evidence for the latter effect is that
tions) whose variation does not result in amino acid sub- alternative synonymous triplets for an amino acid are
stitutions. These so-called silent or synonymous base-pair not used equally, and the inequality of use is much
polymorphisms are much more common than are more pronounced for genes that are transcribed at a
changes that result in amino acid polymorphism, pre- very high rate.
sumably because many amino acid changes interfere
with normal function of the protein and are eliminated There are also constraints on 5Ј and 3Ј noncoding
by natural selection. sequences and on intron sequences. Both 5Ј and 3Ј non-
coding DNA sequences contain signals for transcription,
An examination of the codon translation table (see and introns may contain enhancers of transcription (see
Figure 9-8) shows that approximately 25 percent of all Chapter 10).
random base-pair changes would be synonymous, giving

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19.2 Effect of sexual reproduction on variation 621

MESSAGE Within species, there is great genetic variation. eration will remain the same. These constant frequencies
This variation is manifest at the morphologic level of form the equilibrium distribution. Box 19-2 gives a gen-
chromosome form and number and at the level of DNA eral form of this equilibrium result.
segments that may have no observable developmental effects.
MESSAGE Meiotic segregation in randomly mating
19.2 Effect of sexual reproduction populations results in an equilibrium distribution of
on variation genotypes after only one generation, so genetic variation is
Meiotic segregation and genetic equilibrium
The equilibrium distribution can be calculated ac-
If inheritance were based on a continuous substance like cording to the formula
blood, then the mating of individuals with different phe-
notypes would produce offspring that were intermediate A/A A/a a/a
in phenotype. When these intermediate types mated p2 2pq q2
with each other, their offspring would again be interme-
diate. A population in which individuals mated at ran- where p is the frequency of the A allele, q is the fre-
dom would slowly lose all its variation, and eventually quency of the a allele, and p ϩ q ϭ 1.
every member of the population would have the same
phenotype. This distribution is called the Hardy-Weinberg equi-
librium after G. H. Hardy and W. Weinberg, the two
The particulate nature of inheritance changes this people who independently discovered it. (A third inde-
picture completely. Because of the discrete nature of pendent discovery was made by the Russian geneticist
genes and the segregation of alleles at meiosis, a cross of Sergei Chetverikov.)
intermediate with intermediate individuals does not re-
sult in all intermediate offspring. On the contrary, some The Hardy-Weinberg equilibrium means that sexual
of the offspring will be of extreme types — those that are reproduction does not cause a constant reduction in ge-
homozygotes. Consider a population in which males and netic variation in each generation; on the contrary, the
females mate with one another at random with respect amount of variation remains constant generation after
to some gene locus A; that is, the genotype at that locus generation, in the absence of other disturbing forces. The
is not a factor in choosing a mate. Such random mating equilibrium is the direct consequence of the segregation
is equivalent to mixing all the sperm and all the eggs in of alleles at meiosis in heterozygotes.
the population together and then matching randomly
drawn sperm with randomly drawn eggs. Numerically, the equilibrium shows that, irrespec-
tive of the particular mixture of genotypes in the
The outcome of such a random pairing of sperm and parental generation, the genotypic distribution after one
eggs is easy to calculate. If, in some population, the allele round of random mating is completely specified by the
frequency of A is 0.60 in both sperm and eggs, then the allelic frequency p. For example, consider three hypo-
chance that a randomly chosen sperm and a randomly thetical populations that have arisen from the mixing of
chosen egg are both A is 0.60 ϫ 0.60 ϭ 0.36. Thus, in a migrants from different sources:
random-mating population with this allele frequency, 36
percent of offspring will be A/A. In the same way, the f (A/A) f (A/a) f (a/a)
frequency of a/a offspring will be 0.40 ϫ 0.40 ϭ 0.16.
Heterozygotes will be produced by the fusion either of I 0.3 0.0 0.7
an A sperm with an a egg or of an a sperm with an A II 0.2 0.2 0.6
egg. If gametes pair at random, then the chance of an A III 0.1 0.4 0.5
sperm and an a egg is 0.60 ϫ 0.40, and the reverse
combination has the same probability, so the frequency The allele frequency p of A in the three populations is
of heterozygous offspring is 2 ϫ 0.60 ϫ 0.40 ϭ 0.48.
I p ϭ f(A/A) ϩ f(A/a) ϭ 0.3 ϩ 1/2(0) ϭ 0.3
We can now understand why variation is retained in
a population. The process of random mating has done II p ϭ 0.2 ϩ 1/2(0.2) ϭ 0.3
nothing to change allele frequencies, as can be easily
checked by calculating the frequencies of the alleles A III p ϭ 0.1 ϩ 1/2(0.4) ϭ 0.3
and a among the offspring in this example, using the
method described in Box 19-1. So the proportions of So, despite their very different genotypic compositions,
homozygotes and heterozygotes in each successive gen- they have the same allele frequency. After one generation

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622 Chapter 19 • Population Genetics

BOX 19-2 The Hardy-Weinberg Equilibrium p2 ϩ pq ϭ p(p ϩ q) ϭ p

If the frequency of allele A is p in both the sperm and Therefore, in the second generation, the frequencies
the eggs, and the frequency of allele a is q ϭ 1 Ϫ p, of the three genotypes will again be
then the consequences of random unions of sperm
and eggs are as shown in the adjoining diagram. The p2 : 2pq : q2
probability that both the sperm and the egg in any
mating will carry A is and so on, forever. These are the Hardy-Weinberg
equilibrium frequencies.
p ϫ p ϭ p2
Eggs a
so this will be the frequency of A/A homozygotes in A
the next generation. Likewise, the chance of het-
erozygotes A/a will be A A/A A/a p
Sperm (p 2) (pq)
( p ϫ q) ϩ (q ϫ p) ϭ 2pq
a A/a a/a q
and the chance of homozygotes a/a will be (pq) (q 2)

q ϫ q ϭ q2 pq

The three genotypes, after a generation of random The Hardy-Weinberg equilibrium frequencies that result
mating, will be in the frequencies from random mating.

p2 : 2pq : q2

The frequency of A in the F1 will not change (it will
still be p), because as the diagram shows, the fre-
quency of A in the zygotes is the frequency of A/A
plus half the frequency of A/a, or

of random mating within each population, however, 2pq p
each of them will have the same genotypic frequencies: 2q2 ϭ q

A/A which for q ϭ 0.001 is a ratio of 999 : 1. For example, a
p2 ϭ (0.3)2 ϭ 0.09 recessive mutation causes the potentially lethal disease
phenylketonuria (PKU) when it is homozygous. The
A/a mutant allele has a frequency of approximately .01 in
2pq ϭ 2(0.3)(0.7) ϭ 0.42 European and American populations. The frequency of
the disease, however, is only about 1 in 10,000 new-
a/a borns. The general relation between homozygote and
q2 ϭ (0.7)2 ϭ 0.49 heterozygote frequencies as a function of allele frequen-
cies is shown in Figure 19-6.
and they will remain so indefinitely.
One consequence of the Hardy-Weinberg propor- In our derivation of the equilibrium, we assumed
that the allelic frequency p is the same in sperm and
tions is that rare alleles are virtually never in homozy- eggs. The Hardy-Weinberg equilibrium theorem does
gous condition. An allele with a frequency of 0.001 is not apply to sex-linked genes if males and females start
present in homozygotes at a frequency of only 1 in a with unequal gene frequencies.
million; most copies of such rare alleles are found in het-
erozygotes. In general, two copies of an allele are in The principle of Hardy-Weinberg equilibrium can
homozygotes but only one copy of that allele is in be generalized to include cases where there are more
each heterozygote, so the relative frequency of the allele than two alleles in the population. In general, no matter
in heterozygotes (in contrast with homozygotes) is, from how many allelic types are present in the population,
the Hardy-Weinberg equilibrium frequencies, the frequency of homozygotes for a particular allele is

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19.2 Effect of sexual reproduction on variation 623

1.0 A/A Heterozygosity
0.9 A/a
A measure of genetic variation (in contrast with its de-
a/a scription by allele frequencies) is the amount of hetero-
0.8 zygosity for a gene in a population, which is given by the
0.7 total frequency of heterozygotes for the gene. This het-
0.6 erozygosity either can be directly observed by counting
0.5 heterozygotes or it can be calculated from the allele fre-
0.4 quencies, using the Hardy-Weinberg equilibrium propor-
0.3 tions. If one allele is in very high frequency and all oth-
0.2 ers are near zero, then there will be very little
0.1 heterozygosity because most individuals will be ho-
mozygous for the common allele. We expect heterozy-
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p (A) gosity to be greatest when there are many alleles of a
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 q (a) gene, all at equal frequency. In Table 19-1 the heterozy-
gosity is simply equal to the frequency of the M/N
Figure 19-6 Homozygote and heterozygote frequencies as a genotype in each population.
function of allele frequencies. Curves showing the proportions
of homozygotes A/A (blue line), homozygotes a/a (orange line), When more than one locus is considered, there are
and heterozygotes A/a (green line) in populations with two possible ways of calculating heterozygosity. The S
different allele frequencies if the populations are at Hardy- gene (which encodes the secretor factor, determining
Weinberg equilibrium. whether the M and N proteins are also contained in the
saliva) is closely linked to M/N in humans. Table 19-6
equal to the square of the frequency of the allele. The shows the frequencies of the four combinations of the
two alleles for the two genes (M S, M s, N S, and N s) in
frequency of heterozygotes for a particular pair of alleles various populations. For the first way of measuring het-
erozygosity, we can calculate the frequency of heterozy-
is twice the product of the frequency of those two al- gotes at each locus separately (allelic heterozygosity).
For the second way, we can consider whether an individ-
leles. For example, suppose there are three alleles, A1, ual’s homologous chromosomes carry the same combi-
A2, and A3, whose frequencies are .5, .3, and .2, respec- nation of alleles. The combination of alleles of different
tively. Then the Hardy-Weinberg equilibrium frequen- genes on the same chromosomal homolog is called a
haplotype. To determine whether two alleles of different
cies of the homozygotes would be genes are associated on the same chromosomal homolog
it is necessary either to sequence the DNA from the in-
A1A1 A2A2 A3A3 dividuals or to have information about their parents or
(.5)2 ϭ .25 (.3)2 ϭ .09 (.2)2 ϭ .04 offspring. Once we have that information, we consider
each haplotype as a unit, as in Table 19-6, and calculate
and the frequencies of the heterozygotes would be the proportion of all individuals who carry two different
haplotypic or gametic forms. This form of heterozygos-
A1A2 A1A3 A2A3 ity is also referred to as haplotype diversity or gametic

2(.5)(.3) ϭ .30 2(.5)(.2) ϭ .20 2(.3)(.2) ϭ .12

TABLE 19-6 Frequencies of Gametic Types for MNS System in Various
Human Populations

Gametic type Heterozygosity (H)

Population MS Ms NS Ns From gametes From alleles

Ainu 0.024 0.381 0.247 0.348 0.672 0.438
Ugandan 0.134 0.357 0.071 0.438 0.658 0.412
Pakistani 0.177 0.405 0.127 0.291 0.704 0.455
English 0.247 0.283 0.080 0.290 0.700 0.469
Navaho 0.185 0.702 0.062 0.051 0.467 0.286

Source: A. E. Mourant, The Distribution of the Human Blood Groups. Blackwell Scientific, 1954.

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624 Chapter 19 • Population Genetics

diversity. The results of both calculations are given in blood group. Within Eskimo, Egyptian, Chinese, and
Table 19-6. Note that the haplotype diversity is always Australian subpopulations, females do not choose their
greater than the average heterozygosity of the separate mates by MN type, and thus Hardy-Weinberg equilib-
loci, because an individual is a haplotypic heterozygote rium exists within the subpopulations. But Egyptians do
if either of its genes is heterozygous. not often mate with Eskimos or Australian Aborigines,
so the nonrandom associations in the human species as a
Random mating whole result in large differences in genotype frequencies
from group to group. It follows that if we took the hu-
The Hardy-Weinberg equilibrium was derived on the man species as a whole and could calculate the average
assumption of “random mating,” but we must carefully allelic frequency in the entire species, we would observe
distinguish two meanings of that process. First, we may a departure from Hardy-Weinberg equilibrium for the
mean that individuals do not choose their mates on the species. To perform such a calculation, however, we
basis of some heritable character. Human beings are ran- would need to know the population size and allele fre-
domly mating with respect to blood groups in this first quencies of every local population. To illustrate the ef-
sense, because they generally do not know the blood fect, suppose we formed a merged group made up of an
type of their prospective mates, and even if they did, it is equal number of Eskimos and Australian Aborigines.
unlikely that they would use blood type as a criterion From the observed genotype frequencies in Table 19-7
for choice. In this first sense, random mating will occur we can calculate that the allele frequencies in the two
with respect to genes that have no effect on appearance, subgroups and the merged group are
behavior, smell, or other characteristics that directly in-
fluence mate choice. Eskimos p(M) q(m)
Australian Aborigines
The second sense of random mating is relevant Merged average 0.915 0.085
when there is any division of a species into subgroups. If 0.178 0.822
there is genetic differentiation between subgroups so 0.546 0.454
that the frequencies of alleles differ from group to group
and if individuals tend to mate within their own sub- If the merged group were really a single random mating
group (endogamy), then with respect to the species as a population, we would expect to find the Hardy-
whole, mating is not at random and frequencies of geno- Weinberg proportions given by the average allele
types will depart more or less from Hardy-Weinberg fre- frequencies,
quencies. In this sense, human beings are not random
mating, because ethnic and racial groups and geographi- p2 (M/M) 2pq (M/N) q2 (N/N)
cally separated populations differ from one another in 0.298 0.496 0.206
gene frequencies, and people show high rates of en-
dogamy not only within major geographical races, but whereas what we actually find is the averaged propor-
also within local ethnic groups. Spaniards and Russians tion of homozygotes and heterozygotes from the two
differ in their ABO blood group frequencies, Spaniards original parental populations
usually marry Spaniards and Russians usually marry Rus-
sians, so there is unintentional nonrandom mating with (M/M) (M/N) (N/N)
respect to ABO blood groups. 0.430 0.230 0.340

Table 19-7 shows random mating in the first sense
and nonrandom mating in the second sense for the MN

TABLE 19-7 Comparison Between Observed Frequencies of Genotypes for the MN Blood
Group Locus and the Frequencies Expected from Random Mating

Population M/M Observed N/N M/M Expected N/N

Eskimo 0.835 M/N 0.009 0.834 M/N 0.008
Egyptian 0.278 0.233 0.274 0.228
Chinese 0.332 0.156 0.182 0.331 0.159 0.181
Australian Aborigine 0.024 0.489 0.672 0.031 0.499 0.679
0.486 0.488
0.304 0.290

Note: The expected frequencies are computed according to the Hardy-Weinberg equilibrium, using the values of p and q computed
from the observed frequencies.

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19.2 Effect of sexual reproduction on variation 625

Inbreeding and assortative mating cient (F). Figure 19-7 illustrates the calculation of the
probability of homozygosity by descent. Individuals I
Random mating with respect to a locus is common and II are full sibs because they share both parents. We
within populations, but it is not universal. Two kinds of label each allele in the parents uniquely to keep track of
deviation from random mating must be distinguished. them. Individuals I and II mate to produce individual III.
First, individuals may mate with others with whom they Suppose individual I is A1/A3 and the gamete that it
share some degree of common ancestry, that is, some de- contributes to III contains the allele A1; then we would
gree of genetic relationship. If mating between relatives like to calculate the probability that the gamete pro-
occurs more commonly than would occur by pure duced by II is also A1. The chance is 1/2 that II will re-
chance, then the population is inbreeding. If mating be- ceive A1 from its father, and, if it does, the chance is 1/2
tween relatives is less common than would occur by that II will pass A1 on to the gamete in question. Thus,
chance, then the population is said to be undergoing the probability that III will receive an A1 from II is
enforced outbreeding, or negative inbreeding. 1/2 ϫ 1/2 ϭ 1/4, and this is the chance that III — the
product of a full-sib mating — will be homozygous
Second, individuals may tend to choose each other A1/A1 by descent from the original ancestor.
as mates, not because they are related but because of
their resemblance to each other in some trait. Bias to- Such close inbreeding can have deleterious conse-
ward mating of like with like is called positive assorta- quences. Let’s consider a rare deleterious allele a that,
tive mating. Mating with unlike partners is called nega- when homozygous, causes a metabolic disorder. If the
tive assortative mating. Assortative mating is never com- frequency of the allele in the population is p, then the
plete, so that in any population some matings will be at probability that a random couple will produce a homo-
random and some the result of assortative mating. zygous offspring is only p2 (from the Hardy-Weinberg
equilibrium). Thus, if p is, say, 1/1000, the frequency of
Inbreeding and assortative mating are not the same. homozygotes will be 1 in 1,000,000. Now suppose that
Close relatives resemble each other more than unrelated the couple are brother and sister. If one of their common
individuals on the average but not necessarily for any parents is a heterozygote for the disease, they may both
particular phenotypic trait in particular individuals. So receive the deleterious allele and may both pass it on to
inbreeding can result in the mating of quite dissimilar their offspring. As the calculation shows, there is a 1/4
individuals. On the other hand, individuals who resem- chance that an offspring of a brother-sister mating will
ble each other for some character may do so because be homozygous for one of the alleles carried by its
they are relatives, but unrelated individuals also may grandparents. Suppose that among the four copies of the
have specific resemblances. Brothers and sisters do not gene possessed by the grandparents, one was a deleteri-
all have the same eye color, and blue-eyed people are ous mutation. Therefore the chance that an offspring of
not all related to one another.
A1 / A2 A3 /A4
Assortative mating for some traits is common. In
humans, there is a positive assortative mating bias for p= 1
skin color and height, for example. An important differ-
ence between assortative mating and inbreeding is that 2
the former is specific to a particular phenotype, whereas
the latter applies to the entire genome. Individuals may I A1 /A3 A1 / A4 II
mate assortatively with respect to height but at random
with respect to blood group. Cousins, on the other hand, p= 1
resemble each other genetically on the average to the
same degree at all loci. 2

For both positive assortative mating and inbreeding, A1 /A1
the consequence to population structure is the same: III
there is an increase in homozygosity above the level pre-
dicted by the Hardy-Weinberg equilibrium. If two indi- Figure 19-7 Calculation of homozygosity by descent for an
viduals are related, they have at least one common an- offspring (III) of a brother-sister (I-II) mating. Assume that
cestor. Thus, there is some chance that an allele carried individual III has received one copy of A1 from its grandfather
by one of them and an allele carried by the other are through individual I. The probability that II will receive A1
both descended from the identical DNA molecule. The from its father is 12; if it has, the probability that II will pass A1
result is that there is an extra chance of this homozygos- on to III is 21. Thus, the probability that III will receive an A1
ity by descent, to be added to the chance of homozygos- from II is 1/2 ϫ 1/2 ϭ 1/4.
ity (p2 ϩ q2) that arises from the random mating of un-
related individuals. The probability of this extra
homozygosity by descent is called the inbreeding coeffi-

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626 Chapter 19 • Population Genetics

the brother-sister mating will be homozygous for the example, the rabbits now in Australia probably have de-
deleterious allele is 1/4 ϫ 1/4 ϭ 1/16. There are so
many rare deleterious alleles for different genes in the scended from a single introduction of a few animals in
human populations that each one of us is a heterozygote
for many such rare alleles. Thus the chances are very the nineteenth century.) Even though mating is at ran-
high that an offspring of a brother-sister mating will be
homozygous for at least one of them. dom within the population, in later generations every-

Systematic inbreeding between close relatives even- one is related to everyone else, because their family trees
tually leads to complete homozygosity of the population
but at different rates, depending on the degree of rela- have common ancestors here and there in their pedi-
tionship. If two alleles are present in an inbreeding pop-
ulation, one will eventually be lost and the other will grees. Such a population is then inbred, in the sense that
have a frequency of 1.0 — in other words, it will become
fixed. For alleles that are not deleterious, which allele there is some probability of a gene’s being homozygous
will become fixed is a matter of chance. Suppose, for ex-
ample, that several groups of individuals are taken from by descent. Because the population is, of necessity, finite
a population and subjected to inbreeding. If, in the origi-
nal population from which the inbred lines are taken, al- in size, some of the originally introduced family lines
lele A has frequency p and allele a has frequency
q ϭ 1 Ϫ p, then a proportion p of the homozygous lines will become extinct in every generation, just as family
established by inbreeding will be homozygous A/A and
a proportion q of the lines will be a/a. Inbreeding takes names disappear in a human population that never re-
the genetic variation present within the original popula-
tion and converts it into variation between homozygous ceives any migrants, because, by chance, no male off-
inbred lines sampled from the population (Figure 19-8).
spring are left. As original family lines disappear, the
Let’s consider how inbreeding leads to a loss of vari-
ation. Suppose that a population is founded by some population comes to be made up of descendants of
small number of individuals who mate at random to
produce the next generation. Assume that no further fewer and fewer of the original founder individuals, and
immigration into the population ever occurs again. (For
all the members of the population become more and

more likely to carry the same alleles by descent. In other

words, the inbreeding coefficient F increases, and the

heterozygosity decreases over time until finally F reaches

1.00 and heterozygosity reaches 0.

The rate of loss of heterozygosity per generation in

such a closed, finite, randomly breeding population is in-

versely proportional to the total number (2N) of hap-

loid genomes, where N is the number of diploid individ-

uals in the population. In each generation, 1 of the
remaining heterozygosity is lost.

Generation 0 p2 A /A 2 pq A / a q2 a /a 19.3 Sources of variation
p (A) = 0.5
For a given population, there are three sources of varia-
all 1 1 1 all tion: mutation, recombination, and immigration of
4 2 4 genes. However, recombination between genes by itself
does not produce variation unless there is already allelic
Generation 1 A / A pq A / a a /a variation segregating at the different loci. Otherwise
p (A) = 0.5 there is nothing to recombine. Similarly, migration can-
not provide variation if the entire species is homozygous
all 1 1 1 all for the same allele. Ultimately, the source of all variation
4 2 4 must be mutation.

Generation 2 A / A pq / 2 A / a a /a Variation from mutation
p (A) = 0.5
Mutations are the source of variation, but the process of
Generation n ~p A / A (pq / 2n) A / a ~q a / a mutation does not itself drive genetic change in popula-
p (A) = 0.5 tions. The rate of change in gene frequency from the
mutation process is very low because spontaneous muta-
Figure 19-8 Repeated generations of inbreeding (or self- tion rates are low (Table 19-8). The mutation rate is de-
fertilization) will eventually split a heterozygous population into a fined as the probability that a copy of an allele changes
series of completely homozygous lines. The frequency of A/A to some other allelic form in one generation. Thus, the
lines among the homozygous lines will be equal to the increase in the frequency of a mutant allele will be the
frequency (p) of allele A in the original heterozygous product of the mutation rate times the frequency of the
population, while the frequency of a/a lines will be equal to nonmutant allele. Suppose that a population were com-
the original frequency of a (q). pletely homozygous A and mutations to a occurred at
the rate of 1/100,000 per newly formed gamete. Then in
the next generation, the frequency of a alleles would be

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19.3 Sources of variation 627

Table 19-8 Point-Mutation Rates in Different Organisms

Organism Gene Mutation rate per generation

Bacteriophage Host range 2.5 ϫ 10Ϫ9
Escherichia coli Phage resistance 2 ϫ 10Ϫ8
Zea mays (corn) R (color factor)
Y (yellow seeds) 2.9 ϫ 10Ϫ4
Drosophila melanogaster Average lethal 2 ϫ 10Ϫ6

2.6 ϫ 10Ϫ5

Source: T. Dobzhansky, Genetics and the Origin of Species, 3d ed., rev. Columbia University Press, 1951.

only 1.0 ϫ 1/100,000 ϭ 0.00001, and the frequency fewer copies of the old allele still left to mutate. A gen-
of A alleles would be 0.99999. After yet another genera- eral formula for the change in allele frequency under
tion of mutation, the frequency of a would be increased mutation is given in Box 19-3.
by 0.99999 ϫ 1/100,000 ϭ 0.000009 to a new fre-
quency of 0.000019, whereas the original allele would MESSAGE Mutation rates are so slow that mutation alone
be reduced in frequency to 0.999981. It is obvious that cannot account for rapid genetic changes of populations
the rate of increase of the new allele is extremely slow and species.
and that it gets slower every generation because there are

BOX 19-3 The Effect of Mutation on Allele Frequency

Let ␮ be the mutation rate from allele A to some If the population starts with only A alleles (p0 ϭ 1.0),
other allele a (the probability that a copy of gene A it would still have only 10 percent a alleles after
10,000 generations at this rather high mutation rate
will become a during the DNA replication preceding and would require 60,000 additional generations to
reduce p to 0.5.
meiosis). If pt is the frequency of the A allele in gener-
ation t, if qt ϭ 1 Ϫ pt is the frequency of the a allele in Even if mutation rates were doubled (say, by en-
generation t, and if there are no other causes of gene vironmental mutagens), the rate of change would be
very slow. For example, radiation levels of sufficient
frequency change (no natural selection, for example), intensity to double the mutation rate over the repro-
ductive lifetime of an individual human are at the
then the change in allele frequency in one generation limit of occupational safety regulations, and a dose of
radiation sufficient to increase mutation rates by an
is order of magnitude would be lethal, so rapid genetic
change in the species would not be one of the effects
⌬p ϭ pt Ϫ ptϪ1 ϭ (ptϪ1 Ϫ ␮ptϪ1) Ϫ ptϪ1 ϭ Ϫ␮ptϪ1 of increased radiation. Although we have many things
to fear from environmental radiation pollution, turn-
where ptϪ1 is the frequency in the preceding genera- ing into a species of monsters is not one of them.
tion. This tells us that the frequency of A decreases
(and the frequency of a increases) by an amount that 1.0
is proportional to the mutation rate ␮ and to the pro-
portion p of all the genes that are still available to mu- 0.9
tate. Thus ⌬p gets smaller as the frequency of p itself
decreases, because there are fewer and fewer A alleles 0.8 µ = 10−5
to mutate into a alleles. We can make an approxima- 0.7
tion that, after n generations of mutation,

p (A) 0.6

pn ϭ p0eϪn␮ 0.5

where e is the base of the natural logarithms. 0.4
This relation of allele frequency to number of
generations is shown in the adjoining figure for ␮ ϭ
10Ϫ5. After 10,000 generations of continued mutation 0.2
of A to a,

0.0 50,000 100,000 150,000 200,000

Number of generations

p ϭ p eϪ(104) ϫ (10Ϫ5) ϭ p0eϪ0.1 ϭ 0.904p0 The change over generations in the frequency of a gene A due to
0 mutation from A to a at a constant mutation rate (␮) of 10Ϫ5.

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628 Chapter 19 • Population Genetics

Most mutation rates that have been determined are The creation of genetic variation by recombination
the sum of all mutations of A to any mutant form with a can be a much faster process than its creation by muta-
detectable effect. The mutation process is even slower if tion. This high rate of the production of variation is sim-
we consider the increase of a particular new allelic type. ply a consequence of the very large number of different
Any specific base substitution is likely to be at least two recombinant chromosomes that can be produced even if
orders of magnitude lower in frequency than the sum of we take into account only single crossovers. If a pair of
all changes. homologous chromosomes is heterozygous at n loci,
then a crossover can take place in any one of the n Ϫ 1
Variation from recombination intervals between them, and because each recombina-
tion produces two recombinant products, there are
When a new mutation of a gene arises in a population, 2(n Ϫ 1) new unique gametic types from a single gener-
it occurs as a single event on a particular copy of a ation of crossing-over, even considering only single
chromosome carried by some individual. But that chro- crossovers. If the heterozygous loci are well spread out
mosome copy has a particular allelic composition for all along the chromosome, these new gametic types will be
the other polymorphic genes on the chromosome. So, if frequent and considerable variation will be generated.
the mutant allele a arose at the A locus on a chromo- Asexual organisms or organisms such as bacteria that
some copy that already had the allele b at the B locus, very seldom undergo sexual recombination do not have
then without recombination all gametes carrying the a this source of variation, so new mutations are the only
allele would also carry the b allele in future generations. way in which a change in gene combinations can be
The population would then contain only the original achieved. As a result, populations of asexual organisms
A B haplotype and the new a b haplotype that arose may change more slowly than sexual organisms.
from the mutation. Recombination between the A gene
and the B gene in the double heterozygote A B/a b, how- Variation from migration
ever, would produce two new haplotypes A b and a B.
A further source of variation is migration into a popula-
The consequence of repeated recombination be- tion from other populations with different gene fre-
tween genes is to randomize combinations of alleles of quencies. The resulting mixed population will have an
different genes. If the allele frequency of a at locus A is, allele frequency that is somewhere intermediate be-
say, .2, and the frequency of allele b at locus B is, say, .4, tween its original value and the frequency in the donor
then the frequency of a b would be (.2)(.4) ϭ .08 if the population.
combinations were randomized. This randomized condi-
tion is linkage equilibrium. Suppose a population receives a group of migrants
and the number of immigrants is equal to, say, 10 per-
Recombination between genes on the same chromo- cent of the native population size. Then the newly
some will not produce linkage equilibrium in a single formed mixed population will have an allele frequency
generation if the alleles at the different genes began in that is a 0.90 : 0.10 mixture between its original allele
nonrandom association with each other. This original as- frequency and the allele frequency of the donor popula-
sociation, linkage disequilibrium, decays only slowly tion. If its original allele frequency of A were, say, 0.70,
from generation to generation at a rate that is propor- whereas the donor population had an allele frequency
tional to the amount of recombination between the of A that was only, say, 0.40, the new mixed population
genes. This fact can be used to find the location of un- would have an allele frequency of A that was
known genes on chromosomes and to provide evidence 0.70 ϫ 0.90 ϩ 0.40 ϫ 0.10 ϭ 0.67. Box 19-4 de-
that some phenotypic variant is, in fact, influenced by an rives the general result. As shown in Box 19-4, the
unknown gene. Suppose that people who suffered from change in gene frequency is proportional to the differ-
some disease, say, diabetes, also turned out to carry an al- ence in frequency between the recipient population and
lele of some marker gene that has nothing to do with in- the average of the donor populations. Unlike the muta-
sulin formation, more often than would be expected if tion rate, the migration rate (m) can be large, so if the
the association between diabetes and the marker allele difference in allele frequency between the donor and re-
were random. This finding would be evidence that dia- cipient population is large, the change in frequency may
betes is influenced by a gene on the same chromosome be substantial.
as the marker gene, and if the linkage disequilibrium
were quite strong, that the diabetes-related gene was We must understand migration as meaning any form
fairly close to the marker. The existence of such a link- of the introduction of genes from one population into
age disequilibrium would presumably be the accidental another. So, for example, genes from Europeans have
result of the original mutational origin of the marker al- “migrated” into the population of African origin in
lele on the same chromosome copy as the allele associ- North America steadily since the Africans were intro-
ated with diabetes. duced as slaves. We can determine the amount of this

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19.4 Selection 629

BOX 19-4 The Effect of Migration on Allele Frequency

If pt is the frequency of an allele in a recipient popu- from the recipient population with m genes from
lation in generation t, P is the frequency of that the donor population. Thus
allele in a donor population (or the average over
several donor populations), and m is the proportion ptϩ1 ϭ (1 Ϫ m)pt ϩ mP ϭ pt ϩ m(P Ϫ pt)
of the recipient population that is made up of new and
migrants from the donor population, then the allele
frequency in the recipient population in the next ⌬p ϭ ptϩ1 Ϫ pt ϭ m(P Ϫ pt)
generation, ptϩ1, is the result of mixing 1 Ϫ m genes

migration by looking at the frequency of an allele that is rates in these cities than in Georgia or differential move-
found only in Europeans and not in Africans and com- ment into these cities by American blacks who have
paring its frequency among blacks in North America. We more European ancestry. In any case, the genetic varia-
can use the formula for the change in gene frequency tion at the Fy locus has been increased by this admixture.
from migration if we modify it slightly to account for At the same time the frequency of the sickle-cell muta-
the fact that several generations of admixture have taken tion Hb-S has been decreased in African Americans by
place. If the rate of admixture has not been too great, between 10 and 20 percent of its value in their ancestral
then (to a close order of approximation) the sum of the African populations as a result of admixture.
single-generation migration rates over several genera-
tions (let’s call this M) will be related to the total change 19.4 Selection
in the recipient population after these several genera-
tions by the same expression as the one used in Box So far in this chapter, we have considered changes in a
19-4 for changes due to a single generation of migration. population arising from forces of mutation, migration,
If, as before, P is the allelic frequency in the donor popu- recombination, and breeding structure. But these
lation and p0 is the original frequency among the recipi- changes cannot explain why organisms seem so well
ents, then adapted to their environments, because they are random
with respect to the way in which organisms make a liv-
⌬ptotal ϭ M(P Ϫ p0) ing in the environments in which they live. Changes in a
species in response to a changing environment occur be-
so cause the different genotypes produced by mutation and
recombination have different abilities to survive and re-
Mϭ ⌬ptotal produce. The differential rates of survival and reproduc-
P Ϫ p0 tion are what is meant by selection, and the process of
selection alters the frequencies of the various genotypes
For example, the Duffy blood group allele Fya is absent in the population. Darwin called the process of differen-
in Africa but has a frequency of 0.42 in whites from the tial survival and reproduction of different types natural
state of Georgia. Among blacks from Georgia, the Fya selection by analogy with the artificial selection carried
frequency is 0.046. Therefore, the total migration of out by animal and plant breeders when they deliberately
genes from whites into the black population since the select some individuals of a preferred type.
introduction of slaves in the eighteenth century is
The relative probability of survival and rate of re-
Mϭ ⌬ptotal ϭ (0.046 Ϫ 0.0) ϭ .1095 production of a phenotype or genotype is now called its
P Ϫ p0 (0.42 Ϫ 0.0) Darwinian fitness. Although geneticists sometimes speak
loosely of the fitness of an individual, the concept of fit-
That is, on the average over all Americans of African an- ness really applies to the average probability of survival
cestry in Georgia, about 11 percent of their gene alleles and average reproductive rate of individuals in a pheno-
have been derived from a European ancestor. This is only typic or genotypic class. Because of chance events in the
an average, however, and different individuals have dif- life histories of individuals, even two organisms with
ferent proportions of European and African ancestry. identical genotypes, living in identical environments, will
When the same analysis is carried out on American not live to the same age or leave the same number of
blacks from Oakland (California) and Detroit, M is 0.22 offspring. It is the fitness of a genotype on average over
and 0.26, respectively, showing either greater admixture all its possessors that matters.

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630 Chapter 19 • Population Genetics

Fitness is a consequence of the relation between the will affect their relative fitnesses. An example is Müller-
phenotype of the organism and the environment in ian mimicry in butterflies. Some species of brightly col-
which the organism lives, so the same genotype will ored butterflies (such as monarchs and viceroys) are dis-
have different fitnesses in different environments. One tasteful to birds, which learn, after a few trials, to avoid
reason is that even genetically identical organisms may attacking butterflies with a pattern that they associate
develop different phenotypes if exposed to different en- with distastefulness. Within a species that has more than
vironments during development. But, even if the pheno- one pattern, rarer patterns will be selected against. The
type is the same, the success of the organism depends on rarer the pattern, the greater is the selective disadvan-
the environment. Having webbed feet is fine for pad- tage, because birds will be unlikely to have had a prior
dling in water but a positive disadvantage for walking on experience of a low-frequency pattern and therefore will
land, as a few moments spent observing how a duck not avoid it. This selection to blend in with the crowd is
walks will reveal. No genotype is unconditionally supe- an example of frequency-dependent fitness, because the
rior in fitness to all others in all environments. fitness of a type changes as it becomes more or less fre-
quent in the population.
Reproductive fitness is not to be confused with
“physical fitness” in the everyday sense of the term, al- For reasons of mathematical convenience, most
though they may be related. No matter how strong, models of natural selection are based on frequency-
healthy, and mentally alert the possessor of a genotype independent fitness. In fact, however, a very large num-
may be, that genotype has a fitness of zero if for some ber of selective processes (perhaps most) are frequency-
reason its possessors leave no offspring. The fitness of a dependent. The kinetics of the change in allele fre-
genotype is a consequence of all the phenotypic effects quency depends on the exact form of frequency
of the genes involved. Thus, an allele that doubles the fe- dependence, and for that reason alone, it is difficult to
cundity of its carriers but at the same time reduces the make any generalizations. For the sake of simplicity
average lifetime of its possessors by 10 percent will be and as an illustration of the main qualitative features
more fit than its alternatives, despite its life-shortening of selection, we deal only with models of frequency-
property. The most common example is parental care. independent selection in this chapter, but convenience
An adult bird that expends a great deal of its energy should not be confused with reality.
gathering food for its young will have a lower probabil-
ity of survival than one that keeps all the food for itself. Measuring fitness differences
But a totally selfish bird will leave no offspring, because
its young cannot fend for themselves. As a consequence, For the most part, we can measure the differential fit-
parental care is favored by natural selection. ness of different genotypes most easily when the geno-
types differ at many loci. In very few cases, such as labo-
Two forms of selection ratory mutants, horticultural varieties, and major
metabolic disorders, does an allelic substitution at a sin-
Because the differences in reproduction and survival be- gle locus make enough difference to the phenotype to
tween genotypes depend on the environment in which measurably alter fitness. Figure 19-9 shows the probabil-
the genotypes live and develop and because organisms ity of survival from egg to adult — that is, the viability —
may alter their own environments, there are two funda- at three different temperatures of a number of different
mentally different forms of selection. In the simple case, lines made homozygous for the second chromosomes of
the fitness of an individual does not depend on the com- D. pseudoobscura. These chromosomes were sampled
position of the population; rather it is a fixed property of from a natural population and carried a variety of differ-
the individual’s phenotype and the external physical en- ent alleles at different loci, as we expect from the very
vironment. For example, the relative ability of two large amount of nucleotide variation present in nature
plants that live at the edge of the desert to get sufficient (see pages 619 – 620). As is generally the case, the fitness
water will depend on how deep their roots grow and (in this case, a component of the total fitness, viability) is
how much water they lose through their leaf surfaces. different in different environments. The homozygous
These characteristics are a consequence of their develop- state is lethal or nearly so in a few cases at all three tem-
mental patterns and are not sensitive to the composition peratures, whereas a few cases have consistently high vi-
of the population in which they live. The fitness of a ability. Most genotypes, however, are not consistent in
genotype in such a case does not depend on how rare viability between temperatures, and no genotype is un-
or how frequent it is in the population. Fitness is then conditionally the most fit at all temperatures.
There are cases in which single-gene substitutions
In contrast, consider organisms that are competing lead to clear-cut fitness differences. Examples are the
to catch prey or to avoid being captured by a predator. many “inborn errors of metabolism,” where a recessive
Then the relative abundances of two different genotypes allele interferes with a metabolic pathway and is lethal

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19.4 Selection 631

1.00 A/A A/a a/a
0.90 0.81 0.18 0.01
0.60 At reproductive age, however, the homozygotes a/a will
0.45 have already died, leaving the genotypes at this stage as
0.15 A/A A/a a/a
0.81 0.18 0.00

Viability But these proportions add up to only 0.99 because only
99 percent of the population is still surviving. Among
the actual surviving reproducing population, the propor-
tions must be recalculated by dividing by 0.99, so that
the total proportions add up to 1.00. After this readjust-
ment, we have

A/A A/a a/a
0.818 0.182 0.00

The frequency of the lethal a allele among the gametes
produced by these survivors is then

0.00 ϩ 0.182/2 ϭ 0.091

16.5 21 25.5

Temperature (˚C) and the change in allelic frequency of the lethal in one
generation, expressed as the new value minus the old
Figure 19-9 Viabilities of various chromosomal homozygotes one, has been 0.091 Ϫ 0.100 ϭ Ϫ0.019. Conversely, the
of Drosophila pseudoobscura at three different temperatures. change in the frequency of the normal allele has been
ϩ0.019. We can repeat this calculation in each succes-
in homozygotes. One example is sickle-cell anemia. Indi- sive generation to obtain the predicted frequencies of
viduals with this disorder are homozygous for the allele the lethal and normal alleles in a succession of future
that codes for hemoglobin-S instead of the normal generations.
hemoglobin. They die from a severe anemia because
hemoglobin-S crystallizes at low oxygen concentrations, The same kind of calculation can be carried out if
causing the red blood cells to become sickle-shaped and genotypes are not simply lethal or normal, but if each
then to rupture (Figure 19-10).
Figure 19-10 Red blood cells of a person with sickle-cell
As we saw in Chapter 6, another example in hu- anemia. A few normal disk-shaped red blood cells are
mans is phenylketonuria, where tissue degenerates as the surrounded by distorted sickle-shaped cells.
result of the accumulation of a toxic intermediate in the
pathway of tyrosine metabolism. This case also illus-
trates how fitness is altered by changes in the environ-
ment. People born with PKU will survive if they observe
a strict diet that contains no tyrosine.

How selection works

Selection acts by altering allele frequencies in a popula-
tion. The simplest way to see the effect of selection is to
consider an allele a that is completely lethal before re-
productive age in homozygous condition, such as the al-
lele that leads to Tay-Sachs disease. Suppose that in
some generation the allele frequency of this gene is 0.10.
Then, in a random-mating population, the proportions
of the three genotypes after fertilization are

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632 Chapter 19 • Population Genetics

genotype has some relative probability of survival. This greater than the average fitness of all alleles, then WA/ W
general calculation is shown in Box 19-5. After one gen- is greater than unity and pЈ is larger than p. Thus, the al-
eration of selection, the new value of the frequency of A lele A increases in the population. Conversely, if WA/ W
is equal to the old value (p) multiplied by the ratio of is less than unity, A decreases. But the mean fitness of the
the mean fitness of A alleles, WA, to the mean fitness of
the whole population, W. If the fitness of A alleles is population (W) is the average fitness of the A alleles and

of the a alleles. So if WA is greater than the mean fitness

BOX 19-5 The Effect of Selection on Allele Frequencies

Suppose that a population is mating at random with We can now determine the frequency pЈ of the allele
respect to a given locus with two alleles and that the A in the next generation by summing up genes:
population is so large that (for the moment) we can
ignore inbreeding. Just after the eggs have been fertil- pЈ ϭ A/A ϩ 1 A/a ϭ p2 WA/A ϩ pq WA/a
ized, the genotypes of the zygotes will be in Hardy- 2 W W
Weinberg equilibrium:
ϭ p pWA/A ϩ qWA/a
Genotype A/A A/a a/a
Frequency p2 2pq q2 Finally, we note that the expression pWA/A ϩ qWA/a is
the mean fitness of A alleles because, from the Hardy-
Weinberg frequencies, a proportion p of all A alleles
p2 ϩ 2pq ϩ q2 ϭ ( p ϩ q)2 ϭ 1.0
are present in homozygotes with another A, in which
where p is the frequency of A.
Further suppose that the three genotypes have case they have a fitness of WA/A, whereas a proportion
q of all the A alleles are present in heterozygotes with
the relative probabilities of survival to adulthood (via-
bilities) of WA/A, WA/a, and Wa/a. For simplicity, let us a and have a fitness of WA/a. Using WA to denote
also assume that all fitness differences are differences pWA/A ϩ qWA/a, the mean fitness of the allele A yields
in survivorship between the fertilized egg and the the final new allele frequency
adult stage. (Differences in fertility give rise to much
more complex mathematical formulations.) Among pЈ ϭ p WA
the progeny, once they have reached adulthood, the W
frequencies will be
An alternative way to look at the process of selection
is to solve for the change in allele frequencies in one

Genotype A/A A/a a/a ⌬p ϭ pЈ Ϫ p ϭ p WA Ϫ p
Frequency p2WA/A 2pqWA/a q2Wa/a W

These adjusted frequencies do not add up to unity, be- ϭ p(WA Ϫ W )
cause the W’s are all fractions smaller than 1. However, W
we can readjust them so that they do, without changing
their relation to one another, by dividing each frequency But W , the mean fitness of the population, is the av-
by the sum of the frequencies after selection (W): erage of the allele fitnesses WA and Wa, so

W ϭ p2WA/A ϩ 2pqWA/a ϩ q2Wa/a W ϭ pWA ϩ qWa

So defined, W is called the mean fitness of the popu- where Wa is the mean fitness of a alleles. Substituting
lation because it is, indeed, the mean of the fitnesses this expression for W in the formula for ⌬p and re-
of all individuals in the population. After this adjust- membering that q ϭ 1 Ϫ p, we obtain (after some al-
ment, we have gebraic manipulation)

Genotype A/A A/a a/a ⌬p ϭ pq(WA Ϫ Wa)
Frequency p2 WA/A 2pq WA/a q2 Wa/a W


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19.4 Selection 633

of the population, it must be greater than Wa, the mean 1.0Frequency of A
fitness of a alleles. Thus the allele with the higher mean 0.9
fitness increases in frequency. 0.8
It should be noted that the fitnesses WA/A, WA/a, and 0.6
Wa/a may be expressed as absolute probabilities of sur- 0.5
vival and absolute reproduction rates, or they may all be 0.4
rescaled relative to one of the fitnesses, which is given 0.3
the standard value of 1.0. This rescaling has absolutely 0.2
no effect on the formula for pЈ, because it cancels out in 0.1
the numerator and denominator. 0.0

MESSAGE As a result of selection, the allele with the Number of generations
higher mean fitness relative to the mean fitnesses of other
alleles increases in frequency in the population. Figure 19-11 The time pattern of increasing frequency of a
new favorable allele A that has entered a population of a/a
An increase in the allele with the higher fitness homozygotes.
means that the average fitness of the population as a
whole increases, so selection can also be described as a recently entered a population of homozygotes a/a. At
process that increases mean fitness. This rule is strictly first, the change in frequency is very small because p is
true only for frequency-independent genotypic fitnesses, still close to 0. Then it accelerates as A becomes more
but it is close enough to a general rule to be used as a frequent, but it slows down again as A takes over and a
fruitful generalization. This maximization of fitness does becomes very rare (q gets close to 0). This is precisely
not necessarily lead to any optimal property for the what is expected from a selection process. When most of
species as a whole, because fitnesses are defined only rel- the population is of one type, there is nothing to select.
ative to one another within a population. It is relative For change by natural selection to occur, there must
(not absolute) fitness that is increased by selection. The be genetic variation; the more variation, the faster the
population does not necessarily become larger or grow process.
faster, nor is it less likely to become extinct. For example
suppose that an allele causes its carriers to lay more eggs One consequence of the dynamics shown in Figure
than do other genotypes in the population. This higher 19-11 is that it is extremely difficult to significantly re-
fecundity allele will increase in the population. But the duce the frequency of an allele that is already rare in a
population size at the adult stage may depend on the to- population. Thus, eugenics programs designed to elimi-
tal food supply available to the immature stages, so there nate deleterious recessive alleles from human popula-
will not be an increase in the total population size, but tions by preventing the reproduction of affected persons
only an increase in the number of immature individuals do not work. Of course, if all heterozygotes could be
that starve to death before adulthood. prevented from reproducing, the allele could be elimi-
nated (except for new mutations) in a single generation.
Rate of change in gene frequency Because every human being is heterozygous for a num-
ber of different deleterious genes, however, no one
The general expression for the change in allele fre- would be allowed to reproduce.
quency derived in Box 19-5 is particularly illuminating.
It says that ⌬p will be positive (A will increase) if the When alternative alleles are not rare, selection can
mean fitness of A alleles is greater than the mean fitness cause quite rapid changes in allelic frequency. Figure
of a alleles, as we saw before. But it also shows that the 19-12 shows the course of elimination of a malic dehy-
speed of the change depends not only on the difference drogenase allele that had an initial frequency of 0.5 in a
in fitness between the alleles, but also on the factor pq, laboratory population of D. melanogaster. The fitnesses in
which is proportional to the frequency of heterozygotes this case are
(2pq). For a given difference in fitness of alleles, their
frequency will change most rapidly when the alleles A WA/A ϭ 1.0 WA/a ϭ 0.75 Wa/a ϭ 0.40
and a are in intermediate frequency, so pq is large. If p is
near 0 or 1 (that is, if A or a is nearly fixed at frequency The frequency of a declines rapidly but is not reduced
0 or 1), then pq is nearly 0 and selection will proceed to 0, and to continue reducing its frequency would re-
very slowly. quire longer and longer times, as shown in the negative
eugenics case.
The S-shaped curve in Figure 19-11 represents the
course of selection of a new favorable allele A that has MESSAGE Unless alternative alleles are present in
intermediate frequencies, selection (especially against
recessives) is quite slow. Selection is dependent on genetic

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634 Chapter 19 • Population Genetics

0.70 equilibrium will be counteracted by the force of selec-
tion. We can symbolize the fitnesses of the three geno-
0.60 types by

0.50Frequency of MDH F WA/A WA/a Wa/a
1Ϫt 1 1Ϫs
where t and s are the selective disadvantages of the two
0.30 homozygotes. Then the equilibrium frequency of the al-
lele A is simply the ratio
p(A) ϭ s/(s ϩ t)
(As an advanced exercise, the reader can derive this
0 2 4 6 8 10 12 14 result by noting that at equilibrium the average fitness of
Generations the A allele, WA, is equal to the average fitness of the a
allele, Wa. Setting these equal to each other and solving
Figure 19-12 The loss of an allele MDH F at the malic for p(A) give the result.) This equilibrium explains the
dehydrogenase locus due to selection in a laboratory population high frequency of the sickle-cell condition in West
of Drosophila melanogaster. The red dashed line shows the Africa. Homozygotes for the abnormal allele Hb-S die
theoretical curve of change computed for fitnesses WA/A ϭ prematurely from anemia. But there is a high mortality
1.0, WA/a ϭ 0.75, Wa/a ϭ 0.4. [From R. C. Lewontin, The Genetic in West Africa from falciparum malaria, which kills
many of the homozygotes for the normal allele, Hb-A.
Basis of Evolutionary Change. Copyright 1974 by Columbia University Heterozygotes, Hb-A/Hb-S, suffer only a mild, nonfatal
Press. Data courtesy of E. Berger.] anemia, and they are protected against falciparum
malaria by the presence of the abnormal hemoglobin in
19.5 Balanced polymorphism their red blood cells. This overdominance in fitness was
lost, however, when slaves were brought to the new
Thus far we have considered the changes in allelic fre- world because the falciparum form of malaria does not
quency that occur when the homozygous carriers of one exist in the western hemisphere. As a consequence,
allele, say, A/A, are more fit than homozygous carriers among slaves and their descendants, selection was only
for another allele, say, a/a, while the heterozygotes, A/a, against the homozygous Hb-S/Hb-S, leading to a reduc-
are somewhere between A/A and a/a in their fitness. tion in the frequency of this allele through mortality. Re-
But there are other possibilities. cently, sickle-cell anemia has received sufficient medical
attention that it is no longer a significant source of mor-
Overdominance and underdominance tality, so selection against the Hb-S allele is no longer so
powerful. Further reductions in the frequency of the al-
First, the heterozygote might be more fit than either ho- lele will then be mostly the consequence of continued
mozygote, a condition termed overdominance in fitness. admixture with populations of non-African ancestry.
When one of the alleles, say, A, is in low frequency, there
are virtually no homozygotes A/A and the allele occurs Another possible fitness relation among alleles is
almost entirely in heterozygous condition. Since hetero- that the heterozygote is less fit than either homozygote
zygotes are more fit than homozygotes, A alleles are al- (underdominance in fitness) In this case selection favors
most all carried by the most fit genotype, so A will in- an allele when it is common, not when it is rare, so an
crease in frequency, while a decreases in frequency. On intermediate allele frequency is unstable, and the popu-
the other hand when a is in very low frequency, it oc- lation should become fixed for either the A allele or the
curs almost entirely in heterozygous condition. In this a allele. Polymorphism resulting from a mixture of an
case, a alleles are almost all carried by the most fit geno- A/A population with an a/a population should be
type, and they will increase in frequency at the expense rapidly lost. A well-known, but mysterious example of
of A alleles. The net effect of these two pressures, one underdominance in fitness is Rh incompatibility in hu-
increasing the frequency of A alleles when they are rare, mans. Rh-positive children born to Rh-negative mothers
and the other increasing a alleles when they are rare, is often suffer hemolytic anemia as newborns because
to bring the allele frequencies to a stable equilibrium their mothers produce antibodies against the blood cells
that is intermediate between a composition consisting of of the fetus. Rh-negative mothers are homozygotes,
all of one allele or all of the other. Any chance deviation RhϪ/RhϪ, so their Rh-positive offspring who die from
of the allele frequencies on one side or the other of the anemia must be heterozygotes, RhϪ/Rhϩ. The mystery is

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19.5 Balanced polymorphism 635

that all human populations are polymorphic for the two So, for example, a recessive lethal (s ϭ 1) mutating at
Rh alleles. Thus, this human polymorphism must be very the rate of ␮ ϭ 10Ϫ6 will have an equilibrium fre-
old, antedating the origin of modern geographical races. quency of 10Ϫ3. Indeed, if we knew that an allele was a
Yet the simple theoretical prediction is that such a poly- recessive lethal and had no heterozygous effects, we
morphism is unstable and should have disappeared. could estimate its mutation rate as the square of its fre-
quency. But the biological basis for the assumptions be-
Balance between mutation and selection hind such calculations must be firm. Sickle-cell anemia
was once thought to be a recessive lethal with no het-
The overdominant balance of selective forces is not the erozygous effects, which led to an estimated mutation
only situation in which a stable equilibrium of allelic rate in Africa of 0.1 for this locus, but now we know
frequencies may arise. Allele frequencies may also reach that its equilibrium is a result of higher fitness of
equilibrium in populations when the introduction of heterozygotes.
new alleles by repeated mutation is balanced by their re-
moval by natural selection. This balance probably ex- A similar result can be obtained for a deleterious
plains the persistence of genetic diseases as low-level allele that has some effect in heterozygotes. If we let
polymorphisms in human populations. New deleterious the fitnesses be WA/A ϭ 1.0, WA/a ϭ 1 Ϫ hs, and Wa/a ϭ
mutations are constantly arising spontaneously or as the 1 Ϫ s for a partly dominant allele a, where h is the de-
result of the action of mutagens. These mutations may gree of dominance of the deleterious allele, then a calcu-
be completely recessive or partly dominant. Selection lation similar to the one in Box 19-6 gives us
removes them from the population, but there will be an
equilibrium between their appearance and removal. qˆ ϭ ␮
The general equation for this equilibrium is given in
detail in Box 19-6. It shows that the frequency of the Thus, if ␮ ϭ 10Ϫ6 and the lethal is not totally recessive
deleterious allele at equilibrium depends on the ratio but has a 5 percent deleterious effect in heterozygotes
␮/s, where ␮ is the probability of a mutation’s occurring (s ϭ 1.0, h ϭ 0.05), then
in a newly formed gamete (mutation rate) and s is the
intensity of selection against the deleterious genotype. qˆ ϭ 5 10Ϫ6 ϭ2 ϫ 10Ϫ5
For a completely recessive deleterious allele whose fit- ϫ 10Ϫ2
ness in homozygous state is 1 Ϫ s, the equilibrium fre-
quency is

√q ϭ ␮ which is smaller by two orders of magnitude than the
s equilibrium frequency for the purely recessive case. In
general, then, we can expect deleterious, completely

BOX 19-6 The Balance Between Selection and Mutation

If we let q be the frequency of the deleterious allele a Equilibrium means that the increase in the allele fre-
and p ϭ 1 Ϫ q be the frequency of the normal allele quency due to mutation must exactly balance the de-
A, then the change in allele frequency due to the mu- crease in the allele frequency due to selection, so
tation rate ␮ is
⌬qˆmut ϩ ⌬qˆsel ϭ 0
⌬qmut ϭ ␮p
Remembering that qˆ at equilibrium will be quite
A simple way to express the fitnesses of the geno- small, so 1 Ϫ sqˆ2 Ϸ 1, and substituting the terms for
types in the case of a recessive deleterious allele a is ⌬qˆmut and ⌬qˆsel in the preceding formula, we have
WA/A ϭ WA/a ϭ 1.0, and Wa/a ϭ 1 Ϫ s, where s is
the loss of fitness in the recessive homozygotes. We ␮pˆ Ϫ s pˆ qˆ 2 Ϸ ␮pˆ Ϫ spˆqˆ 2 ϭ 0
now can substitute these fitnesses in our general ex- 1 Ϫ sqˆ2
pression for allele frequency change (see Box 19-5)
and obtain or

⌬qsel ϭ Ϫpq(sq) ϭ Ϫspq2 √qˆ2 ϭ ␮ and qˆ ϭ ␮
1 Ϫ sq2 1 Ϫ sq2 s s

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636 Chapter 19 • Population Genetics

recessive alleles to have frequencies much higher than cestral individuals have a high probability that all theFrequency of new mutation
those of partly dominant alleles, because the recessive al- copies of a particular allele are identical by descent from
leles are protected in heterozygotes. a single common ancestor (see Figure 19-7). Whether
regarded as inbreeding or as random sampling of genes,
19.6 Random events the effect is the same. Populations do not exactly repro-
duce their genetic constitutions; there is a random com-
If a population consists of a finite number of individuals ponent of gene frequency change.
(as all real populations do) and if a given pair of parents
has only a small number of offspring, then even in the One result of random sampling is that most new
absence of all selective forces, the frequency of a gene mutations, even if they are not selected against, never
will not be exactly reproduced in the next generation, succeed in becoming part of the long-term genetic com-
because of sampling error. If, in a population of 1000 in- position of the population. Suppose that a single individ-
dividuals, the frequency of a is 0.5 in one generation, ual is heterozygous for a new mutation. There is some
then it may by chance be 0.493 or 0.505 in the next chance that the individual in question will have no off-
generation because of the chance production of slightly spring at all. Even if it has one offspring, there is a
more or slightly fewer progeny of each genotype. In the chance of 1/2 that the new mutation will not be trans-
second generation, there is another sampling error based mitted to that offspring. If the individual has two off-
on the new gene frequency, so the frequency of a may spring, the probability that neither offspring will carry
go from 0.505 to 0.511 or back to 0.498. This process of the new mutation is 1/4, and so forth. Suppose that the
random fluctuation continues generation after genera- new mutation is successfully transmitted to an offspring.
tion, with no force pushing the frequency back to its ini- Then the lottery is repeated in the next generation, and
tial state, because the population has no “genetic mem- again the allele may be lost. In fact, if a population is of
ory” of its state many generations ago. Each generation is size N, the chance that a new mutation is eventually lost
an independent event. This random change in allele fre- by chance is (2N Ϫ 1)/2N. (For a derivation of this re-
quencies is known as genetic drift. sult, which is beyond the scope of this book, see Chap-
ters 2 and 3 of Hartl and Clark, Principles of Population
The final result of genetic drift is that the population Genetics, 3d ed. Sinauer Associates, 1997.) But, if the
eventually drifts to p ϭ 1 or p ϭ 0. After this point, no new mutation is not lost, then the only thing that can
further change is possible; the population has become ho- happen to it in a finite population is that eventually it
mozygous. A different population, isolated from the first,
also undergoes this random genetic drift, but it may be- 1.0
come homozygous for allele A, whereas the first popula-
tion has become homozygous for allele a. As time goes on, 0.5
isolated populations diverge from one another, each losing
heterozygosity. The variation originally present within pop- 0.0
ulations now appears as variation between populations. Number of generations

One form of genetic drift occurs when a small group Figure 19-13 The appearance, loss, and eventual incor-
breaks off from a larger population to found a new poration of new mutations in the life of a population. If
colony. This “acute drift,” called the founder effect, re- random genetic drift does not cause the loss of a new
sults from a single generation of sampling of a small mutation, then it must eventually cause the entire population
number of colonizers from the original large population, to become homozygous for the mutation (in the absence of
followed by several generations during which the new selection). In the figure, 10 mutations arise, of which 9 (light
colony remains small in number. Even if the population red at bottom of graph) increase slightly in frequency and then
grew large after some time, it would continue to drift, die out. Only the fourth mutation to occur (blue line)
but at a slower rate. The founder effect is probably re- eventually spreads into the population. [After J. Crow and
sponsible for the virtually complete lack of blood group
B in Native Americans, whose ancestors arrived in very M. Kimura, An Introduction to the Population Genetics Theory.
small numbers across the Bering Strait at the end of the Copyright 1970 by Harper & Row.]
last ice age, about 20,000 years ago, but whose ancestral
population in northeastern Asia had an intermediate fre-
quency of group B.

The process of genetic drift should sound familiar. It
is, in fact, another way of looking at the inbreeding ef-
fect in small populations discussed earlier. Populations
that are the descendants of a very small number of an-

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19.5 Key questions revisited 637

will sweep through the population and become fixed. zygous, but the pattern of frequencies of the alleles is
This event has the probability of 1/2N. In the absence of very different in the two.
selection, then, the history of a population looks like Fig-
ure 19-13. For some period of time, it is homozygous; Even a new mutation that is slightly favorable selec-
then a new mutation appears. In most cases, the new tively will usually be lost in the first few generations after
mutant allele will be lost immediately or very soon after it appears in the population, a victim of genetic drift. If a
it appears. Occasionally, however, a new mutant allele new mutation has a selective advantage of s in the het-
drifts through the population, and the population be- erozygote in which it appears, then the chance is only 2s
comes homozygous for the new allele. The process then that the mutation will ever succeed in taking over the
begins again. population. So a mutation that is 1 percent better in fit-
ness than the standard allele in the population will be lost
A striking example of the effect of genetic drift in 98 percent of the time by genetic drift. It is even possible
human populations is the variation in frequencies of the for a very slightly deleterious mutation to rise in fre-
VNTR repeat length variants among populations of quency and become fixed in a population by drift.
South American Indians that we saw illustrated in Table
19-5. For one VNTR, D14S1, the Surui are very vari- MESSAGE New mutations can become established in a
able, but the Karitiana, living several hundred miles population even though they are not favored by natural
away in the Brazilian rain forest, are nearly homozygous selection simply by a process of random genetic drift. Even
for one allele, presumably because of genetic drift in new favorable mutations are often lost, and occasionally a
these very small isolated populations. For the other slightly deleterious mutation can take over a population by
VNTR, D14S13, neither population has become homo- drift.

KEY QUESTIONS REVISITED solely between relatives, then eventually the population
becomes completely homozygous.
• How much genetic variation is there in natural
populations of organisms? • What are the sources of the genetic variation that is
observed in populations?
Genetic variation among individuals in populations is
extremely common. In many species there is polymor- The ultimate source of all genetic variation is mutation.
phism within populations for chromosomal rearrange- Variation for a gene in a given population will be in-
ments such as inversions and translocations. Variation at creased if migration from other populations brings into
the DNA sequence level is present in all species. Typi- the recipient population gene alleles that are not already
cally a population is polymorphic for 25 to 33 percent present or are in lower frequency than in the donor pop-
of its protein coding genes, where polymorphism is de- ulation. Variation for the genome as a whole is increased
fined as having two or more alleles at frequencies of by recombination, which brings together new combina-
1 percent or greater in the population, and an average tions of alleles at different loci.
individual is heterozygous for about 10 percent of
the nonsynonymous nucleotides in protein coding se- • What are the processes that cause changes in the kind
quences. On the average individuals within a population and amount of genetic variation in populations?
differ by between one-tenth and one-half of all their nu-
cleotides in their genomes. Any two humans differ by Changes in the amount and pattern of variation in a
about 3 million nucleotides. population are the result of (a) recurrent mutation’s
putting a constant flow of mutations into the popula-
• What are the effects of patterns of mating on genetic tion, (b) migration from populations with allele frequen-
variation? cies different from those of the recipient population,
(c) recombination of genotypes within the population,
If mating is at random with respect to genotype, then (d) natural selection that increases or decreases the fre-
the proportion of heterozygotes and homozygotes for a quency of particular genotypes as a result of their differ-
genetically variable gene is at an equilibrium that de- ential rates of survival and reproduction, (e) random ge-
pends only on the frequency of the alternative alleles netic drift, which causes random changes in the
(the Hardy-Weinberg equilibrium). If there is preferen- frequencies of genotypes as a result of the sampling of
tial mating between relatives (inbreeding) or between gametes that occurs in successive generations because
individuals who are more alike (positive assortative mat- the population is finite in size.
ing), the proportion of homozygotes is greater than pre-
dicted by the Hardy-Weinberg equilibrium. If mating is

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638 Chapter 19 • Population Genetics

SUMMARY converted into differences between populations by mak-
ing each separate population homozygous for a ran-
The study of changes within a population, or population domly chosen allele. On the other hand, for most popu-
genetics, relates the heritable changes in populations or lations, a balance is reached between inbreeding,
organisms to the underlying individual processes of in- mutation from one allele to another, and immigration.
heritance and development. Population genetics is the
study of inherited variation and its modification in time An allele may go up or down in frequency within a
and space. population through the natural selection of genotypes
with higher probabilities of survival and reproduction. In
Identifiable inherited variation within a population many cases, such changes lead to homozygosity at a par-
can be studied by examining the differences in specific ticular locus. On the other hand, the heterozygote may
amino acid sequences of proteins, or even examining, most be more fit than either of the homozygotes, leading to a
recently, the differences in nucleotide sequences within balanced polymorphism.
the DNA. These kinds of observations have revealed that
there is considerable polymorphism at many loci within a In general, genetic variation is the result of the inter-
population. A measure of this variation is the amount of action of forces. For instance, a deleterious mutant may
heterozygosity in a population. Population studies have never be totally eliminated from a population, because
shown that in general the genetic differences between in- mutation will continue to reintroduce it into the popu-
dividuals within human races are much greater than the lation. Immigration may also reintroduce alleles that
average differences between races. have been eliminated by natural selection.

The ultimate source of all variation is mutation. Unless alternative alleles are intermediate in fre-
However, within a population, the quantitative fre- quency, selection (especially against recessives) is very
quency of specific genotypes can be changed by recom- slow, requiring many generations. In many populations,
bination, immigration of genes, continued mutational especially those of small size, new mutations can be-
events, and chance. come established even though they are not favored by
natural selection, or they may become eliminated even
One property of Mendelian segregation is that ran- though they are favored, simply by a process of random
dom mating results in an equilibrium distribution of genetic drift.
genotypes after one generation. However, if there is in-
breeding, the genetic variation within a population is

KEY TERMS Hardy-Weinberg overdominance (p. 634)
equilibrium (p. 621) polymorphism (p. 614)
allele frequency (p. 614) population (p. 612)
artificial selection (p. 629) heterozygosity (p. 623) population genetics (p. 612)
Darwinian fitness (p. 629) homozygosity by descent (p. 625) positive assortative mating (p. 625)
endogamy (p. 624) inbreeding (p. 625) random genetic drift (p. 636)
enforced outbreeding (p. 625) inbreeding coefficient (p. 625) selection (p. 629)
equilibrium distribution (p. 621) linkage disequilibrium (p. 628) single-nucleotide
fixed (p. 626) linkage equilibrium (p. 628)
founder effect (p. 636) mean fitness (p. 632) polymorphism (SNP) (p. 619)
frequency-dependent mutation (p. 627) underdominance (p. 634)
natural selection (p. 629) variable number tandem repeat
fitness (p. 630) negative assortative
frequency-independent (p. 630) (VNTR) (p. 618)
genetic drift (p. 636) mating (p. 625) viability (p. 630)
genotype frequency (p. 614) negative inbreeding (p. 625) wild type (p. 615)
haplotype (p. 623)

SOLVED PROBLEMS an experimental program that would reveal the
forces that determine the frequency and geographi-
1. The polymorphisms for shell color (yellow or pink) cal distribution of these polymorphisms.
and for the presence or absence of shell banding in
the snail Cepaea nemoralis are each the result of a
pair of segregating alleles at a separate locus. Design

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Solved problems 639

Solution Now we can calculate

a. Describe the frequencies of the different morphs for p2 ϭ (0.45)2 ϭ 0.20, the frequency of T/T
samples of snails from a large number of populations 2pq ϭ 2 ϫ 0.45 ϫ 0.55 ϭ 0.50, the frequency of T/t
covering the geographical and ecological range of the
species. Each snail must be scored for both polymor- q2 ϭ 0.3, the frequency of t/t
phisms. At the same time, record a description of the
habitat of each population. In addition, estimate the 3. In a large natural population of Mimulus guttatus,
number of snails in each population. one leaf was sampled from each of a large number
of plants. The leaves were crushed and subjected to
b. Measure migration distances by marking a sample of gel electrophoresis. The gel was then stained for a
snails with a spot of paint on the shell, replacing them in specific enzyme, X. Six different banding patterns
the population, and then resampling at a later date. were observed, as shown in the accompanying
c. Raise broods from eggs laid by individual snails so
that the genotype of male parents can be inferred and 123456
nonrandom mating patterns can be observed. The segre-
gation frequencies within each family will reveal differ- 0.04 0.09 0.25 0.12 0.20 0.30
ences between genotypes in probability of survivorship Frequency
of early developmental stages.
a. Assuming that these patterns are produced by a
d. Seek further evidence of selection from (1) geograph- single locus, propose a genetic explanation for the six
ical patterns in the frequencies of the alleles, (2) correla- types.
tion between allele frequencies and ecological variables, b. How can you test your hypothesis?
including population density, (3) correlation between c. What are the allele frequencies in this population?
the frequencies of the two different polymorphisms (are d. Is the population in Hardy-Weinberg equilibrium?
populations with, say, high frequencies of pink shells
also characterized by, say, high frequencies of banded Solution
shells), and (4) nonrandom associations within popula- a. Inspection of the gel reveals that there are only three
tions of the alleles at the two loci, indicating that certain band positions: we shall call them slow, intermediate,
combinations may have a higher fitness. and fast, according to how far each has migrated in the
gel. Furthermore, any individual can show either one
e. Seek evidence of the importance of random genetic band or two. The simplest explanation is that there are
drift by comparing the variation in allele frequencies three alleles of one locus (let’s call them S, I, and F ) and
among small populations with the variation among that the individuals with two bands are heterozygotes.
large populations. If small populations vary more Hence, lane 1 ϭ S/S, 2 ϭ I/I, 3 ϭ F/F, 4 ϭ S/I, 5 ϭ S/F,
from each other than do large ones, random drift is and 6 ϭ I/F.
implicated. b. The hypothesis can be tested by making controlled
crosses. For example, from a self of type 5, we can pre-
2. About 70 percent of all white North Americans can dict 1/4 S/S, 1/2 S/F, and 1/4 F/F.
taste the chemical phenylthiocarbamide, and the re- c. The frequencies can be calculated by a simple gener-
mainder cannot. The ability to taste this chemical is alization from the two-allele formulas. Hence:
determined by the dominant allele T, and the inabil-
ity to taste is determined by the recessive allele t. If fS ϭ 0.04 ϩ 1/2(0.12) ϩ 1/2(0.20) ϭ 0.20 ϭ p
the population is assumed to be in Hardy-Weinberg fI ϭ 0.09 ϩ 1/2(0.12) ϩ 1/2(0.30) ϭ 0.30 ϭ q
equilibrium, what are the genotype and allele fre- fF ϭ 0.25 ϩ 1/2(0.20) ϩ 1/2(0.30) ϭ 0.50 ϭ r
quencies in this population?


Because 70 percent are tasters (T/T and T/t), 30 percent
must be nontasters (t/t). This homozygous recessive fre-
quency is equal to q2; so to obtain q, we simply take the
square root of 0.30:

q ϭ √0.30 ϭ 0.55

Because p ϩ q ϭ 1, we can write

p ϭ 1 Ϫ q ϭ 1 Ϫ 0.55 ϭ 0.45

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640 Chapter 19 • Population Genetics

d. The Hardy-Weinberg genotypic frequencies are Solution

(p ϩ q ϩ r)2 ϭ p2 ϩ q2 ϩ r 2 ϩ 2pq ϩ 2pr ϩ 2qr Here mutation and selection are working in opposite di-
ϭ 0.04 ϩ 0.09 ϩ 0.25 rections, so an equilibrium is predicted. Such an equilib-
ϩ 0.12 ϩ 0.20 ϩ 0.30 rium is described by the formula

which are precisely the observed frequencies. So it ap- √qˆ ϭ ␮
pears that the population is in equilibrium. s

4. In a large experimental Drosophila population, the In the present question, ␮ ϭ 5 ϫ 10Ϫ5 and s ϭ 1 Ϫ W ϭ
fitness of a recessive phenotype is calculated to be 1 Ϫ 0.9 ϭ 0.1. Hence
0.90, and the mutation rate to the recessive allele
is 5 ϫ 10Ϫ5. If the population is allowed to come √qˆ ϭ 5 ϫ 10Ϫ5 ϭ 2.2 ϫ 10Ϫ2 ϭ 0.022
to equilibrium, what allele frequencies can be 10Ϫ1
pˆ ϭ 1 Ϫ 0.022 ϭ 0.978

PROBLEMS 7. In a survey of Native American tribes in Arizona and
New Mexico, albinos were completely absent or
BASIC PROBLEMS very rare in most tribes (there is 1 albino per 20,000
North American Caucasians). However, in three
1. What are the forces that can change the frequency Native American populations, albino frequencies are
of an allele in a population? exceptionally high: 1 per 277 Native Americans in
Arizona; 1 per 140 Jemez in New Mexico; and 1 per
2. In a population of mice, there are two alleles of the 247 Zuni in New Mexico. All three of these popula-
A locus (A1 and A2). Tests showed that in this popu- tions are culturally but not linguistically related.
lation there are 384 mice of genotype A1/A1, 210 of What possible factors might explain the high inci-
A1/A2, and 260 of A2/A2. What are the frequencies dence of albinos in these three tribes?
of the two alleles in the population?
3. In a randomly mating laboratory population of
Drosophila, 4 percent of the flies have black bodies 8. In a population, the D : d mutation rate is
(encoded by the autosomal recessive b), and 96 per- 4 ϫ 10Ϫ6. If p ϭ 0.8 today, what will p be after
cent have brown bodies (the wild type, encoded by 50,000 generations?
B). If this population is assumed to be in Hardy-
Weinberg equilibrium, what are the allele frequen- 9. You are studying protein polymorphism in a natural
cies of B and b and the genotypic frequencies of B/B population of a certain species of a sexually repro-
and B/b? ducing haploid organism. You isolate many strains
from various parts of the test area and run extracts
4. In a wild population of beetles of species X, you no- from each strain on electrophoretic gels. You stain
tice that there is a 3 : 1 ratio of shiny to dull wing the gels with a reagent specific for enzyme X and
covers. Does this ratio prove that the shiny allele is find that in the population there are a total of five
dominant? (Assume that the two states are caused electrophoretic variants of enzyme X. You speculate
by two alleles of one gene.) If not, what does it that these variants represent various alleles of the
prove? How would you elucidate the situation? structural gene for enzyme X.

5. The fitnesses of three genotypes are WA/A ϭ 0.9, a. How could you demonstrate that your specula-
WA/a ϭ 1.0, and Wa/a ϭ 0.7. tion is correct, both genetically and biochemically?
(You can make crosses, make diploids, run gels, test
a. If the population starts at the allele frequency p ϭ enzyme activities, test amino acid sequences, and so
0.5, what is the value of p in the next generation? forth.) Outline the steps and conclusions precisely.

b. What is the predicted equilibrium allele fre- b. Name at least one other possible way of generat-
quency? ing the different electrophoretic variants, and ex-
plain how you would distinguish this possibility
6. A/A and A/a individuals are equally fertile. If 0.1 from your speculation above.
percent of the population is a/a, what selection
pressure exists against a/a if the A Ϫ a mutation
rate is 10Ϫ5?

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Problems 641

10. A study made in 1958 in the mining town of d. In population 6, the a allele is deleterious; fur-
Ashibetsu in Hokkaido, Japan, revealed the frequen- thermore, the A allele is incompletely dominant, so
cies of MN blood type genotypes (for individuals that A/A is perfectly fit, A/a has a fitness of 0.8, and
and for married couples) shown in the following a/a has a fitness of 0.6. If there is no mutation, what
table: will p and q be in the next generation?

Genotype Number of individuals 12. Color blindness results from a sex-linked recessive
or couples allele. One in every ten males is color-blind.

Individuals a. What proportion of all women are color-blind?

LM/LM 406 b. By what factor is color blindness more common
LM/LN 744 in men (or, how many color-blind men are there for
LN/LN 332 each color-blind woman)?
Total c. In what proportion of marriages would color
blindness affect half the children of each sex?
d. In what proportion of marriages would all chil-
LM/LM ϫ LM/LM 58 dren be normal?
LM/LM ϫ LM/LN 202
LM/LN ϫ LM/LN 190 e. In a population that is not in equilibrium, the fre-
LM/LM ϫ LN/LN quency of the allele for color blindness is 0.2 in
LM/LN ϫ LN/LN 88 women and 0.6 in men. After one generation of ran-
LN/LN ϫ LN/LN 162 dom mating, what proportion of the female progeny
will be color-blind? What proportion of the male
Total 41 progeny?
f. What will the allele frequencies be in the male
a. Show whether the population is in Hardy- and in the female progeny in part e?
Weinberg equilibrium with respect to MN blood
types. (Problem 12 courtesy of Clayton Person.)

b. Show whether mating is random with respect to 13. It seems clear that most new mutations are deleteri-
MN blood types. ous. Why?

(Problem 10 is from J. Kuspira and G. W. Walker, Genetics: 14. Most mutations are recessive to the wild type. Of
Questions and Problems. Copyright 1973 by McGraw-Hill.) those rare mutations that are dominant in
Drosophila, for example, the majority turn out either
11. Consider the populations that have the genotypes to be chromosomal mutations or to be inseparable
shown in the following table: from chromosomal mutations. Explain why the wild
type is usually dominant.
Population A/A A/a a/a
15. Ten percent of the males of a large and randomly
1 1.0 0.0 0.0 mating population are color-blind. A representative
2 0.0 1.0 0.0 group of 1000 people from this population migrates
3 0.0 0.0 1.0 to a South Pacific island, where there are already
4 0.50 0.25 0.25 1000 inhabitants and where 30 percent of the males
5 0.25 0.25 0.50 are color-blind. Assuming that Hardy-Weinberg
6 0.25 0.50 0.25 equilibrium applies throughout (in the two original
7 0.33 0.33 0.33 populations before the migration and in the mixed
8 0.04 0.32 0.64 population immediately after the migration), what
9 0.64 0.32 0.04 fraction of males and females can be expected to be
10 0.986049 0.013902 0.000049 color-blind in the generation immediately after the
arrival of the migrants?
a. Which of the populations are in Hardy-Weinberg
equilibrium? 16. Using pedigree diagrams, find the probability of
homozygosity by descent of the offspring of
b. What are p and q in each population? (a) parent-offspring matings; (b) first-cousin mat-
ings; (c) aunt-nephew or uncle-niece matings.
c. In population 10, it is discovered that the A : a
mutation rate is 5 ϫ 10Ϫ6 and that reverse muta- 17. In an animal population, 20 percent of the individuals
tion is negligible. What must be the fitness of the are A/A, 60 percent are A/a, and 20 percent are a/a.
a/a phenotype?

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642 Chapter 19 • Population Genetics

a. What are the allele frequencies in this population? childhood, and 13 were normal. From this informa-
tion, calculate roughly how many recessive lethal
b. In this population, mating is always with like phe- genes we have, on average, in our human genomes.
notype but is random within phenotype. What geno- (Hint: If the answer were 1, then a daughter would
type and allele frequencies will prevail in the next stand a 50 percent chance of carrying the lethal al-
generation? lele, and the probability of the union’s producing a
lethal combination would be 1/2 ϫ 1/4 ϭ 1/8. So
c. Another type of assortative mating takes place 1 is not the answer.) Consider also the possibility of
only between unlike phenotypes. Answer the pre- undetected fatalities in utero in such matings. How
ceding question with this restriction imposed. would they affect your result?

d. What will the end result be after many genera- 21. If we define the total selection cost to a population of
tions of mating of each type? deleterious recessive genes as the loss of fitness per
individual affected (s) multiplied by the frequency
18. A Drosophila stock isolated from nature has an aver- of affected individuals (q2), then
age of 36 abdominal bristles. By the selective breed-
ing of only those flies with the most bristles, the selection cost ϭ sq2
mean is raised to 56 bristles in 20 generations.
a. Suppose that a population is at equilibrium be-
a. What is the source of this genetic flexibility? tween mutation and selection for a deleterious re-
cessive allele, where s ϭ 0.5 and ␮ ϭ 10Ϫ5. What is
b. The 56-bristle stock is infertile, so selection is re- the equilibrium frequency of the allele? What is the
laxed for several generations and the bristle number selection cost?
drops to about 45. Why doesn’t it drop back to 36?
b. Suppose that we start irradiating individual mem-
c. When selection is reapplied, 56 bristles are soon bers of the population, so that the mutation rate
attained, but this time the stock is not infertile. How doubles. What is the new equilibrium frequency of
can this situation arise? the allele? What is the new selection cost?

19. Allele B is a deleterious autosomal dominant. The c. If we do not change the mutation rate, but we
frequency of affected individuals is 4.0 ϫ 10Ϫ6. lower the selection intensity to 0.3 instead, what
The reproductive capacity of these individuals is happens to the equilibrium frequency and the selec-
about 30 percent that of normal individuals. Esti- tion cost?
mate ␮, the rate at which b mutates to its deleteri-
ous allele B.

20. Of 31 children born of father-daughter matings, 6
died in infancy, 12 were very abnormal and died in

EXPLORING GENOMES Interactive Genetics MegaManual CD-ROM Tutorial

Population Genetics
This activity on the Interactive Genetics CD-ROM includes five interactive
problems designed to improve your understanding of what we can learn by
looking at the distribution of genes in populations.

44200_20_p643-678 3/23/04 14:47 Page 643



The composite flowers of Gaillardia pulchella. Quantitative KEY QUESTIONS
variation in flower color, flower diameter, and number of
flower parts. [J. Heywood, Journal of Heredity, May/June 1986.] • For a particular character, how do we
answer the question, Is the observed
variation in the character influenced at all
by genetic variation? Are there alleles
segregating in the population that produce
some differential effect on the character or
is all the variation simply the result of
environmental variation and developmental
noise (see Chapter 1)?

• If there is genetic variation, what are the
norms of reaction of the various genotypes?

• For a particular character, how important is
genetic variation as a source of total
phenotypic variation? Are the norms of
reaction and the environments such that
nearly all the variation is a consequence of
environmental difference and
developmental instabilities or does genetic
variation predominate?

• Do many loci (or only a few) vary with
respect to a particular character? How are
they distributed throughout the genome?


20.1 Genes and quantitative traits
20.2 Some basic statistical notions
20.3 Genotypes and phenotypic distribution
20.4 Norm of reaction and phenotypic distribution
20.5 Determining norms of reaction
20.6 The heritability of a quantitative character
20.7 Quantifying heritability
20.8 Locating genes


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644 Chapter 20 • Quantitative Genetics

CHAPTER OVERVIEW vated field or wild asters at the side of the road are not
neatly sorted into categories of “tall” and “short,” any
Ultimately, the goal of genetics is the analysis of the more than humans are neatly sorted into categories of
genotypes of organisms. But a genotype can be iden- “black” and “white.” Height, weight, shape, color, meta-
tified — and therefore studied — only through its effect bolic activity, reproductive rate, and behavior are charac-
on the phenotype. We recognize two genotypes as differ- teristics that vary more or less continuously over a range
ent from each other because the phenotypes of their (Figure 20-1). Even when the character is intrinsically
carriers are different. Basic genetic experiments, then, countable (such as eye facet or bristle number in
depend on the existence of a simple relation between Drosophila), the number of distinguishable classes may
genotype and phenotype. That is why studies of DNA be so large that the variation is nearly continuous. If we
sequences are so important, because we can read off the consider extreme individuals — say, a corn plant 8 feet
genotype directly. tall and another one 3 feet tall — a cross between them
will not produce a Mendelian result. Such a corn cross
In general, we hope to find a uniquely distinguish- will produce plants about 6 feet tall, with some clear
able phenotype for each genotype and only a simple variation among siblings. The F2 from selfing the F1 will
genotype for each phenotype. At worst, when one allele not fall into two or three discrete height classes in ratios
is completely dominant, it may be necessary to perform of 3 : 1 or 1 : 2 : 1 . Instead, the F2 will be continuously
a simple genetic cross to distinguish the heterozygote distributed in height from one parental extreme to the
from the homozygote. Where possible, geneticists avoid other.
studying genes that have only partial penetrance and in-
complete expressivity (see Chapter 6) because of the How do we study quantitative traits when they
difficulty of making genetic inferences from such traits. show such a complex relation between genotype and
Imagine how difficult (if not impossible) it would have phenotype? The analysis of a continuously varying char-
been for Benzer to study mutations within the rII gene acter can be carried out by an array of investigations,
in phage, if the only effect of the rII mutants was a 5 shown schematically in Figure 20-2:
percent reduction from wild type in their ability to grow
on E. coli K. For the most part, then, the study of genet- • Norm of reaction studies, in which different
ics presented in the preceding chapters has been the genotypes are allowed to develop in an array of
study of allelic substitutions that cause qualitative differ- different environments to determine the interaction
ences in phenotype — clear-cut differences such as pur- of genotype and environment in the development of
ple flowers versus white flowers. the character.

However, most actual variation between organisms • Selection studies, in which successive generations are
is quantitative, not qualitative. Wheat plants in a culti- produced from the extreme individuals in the

Figure 20-1 Quantitative inheritance of bract color in Indian paintbrush (Castilleja hispida).
The photograph on the left shows the extremes of the color range, and the one on the right
shows examples from throughout the phenotypic range.

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20.1 Genes and quantitative traits 645


Norm of Reaction Studies Figure 20-2 Relations among
the methods of studying
New New quantitative genetics.
environment 1 environment 2

Growth in new


Genetic Many successive Original
difference generations of matings Population in
between individuals Environment
that have an extreme
phenotype in common

Inbreeding Inbreeding Find
Heritability marker
Find marker gene:
gene: allele A

allele a

Quantitative Trait Loci Genetic
Map QTLs by
linkage with F2 Environmental × Environmental
marker gene

variance variance

a/aa/aa/Aa/Aa/AA/A A/A F1 A /a
Interbreeding Environmental variance
of F1

preceding generation. For example we might establish approximate location of a gene affecting the
one population from the cross of the two shortest quantitative character.
plants and another population from the cross of the
two tallest corn plants in the preceding example. 20.1 Genes and quantitative traits
Then, in each successive generation, the “short”
population and the “tall” population would be bred A classic example of the outcome of crosses between
from the most extreme individuals in each. If, after strains that differ in a quantitative character is the ex-
repeated generations of selection, the populations periment shown in Figure 20-3. The length of the
diverge, then the divergent populations must differ corolla (flower tube) was measured in a number of indi-
genetically at one or more loci influencing the vidual plants from two true-breeding lines of Nicotiana
character. longiflora, a relative of tobacco. The distribution of
corolla lengths of the two parental lines is shown in the
• Heritability studies, in which the variation in the top panel of Figure 20-3. The difference between the
progeny of crosses is analyzed statistically to estimate two lines is genetic, but the variation among individual
the proportion of the variation in the original plants within each line is a result of uncontrolled envi-
population that is a consequence of genetic ronmental variation and developmental noise. The F1
differences and the proportion that is a consequence plants, whose mean corolla length is very close to
of environmental differences. halfway between the two parental lines, also vary from
one another because of environmental and developmen-
• Quantitative trait locus (QTL) studies, which tal variation. In the F2, the mean corolla length remains
associate phenotypic differences with alleles of a essentially unchanged from that of the F1, but there is a
marker gene of known chromosomal location. Such
an association with the marker gene reveals the

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