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Published by soedito, 2017-09-20 09:22:25

500_AN-INTRO DUCTION TO GENETICS_ANALYSIS_711

500_AN-INTRO DUCTION TO GENETICS_ANALYSIS_711

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646 Chapter 20 • Quantitative Genetics

Percentage of plants75 The outcome of the cross is clearly different from
P the results obtained when a cross is made between indi-
viduals that differ in their allelic state for a gene with
50 clear-cut phenotypic effects. Offspring do not sort into
neat Mendelian ratios of 1 : 2 : 1 , and there is much more
25 individual variation within each generation of offspring.
This behavior of crosses is not an exception; it is the rule
0 for most characters in most species. Mendel obtained his
40 55 70 85 100 simple results because he worked with horticultural va-
rieties of the garden pea that differed from one another
50 by single allelic differences that had drastic effects on
F1 phenotypes. The behavior of crosses seen in Figure 20-3
is not an exception; it is the rule for most characters in
25 most species. Had Mendel conducted his experiments
on the natural variation of the weeds in his garden, in-
0 stead of on abnormal pea varieties, he would never have
40 55 70 85 100 discovered any of his laws of heredity. In general, size,
shape, color, physiological activity, and behavior do not
50 assort in a simple way in crosses.
F2
The fact that most characters vary continuously
25 does not mean that their variation is the result of some
genetic mechanisms different from those that apply to
0 the Mendelian genes that we have studied in earlier
40 55 70 85 100 chapters. The continuity of phenotype is a result of two
phenomena. First, each genotype does not have a single
50 phenotypic expression but rather a norm of reaction
F3 (see Chapter 1) that covers a wide phenotypic range. As
a result, the phenotypic differences between genotypic
25 classes become blurred, and we are not able to assign a
particular phenotype unambiguously to a particular
0 genotype.

50 Second, there may be many segregating loci having
alleles that make a difference in the phenotype under
25 observation. Suppose, for example, that five equally im-
portant loci affect the number of flowers that will de-
0 velop in an annual plant and that each locus has two al-
leles (call them 1 and Ϫ ). For simplicity, also suppose
25 that there is no dominance and that a 1allele adds one
flower, whereas a Ϫallele adds nothing. Thus, there are
0 35 ϭ 243 different possible genotypes [three possible
40 55 70 85 100 genotypes (1/1, 1/Ϫ, and Ϫ/Ϫ) at each of five loci],
Corolla length (millimeters) ranging from

Figure 20-3 Results of crosses between strains of Nicotiana 11111 through 11111 to ϪϪϪϪϪ
longiflora that differ in corolla length. The graphs show (from 11111 ϪϪϪϪϪ ϪϪϪϪϪ
top to bottom) the frequency distribution of corolla lengths in
the two parental strains (P); the frequency distribution of but there are only 11 phenotypic classes (10, 9, 8, . . . , 0)
corolla lengths in the F1; the frequency distribution in the F2; because many of the genotypes will have the same num-
and the frequency distributions in four F3 crosses made by bers of 1 and Ϫ alleles. For example, although there is
taking parents from the four indicated parts of the F2 only one genotype with 10 1alleles and therefore an aver-
distribution. [Adapted from K. Mather, Biometrical Genetics. age phenotypic value of 10, there are 51 different geno-
types with 5 1alleles and 5 Ϫalleles; for example,
Methuen, 1959. Data from E. M. East, Genetics 1, 1916, 164–176.]
1111Ϫ and 11Ϫ1Ϫ
large increase in the variation because there is now seg- 1ϪϪϪϪ 11ϪϪϪ
regation of the genetic differences that were introduced
from the two original parental lines. A demonstration
that at least part of this variation is the result of genetic
differences among the F2 plants is seen in the F3. Differ-
ent pairs of parents were chosen from four different
parts of the F2 distribution and crossed to produce the
next, F3, generation. In each case, the F3 mean is close to
the value of that part of the F2 distribution from which
its parents were sampled.


44200_20_p643-678 3/23/04 14:47 Page 647

20.2 Some basic statistical notions 647

Thus, many different genotypes may have the same av- cific language spoken) clearly are not. In this chapter, we
erage phenotype. At the same time, because of environ- will develop the basic statistical and genetic concepts
mental variation, two individuals of the same genotype needed to answer these questions and provide some ex-
may not have the same phenotype. This lack of a one-to- amples of the applications of these concepts to particu-
one correspondence between genotype and phenotype lar characters in particular species.
obscures the underlying Mendelian mechanism.
20.2 Some basic
If we cannot study the behavior of the Mendelian statistical notions
factors controlling such traits directly, then what can we
learn about their genetics? Clearly, the methods used to To consider the answers to these questions about the
analyze qualitative traits — such as examining the ratios most common kinds of phenotypic variation, quantita-
of offspring in a genetic cross — will not work for quanti- tive variation, we must first examine a number of statis-
tative traits. Instead, we have to use statistical methods tical tools that are essential in the study of quantitative
to make predictions about the inheritance of phenotypes variation.
in the absence of knowledge about underlying geno-
types. This approach is known as quantitative genetics. Statistical distributions
Quantitative genetics — the study of the genetics of con-
tinuously varying characters — is concerned with answer- For a simple variation that depends only on the allelic dif-
ing the following questions: ferences at a single locus, the offspring of a cross will fall
into several distinct phenotypic classes. For example, a
1. Is the observed variation in a character influenced at cross between a red-flowered plant and a white-flowered
all by genetic variation? Is all the variation simply plant might be expected to yield all red-flowered plants
the result of environmental variation and or, if it were a backcross of an F1 plant to the white-
developmental noise (see Chapter 1)? Or, are there flowered parent, 1/2 red-flowered plants and 1/2
alleles segregating in the population that produce white-flowered plants. However, we require a different
some differential effect on the character? mode of description for quantitative characters. If the
heights of a large number of male undergraduates are
2. If there is genetic variation, what are the norms of measured to the nearest 5 centimeters (cm), they will
reaction of the various genotypes? vary (say, between 145 and 195 cm), but many more of
these undergraduates will fall into the middle measure-
3. How important is genetic variation as a source of ment classes (say, 170, 175, and 180 cm) than into the
total phenotypic variation? Is nearly all the variation classes at the two extremes. Such a description of a set
a consequence of environmental difference and of quantitative measurements is known as a statistical
developmental instabilities or does genetic variation distribution.
predominate?
We can graph such measurements by representing
4. Do many loci (or only a few) contribute to the each measurement class as a bar, with its height propor-
variation in the character? How are they distributed tional to the number of individuals in that class, as
throughout the genome? shown in Figure 20-4a. Such a graph of numbers of indi-
viduals observed against measurement class is called a
In the end, the purpose of answering these questions is frequency histogram. Now suppose that we measure
to be able to predict what kinds of offspring will be pro- five times as many individuals, each to the nearest cen-
duced by crosses of different phenotypes. timeter, so that we divide them into even smaller mea-
surement classes, producing a histogram like the one
The precision with which these questions can be shown in Figure 20-4b. If we continue this process, mak-
framed and answered varies greatly. In experimental or- ing each measurement finer but proportionately increas-
ganisms, on the one hand, it is relatively simple to deter- ing the number of individuals measured, the histogram
mine whether there is any genetic influence at all, but eventually takes on the continuous appearance of Figure
extremely laborious experiments are required to localize 20-4c. Such a continuous curve is called the distribution
the genes (even approximately). In humans, on the other function of the measure in the population.
hand, it is extremely difficult to answer even the ques-
tion of the presence of genetic influence for most traits, The distribution function is an idealization of the
because it is almost impossible to separate environmen- actual frequency distribution of a measurement in any
tal from genetic effects in an organism that cannot be real population, because no measurement can be taken
manipulated experimentally. As a consequence, we with infinite accuracy or on an unlimited number of in-
know a lot about the genetics of bristle number in dividuals. Moreover, the measured character itself may
Drosophila but virtually nothing about the genetics of
complex human traits; a few (such as skin color) clearly
are influenced by genes, whereas others (such as the spe-


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648 Chapter 20 • Quantitative Genetics

Number of individuals400 be intrinsically discontinuous because it is the count of
360 some number of discrete objects, such as eye facets or
320 Number of individuals bristles. It is sometimes convenient, however, to develop
280 concepts by using this slightly idealized curve as short-
240 Distribution function hand for the more cumbersome observed frequency
200 histogram.
160
120 Statistical measures

80 Although a statistical distribution contains all of the in-
40 formation that we need about a set of measurements, it
is often useful to distill this information into a few char-
0 acteristic numbers that convey the necessary informa-
156–160 161–165 166–170 171–175 176–180 181–185 186–190 tion about the distribution without giving it in detail.
Height class (cm) There are several questions about the height distribution
(a) for male undergraduates, for example, that we might like
to answer:
400
360 1. Where is the distribution located along the range of
320 possible values? Are our observed values of height,
280 for example, closer to 100 or to 200 cm? This
240 question can be answered with a measure of central
200 tendency.
160
120 2. How much variation is there among the individual
measurements? Are they all concentrated around
80 the central measurement or do they vary widely
40 across a large range? This question can be answered
with a measure of dispersion.
0
156 160 165 170 175 180 185 190 3. If we are considering more than one measured
Height class (cm) quantity, how are the values of the different
(b) quantities related? Do taller parents, for example,
have taller sons? If they do, we would regard it as
Height (cm) evidence that genes influence height. Thus, we need
(c) measures of relation between measurements.

Figure 20-4 Frequency distributions for height of male Among the most commonly used measures of cen-
undergraduates. (a) A frequency histogram with 5-cm class tral tendency are the mode, which is the most frequent
intervals; (b) a frequency histogram with 1-cm class observation, and the mean, which is the arithmetic av-
intervals; (c) the limiting continuous distribution. erage of the observations. The dispersion of a distribu-
tion is almost always measured by the variance, which
is the average squared deviation of the observations
from their mean. The relation between different vari-
ables is measured by their correlation, which is the av-
erage product of the deviation of one variable from its
own mean times the deviation of the other variable
from its own mean. These common measures are dis-
cussed in detail in the Statistical Appendix on statistical
analysis at the end of this chapter. The detailed discus-
sion of these statistical concepts is placed in a separate
section so as not to interrupt the flow of logic as we
consider quantitative genetics. It should not be as-
sumed, however, that an understanding of these statisti-
cal concepts is somehow secondary. A proper under-
standing of quantitative genetics requires a grasp of the
basics of statistical analysis.


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20.3 Genotypes and phenotypic distribution 649

20.3 Genotypes and Two features of the total distribution are notewor-
phenotypic distribution thy. First, there is only a single mode, the most frequent
observation represented by the location on the height
The critical difference between quantitative axis of the peak of the curve. Despite the existence of
three separate genotypic distributions underlying it, the
and Mendelian traits population distribution as a whole does not reveal the
separate modes. Second, any individual plant whose
Using the concepts of distribution, mean, and variance, height lies between the two arrows could have any one
we can understand the difference between quantitative of the three genotypes, because the phenotypes of those
and Mendelian genetic traits. three genotypes overlap so much. The result is that we
cannot carry out a simple Mendelian analysis to deter-
Suppose that a population of plants contains three mine the genotype of an individual plant. For example,
genotypes, each of which has some differential effect on suppose that the three genotypes are the two homozy-
growth rate. Furthermore, assume that there is some en- gotes and the heterozygote for a pair of alleles at a locus.
vironmental variation from plant to plant because the Let a/a be the short homozygote and A/A be the tall
soil in which the population is growing is not homoge- one, with the heterozygote being of intermediate height.
neous and that there is some developmental noise (see Because the phenotypic distributions overlap so much,
Chapter 1). For each genotype, there will be a separate we cannot know to which genotype a given individual
distribution of phenotypes with a mean and a variance plant belongs. Conversely, if we cross a homozygote a/a
that depend on the genotype and the set of environ- and a heterozygote A/a, the offspring will not fall into
ments. Suppose that these distributions look like the two discrete classes, A/a and a/a, in a 1 : 1 ratio but will
three height distributions in Figure 20-5a. The three dis- cover almost the entire range of phenotypes smoothly.
tributions are concentrated at three different places on Thus, we cannot know from looking at the offspring that
the scale of plant height indicating differences in mean the cross is in fact a/a ϫ A/a and not a/a ϫ A/A or
height. The three distributions also have different A/a ϫ A/a.
amounts of spread, which results in their having differ-
ent variances. Finally, assume that the population con- Suppose we grew the hypothetical plants in Figure
sists of a mixture of the three genotypes but in the un- 20-5 in an environment that exaggerated the differences
equal proportions 1 : 2 : 3 (a/a : A /a : A /A). between genotypes — for example, by doubling the
growth rate of all genotypes. At the same time, we were
Under these circumstances, the phenotypic distribu- very careful to provide all plants with exactly the same
tion of individual plants in the population as a whole will environment. Then, the phenotypic variance of each
look like the black line in Figure 20-5b, which is the re- separate genotype would be reduced because all the
sult of summing the three underlying separate genotypic plants were grown under identical conditions; at the
distributions, weighted by their frequencies in the popu- same time, the phenotypic differences between geno-
lation. This weighting by frequency is indicated in Figure types would be exaggerated by the more rapid growth.
20-5b by the different heights of the component distri- (Figure 20-6a). The result (Figure 20-6b) would be a
butions. The mean of this total distribution is the average separation of the population as a whole into three
of the three genotypic means, again weighted by the fre- nonoverlapping phenotypic distributions, each charac-
quencies of the genotypes in the population. The vari- teristic of one genotype. We could now carry out a per-
ance of the total distribution is produced partly by the fectly conventional Mendelian analysis of plant height. A
environmental variation within each genotype and partly
by the slightly different means of the three genotypes.

Distribution function
Distribution function
0 a/a A /a Figure 20-5 Genotype distribution.
A /A (a) Phenotypic distributions of three
0 A/a plant genotypes. (b) A phenotypic
a /a distribution for the total population
0 A/A 0 (black line) can be obtained by
Height (h) summing the three genotypic
(a) Height (h) distributions in a proportion
(b) 1 : 2 : 3 (a/a : A/a : A/A).


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650 Chapter 20 • Quantitative Genetics

Distribution function 0 a/a evidence that a character is controlled by many genes.
This multiple-factor hypothesis (that large numbers of
0 A/a genes, each with a small effect, are segregating to pro-
duce quantitative variation) has long been the basic
0 A/A model of quantitative genetics, but, as we have just
Height (h) shown, this hypothesis is not necessarily true. If the dif-
(a) ference between genotypic means is small compared
with the environmental variance, then even a simple
Distribution function one-gene – two-allele case can result in continuous
phenotypic variation.
0 A /a A /A
a /a Height (h) If the range of a character is limited and if many seg-
regating loci influence it, then we expect the character
(b) to show continuous variation, because each allelic sub-
stitution must account for only a small difference in the
Figure 20-6 Phenotypic distributions of the same three trait. It is important to remember, however, that the
plant genotypes shown in Figure 20-5 when grown in carefully number of segregating loci that influence a trait is not
controlled environments. The result is a smaller phenotypic what separates quantitative and qualitative characters.
variation within each genotype and a greater difference Even in the absence of large environmental variation, it
between genotypes. The heights of the individual takes only a few genetically varying loci to produce vari-
distributions in part b are proportional to the frequencies ation that is indistinguishable from the effect of many
of the genotypes in the population. loci of small effect. As an example, we can consider one
of the earliest experiments in quantitative genetics, that
“quantitative” character has been converted into a “quali- of Wilhelm Johannsen on pure lines. By inbreeding
tative” one. This conversion has been accomplished by (mating close relatives), Johannsen produced 19 homo-
finding a way to make the difference between the means zygous lines of bean plants from an originally geneti-
of the genotypes large compared with the variation cally heterogeneous population. Each line had a charac-
within genotypes. teristic average seed weight. These weights ranged
widely from 0.64 g per seed for the heaviest line to
MESSAGE A quantitative character is one for which the 0.35 g per seed for the lightest line. Suppose all these
average phenotypic differences between genotypes are lines were genetically different. In that case, Johannsen’s
small compared with the variation between individuals within results would be incompatible with a simple one-
genotypes. locus – two-allele model of gene action. If the original
population were segregating for the two alleles A and a,
Gene number and quantitative traits all inbred lines derived from that population would have
to fall into one of two classes: A/A or a/a. If, in contrast,
Continuous variation in a character is sometimes as- there were, say, 100 loci, each of small effect, segregating
sumed to be necessarily caused by a large number of in the original population, then a vast number of differ-
segregating genes, and so continuous variation is taken as ent inbred lines could be produced, each with a different
combination of homozygotes at different loci.

However, we do not need such a large number of
loci to obtain the results observed by Johannsen. If there
were only five loci, each with three alleles, then 35 ϭ
243 different kinds of homozygotes could be produced
from the inbreeding process. If we make 19 inbred lines
at random, there is a good chance (about 50 percent)
that each of the 19 lines will belong to a different one of
the 243 classes. So Johannsen’s experimental results can
be easily explained by a relatively small number of
genes. Thus, there is no real dividing line between multi-
genic traits and other traits. It is safe to say that no phe-
notypic trait above the level of the amino acid sequence
in a polypeptide is influenced by only one gene. More-
over, traits influenced by many genes are not equally in-
fluenced by all of them. Some genes will have major ef-
fects on a trait; others, minor effects.


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20.4 Norm of reaction and phenotypic distribution 651

MESSAGE The critical difference between Mendelian Phenotype
and quantitative traits is not the number of segregating (height in cm)
loci but the size of phenotypic differences between genotypes
compared with the individual variation within genotypic
classes.

Norm of r
20.4 Norm of reaction eaction
and phenotypic distribution Distribution
Distributionfunction
The phenotype of an organism depends not only on its function
genotype but also on the environment that it has experi-
enced at various critical stages in its development. For a 18° 20° 22°
given genotype, different phenotypes will develop in dif-
ferent environments. The relation between environment Environment (°C)
and phenotype for a given genotype is called the geno-
type’s norm of reaction. The norm of reaction of a geno- Figure 20-8 Outcomes of norm of reaction study. The
type with respect to some environmental variable — say, distribution of environments on the horizontal axis is
temperature — can be visualized by a graph showing converted into the distribution of phenotypes on the
phenotype as a function of that variable, as exemplified vertical axis by the norm of reaction of a genotype.
in Figure 20-7, the norms of reaction of abdominal bris-
tle number for different genotypes of Drosophila. The phenotypic distribution of a character, as we
have seen, is a function of the average phenotypic differ-
35 ences between genotypes and of the phenotypic varia-
tion among genotypically identical individuals. But, as
Number of abdominal bristles 30 the norms of reaction in Figure 20-7 show, both are
functions of the environments in which the organisms
25 develop and live. For a given genotype, each environ-
ment will result in a given phenotype (for the moment,
14 21 26 ignoring developmental noise). Thus, for any given geno-
Temperature (°C) type, a distribution of environments will result in a distri-
bution of phenotypes.
Figure 20-7 Norms of reaction for Drosophila bristle number.
The number of abdominal bristles in different homozygous How different environments affect the phenotype of
genotypes of Drosophila pseudoobscura at three different an organism depends on the norm of reaction, as shown
temperatures. Each colored line represents a different in Figure 20-8, in which the horizontal axis represents
genotype. [Data courtesy of A. P. Gupta. Image: Plate IV, University environment (say, temperature) and the vertical axis
represents phenotype (say, plant height). The norm of
of Texas Publication 4313, Studies in the Genetics of Drosophila III: reaction curve for a genotype shows how each particular
The Drosophilidae of the Southwest, by J. T. Patterson. Courtesy of temperature results in a particular plant height. This
the Life Sciences Library, University of Texas, Austin.] norm of reaction converts a distribution of environments
into a distribution of phenotypes. Thus, for example, the
dashed line from the 18°C point on the horizontal envi-
ronment axis is reflected off the norm of reaction curve
to a corresponding plant height on the vertical pheno-
type axis, and so forth for each temperature. If a large
number of plants develop at, say, 20°C, then a large
number of plants will have the phenotype that corre-
sponds to 20°C, as shown by the dashed line from the
20°C point; if only small numbers develop at 18°C, few
plants will have the corresponding plant height. In other
words, the frequency distribution of developmental en-
vironments will be reflected as a frequency distribution


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652 Chapter 20 • Quantitative Genetics

of phenotypes as determined by the shape of the norm ter 1. It is possible to replicate genotypes in sexually re-
of reaction curve. It is as if an observer, standing at the
vertical phenotype axis, were seeing the environmental produced organisms by the technique of mating close
distribution, not directly, but reflected in the curved
mirror of the norm of reaction. The shape of its curva- relatives, or inbreeding. By selfing (where possible) or by
ture will determine how the environmental distribu-
tion is distorted on the phenotype axis. Thus, the norm mating brother and sister repeatedly generation after
of reaction in Figure 20-8 falls very rapidly at lower
temperatures (the phenotype changes dramatically generation, a segregating line (one that contains both
with small changes in temperature) but flattens out at
higher temperatures, showing that plant height is homozygotes and heterozygotes at a locus) can be made
much less sensitive to temperature differences at the
higher temperatures. The result is that the symmetrical homozygous.
environmental distribution is converted into an asym-
metrical phenotypic distribution with a long tail at Ideally for a norm of reaction study, all the individu-
the larger plant heights, corresponding to the lower
temperatures. als should be absolutely identical genetically, but the

MESSAGE A distribution of environments is reflected process of inbreeding increases the homozygosity of the
biologically as a distribution of phenotypes. The
transformation of environmental distribution into phenotypic group slowly, generation after generation, depending on
distribution is determined by the norm of reaction.
the closeness of the relatives that are mated. In corn, for
20.5 Determining norms
of reaction example, a single individual plant is chosen and self-

Remarkably little is known about the norms of reaction pollinated. Then, in the next generation, a single one of
for any quantitative traits in any species — partly be-
cause determining a norm of reaction requires testing its offspring is chosen and self-pollinated. In the third
many individual members of identical (or near identi-
cal) genotype. In many plants, it is possible to produce generation, a single one of its offspring is chosen and
identical clones by the simple method of cutting a sin-
gle plant into many pieces and growing each piece into self-pollinated, and so forth. Suppose that the original
a complete plant. This method was used to produce the
norms of reactions for Achillea millefolium shown in plant in the first generation is already a homozygote at
Figure 1-21. Animals are not easily clonable, however.
For this reason, for example, we do not have a norm of some locus. Then all of its offspring from self-pollination
reaction for any genotype for any human quantitative
trait. also will be homozygous and identical at the locus. Fu-

Domesticated plants and animals ture generations of self-pollination will simply preserve

To determine a norm of reaction, we must first create a the homozygosity. If, on the other hand, the original
group of genetically identical individuals — a homozy-
gous line. These genetically identical individuals can plant is a heterozygote, then the selfing A/a ϫ A/a will
then be allowed to develop in different environments to 1 1
determine a norm of reaction. Alternatively, two differ- produce offspring that are 4 A/A homozygotes and 4 a/a
ent homozygous lines can be crossed and the heterozy-
gous F1 offspring, all genetically identical with one an- homozygotes. If a single offspring is chosen to propagate
other, can be tested in different environments.
the line, then there is a 50 percent chance that it is now
A few norm of reaction studies have been carried
out with plants that can be clonally propagated. The re- a homozygote. If, by bad luck, the chosen plant should
sults of one of these experiments are presented in Chap-
still be a heterozygote, there is another 50 percent

chance that the selected plant in the third generation is

homozygous, and so forth. Of the ensemble of all het-

erozygous loci, then, after one generation of selfing, only

1 will still be heterozygous; after two generations, 41; after
2
three, 18. In the nth generation,

Hetn ϭ 1 Het 0
2n

where Hetn is the proportion of heterozygous loci in the
nth generation and Het0 is the proportion in the 0 gen-
eration. When selfing is not possible, brother – sister mat-

ing will accomplish the same end, although more slowly.

Table 20-1 is a comparison of the amount of heterozy-

gosity left after n generations of selfing and brother –

sister mating.

Studies of natural populations

To carry out a norm of reaction study of a natural popu-
lation, a large number of lines are sampled from the
population and inbred for a sufficient number of genera-
tions to guarantee that each line is virtually homozygous
at all its loci. Each line is then homozygous at each locus
for a randomly selected allele present in the original
population. The inbred lines themselves cannot be used
to characterize norms of reaction in the natural popula-


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20.5 Determining norms of reaction 653

TABLE 20-1 Heterozygosity Remaining After Various Generations
of Inbreeding for Two Systems of Mating

Remaining Heterozygosity

Generation Selfing Brother – sister mating

0 1.000 1.000
1
2 0.500 0.750
3
4 0.250 0.625
5
10 0.125 0.500
20
n 0.0625 0.406

0.03125 0.338

0.000977 0.114

1.05 ϫ 10Ϫ6 0.014

Hetn ϭ 1 Hetn Ϫ 1 Hetn ϭ 1 HetnϪ1 ϩ 14HetnϪ2
2 2

tion, because such totally homozygous genotypes do not which different environmental factors could be sepa-
exist in the original population. Each inbred line can be rately manipulated.
crossed to every other inbred line to produce heterozy-
gotes that reconstitute the original population, and The consequences of actual plant-breeding practices
an arbitrary number of individuals from each cross can can be seen in Figure 20-9, in which the yields of two
be produced. If inbred line 1 has the genetic consti- varieties of corn are shown as a function of different
tution A/AиB/Bиc/cиd/dиE/E . . . and inbred line 2 is farm environments. Variety 1 is an older variety of hy-
a/aиB/BиC/Cиd/dиe/e . . . , then a cross between them brid corn; variety 2 is a later “improved” hybrid. Their
will produce a large number of offspring, all of whom performances are compared at a low planting density,
are identically A/aиB/BиC/cиd/dиE/e . . . and can be which was usual when variety 1 was developed, and at a
raised in different environments. high planting density, characteristic of farming practice
when variety 2 was created. At the high planting density,
Results of norm of reaction studies variety 2 is clearly superior to variety 1 in all environ-
ments (Figure 20-9a). At the low planting density (Fig-
Very few norm of reaction studies have been carried out ure 20-9b), however, the situation is quite different.
for quantitative characters found in natural populations, First, note that the new variety is less sensitive to envi-
but many have been carried out for domesticated species ronmental variation than the older hybrid, as evidenced
such as corn, which can be self-pollinated, or strawber- by its flatter norm of reaction. Second, the new “im-
ries, which can be clonally propagated. The outcomes of proved” variety actually performs more poorly than the
such studies resemble those given in Figure 20-7. No older variety under the best farm conditions. Third, the
genotype consistently produces a phenotypic value above yield improvement of the new variety does not occur
or below that of the others under all environmental con- under the low planting densities characteristic of earlier
ditions. Instead, there are small differences between agricultural practice.
genotypes, and the direction of these differences varies
over a wide range of environments. The nature of norms of reaction also has implica-
tions for human social relations and policy. Even if it
These features of norms of reaction have important should turn out that there is genetic variation for various
consequences. One consequence is that selection for “su- mental and emotional traits in the human species —
perior” genotypes in domesticated animals and culti- which is by no means clear — this variation is unlikely to
vated plants will result in varieties adapted to very spe- favor one genotype over another across a range of envi-
cific conditions, which may not show their superior ronments. We must beware of hypothetical norms of re-
properties in other environments. To some extent, this action for human cognitive traits that show one geno-
problem can be overcome by deliberately testing geno- type being unconditionally superior to another. Even
types in a range of environments (for example, over putting aside all questions of moral and political judg-
several years and in several locations). It would be ment, there is simply no basis for describing different
even better, however, if plant breeders could test their human genotypes as “better” or “worse” on any scale, un-
selections in a variety of controlled environments in less the investigator is able to make a very exact specifi-
cation of environment.


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654 Chapter 20 • Quantitative Genetics

Variety 2Yield of cornMESSAGE Norm of reaction studies show that, within a
single environment, there are only small phenotypic
Yield of corn100 differences between most genotypes in natural populations
90 Variety 1 and that these differences are not consistent over a wide range
80 of environments. Thus, “superior” genotypes in domesticated
70 animals and cultivated plants may be superior only in certain
60 environments. As with physical traits, if it should turn out that
50 humans exhibit genetic variation for various mental and
40 emotional traits, no one genotype is likely to outperform
another across a range of environments.
40 50 60 70 80 90 100
Environmental quality 20.6 The heritability
(a) of a quantitative character

100 The most basic question that we can ask about a quan-
90 Variety 1 titative character is whether the observed variation in
Variety 2 that character is influenced by genes at all. It is impor-
80 tant to note that this question is not the same as asking
70 whether genes play any role in the character’s develop-
60 ment. Gene-mediated developmental processes lie at
50 the base of every character, but variation in a character
40 from individual to individual is not necessarily the re-
sult of genetic variation. For example, the ability to
40 50 60 70 80 90 100 speak any language at all depends critically on the struc-
Environmental quality tures of the central nervous system as well as on the vo-
(b) cal cords, tongue, mouth, and ears, which depend in
turn on many genes in the human genome. There is no
Figure 20-9 Environment and grain yield. Yields of grain environment in which cows will speak. But, although
of two varieties of corn in different environments: (a) at a the particular language that is spoken by humans varies
high planting density; (b) at a low planting density. [Data from nation to nation, this variation is not genetic. A
character is said to be heritable only if there is genetic
courtesy of W. A. Russell, Proceedings of the 29th Annual Corn variation in that character.
and Sorghum Research Conference, 1974. Photograph copyright
by Bonnie Sue/Photo Researchers.] MESSAGE The question “Is a trait is heritable?” is a
question about the role that differences in genes play in
the phenotypic differences between individuals or groups.

Familiality and heritability

In principle, it is easy to determine whether any genetic
variation influences the phenotypic variation in a partic-
ular trait. If genes play a role, then (on average) biologi-
cal relatives should resemble one another more than un-
related individuals do. This resemblance would be seen
as a positive correlation in the values of a trait between
parents and offspring or between siblings (offspring of
the same parents). Parents who are larger than the aver-
age, for example, would have offspring who are larger
than the average; the more seeds that a plant produces,
the more seeds that its siblings would produce. Such
correlations between relatives, however, are evidence for
genetic variation only if the relatives do not share common
environments more than nonrelatives do. It is absolutely


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20.6 The heritability of a quantitative character 655

fundamental to distinguish familiality from heritability. we shall begin our examination of the problem of heri-
Character states are familial if members of the same tability by analyzing phenotypic similarity.
family have them in common, for whatever reason. They
are heritable only if the similarity arises from having Phenotypic similarity between relatives
genotypes in common.
In experimental organisms, there is no problem in sepa-
There are two general methods for establishing the rating environmental from genetic similarities. The off-
heritability of a trait as distinct from its familiality. The spring of a cow producing milk at a high rate and the
first depends on phenotypic similarity between relatives. offspring of a cow producing milk at a low rate can be
For most of the history of genetics, this method has raised together in the same environment to see whether,
been the only one available, and so nearly all the evi- despite the environmental similarity, each resembles its
dence about heritability for most traits in experimental own parent. In natural populations, however, and espe-
organisms and in humans has been established by using cially in humans, this kind of study is difficult to per-
this approach. The second method, using marker-gene form. Because of the nature of human societies, mem-
segregation, depends on showing that genotypes carry- bers of the same family have not only genes in common,
ing different alleles of certain marker genes also differ but also similar environments. Thus, the observation of
in their average phenotype for a quantitative character. simple familial similarity of phenotype is genetically un-
If the marker genes (which have nothing to do with the interpretable. In general, people who speak Hungarian
character under study) are seen to vary in relation to have Hungarian-speaking parents and people who speak
the character, then presumably they are linked to genes Japanese have Japanese-speaking parents. Yet the mas-
that do influence the character and its variation. Thus, sive experience of immigration to North America has
heritability is demonstrated even if the actual genes demonstrated that these linguistic differences, although
causing the variation in the character are not known. familial, are nongenetic. The highest correlations be-
This method requires that the organism being studied tween parents and offspring for any social trait in the
have large numbers of detectable, genetically variable United States are those for political party and religious
marker loci spread throughout its genome. Such affiliation, but these traits are not heritable. The distinc-
marker loci can be observed through variants in DNA tion between familiality and heredity is not always so ob-
sequence, electrophoretic studies of protein variation vious, however. The U.S. Public Health Commission,
or, in vertebrates, immunological studies of blood- when it studied the vitamin-deficiency disease pellagra in
group proteins. Within flocks, for example, chickens the southern United States in 1910, came to the conclu-
with different blood groups show some difference in sion that it was genetic because it ran in families. How-
egg weight, but, as far as is known, the blood-group ever, pellagra is now well understood to have been preva-
antigens and antibodies do not themselves cause the lent in southern U.S. populations because of poor diet.
difference in egg size. Presumably, genes that do influ-
ence egg weight are linked to the loci determining To determine whether a human trait is heritable, we
blood group. must use studies of certain adopted persons to avoid the
usual environmental similarity between biological rela-
Since the introduction of molecular methods for tives. The ideal experimental subjects are monozygotic
studying DNA sequences, a great deal of genetic varia- (identical) twins reared apart because they are genetically
tion has been discovered in a great variety of organisms. identical but experience different environments. Such
This variation consists either of substitutions at single adoption studies must be so contrived that there is no
nucleotide positions or of variable numbers of insertions correlation between the social environments of the
or repeats of short sections of DNA. These variations are adopting families and those of the biological families, or
usually detected by the gain or loss of recognition sites else the similarities between the twins’ environments will
for restriction enzymes or by length variation in DNA not have been eliminated by the adoption. These require-
sequences between two fixed restriction sites, both of ments are exceedingly difficult to meet; therefore, in
which are forms of restriction fragment length polymor- practice, we know very little about whether human quan-
phism (RFLP; see Chapter 19). In tomatoes, for exam- titative characters that are familial are also heritable.
ple, strains carrying different RFLP variants differ in fruit
characteristics. It is assumed that the DNA sequences in Skin color is clearly heritable, as is adult height —
these RFLPs do not themselves influence fruit character- but even for characters such as these we must be very
istics; rather, they are landmarks located near genes that careful. We know that skin color is affected by genes,
do and therefore show high levels of cosegregation for both from studies of cross-racial adoptions and from ob-
these characteristics. servations that the offspring of black African slaves were
black even when they were born and reared in North
Because so much of what is known or claimed about America. But are the differences in height between
heritability still depends on phenotypic similarity be- Japanese and Europeans affected by genes? The children
tween relatives, however, especially in human genetics,


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656 Chapter 20 • Quantitative Genetics

of Japanese immigrants who are born and reared in Parental Heritable
North America are taller than their parents but shorter generation
than the North American average, and so we might con-
clude that there is some influence of genetic difference. Mean
However, second-generation Japanese Americans are Same
even taller than their American-born parents. It appears environment
that some environmental-cultural influence, possibly nu-
tritional or perhaps an effect of maternal inheritance, is or
still felt in the first generation of births in North Amer-
ica. We cannot yet say anything definitive about genetic Not heritable
differences that might contribute to the height differ-
ences between North Americans of, say, Japanese and Figure 20-10 Standard method for testing for heritability in
Swedish ancestry. experimental organisms. Crosses are performed within two
populations of individuals selected from the extremes of the
Personality traits, temperament, cognitive perfor- phenotypic distribution in the parental generation. If the
mance (including IQ scores), and a whole variety of be- phenotypic distributions of the two groups of offspring are
haviors such as alcoholism and mental disorders such as significantly different from each other (red curves), then the
schizophrenia have been the subject of heritability stud- character difference is heritable. If both offspring distributions
ies in human populations. Many of these traits show fa- resemble the distribution for the parental generation (blue
miliality (that is, familial similarity). There is a positive curves), then the phenotypic difference is not heritable.
correlation, for example, between the IQ scores of par-
ents and the scores of their children (the correlation is 20.7 Quantifying heritability
about 0.5 in white American families), but this correla-
tion does not distinguish familiality from heritability. To If a character is shown to be heritable in a population,
make that distinction requires that the environmental then it is possible to quantify the degree of heritability.
correlation between parents and children be broken, and In Figures 20-5 and 20-6, we saw that the variation be-
so studies on adopted children are common. Because it tween phenotypes in a population arises from two
is difficult to randomize environments, even in cases of sources. First, there are average differences between the
adoption, evidence of heritability for human personality genotypes; second, each genotype exhibits phenotypic
and behavior traits remains equivocal despite the very variation because of environmental variation. The total
large number of studies that exist. Prejudices about the phenotypic variance of the population (s2p) can thus be
causes of human differences are widespread and deep, broken into two parts: the variance between genotypic
and, as a result, the canons of evidence adhered to in means (sg2) and the remaining variance (s2e). The former
studies of the heritability of IQ, for example, have been is called the genetic variance, and the latter is called the
much more lax than in studies of milk yield in cows. environmental variance; however, as we shall see, these
names are quite misleading. Moreover, the breakdown of
Figure 20-10 summarizes the usual method of test- the phenotypic variance into environmental and genetic
ing for heritability in experimental organisms. Individu- variances leaves out the possibility of some covariance
als from both extremes of the phenotypic distribution between genotype and environment. For example, sup-
are mated with other individuals of their own extreme pose it were true (we do not know this) that there were
group, and the offspring are raised in a common con- genes that influence musical ability in humans. Parents
trolled environment. If there is an average difference be- with such genes might themselves be musicians, who
tween the two offspring groups, the phenotypic differ- would create a more musical environment for their
ence is heritable. Most morphological characters in children, who would then have both the genes and the
Drosophila, for example, turn out to be heritable — but
not all of them. If flies with right wings that are slightly
longer than their left wings are mated with each other,
their offspring have no greater tendency to be “right
winged” than do the offspring of “left winged” flies. As
we shall see, this method can also be used to obtain
quantitative information about heritability.

MESSAGE In experimental organisms, environmental
similarity can often be readily distinguished from genetic
similarity (or heritability). In humans, however, it is very
difficult to determine whether a particular trait is heritable.


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20.7 Quantifying heritability 657

environment promoting musical performance. The result number of homozygous lines, crossing them in pairs to
would be a greater variance among people in musical make heterozygotes typical of the population, and mea-
ability than would be the case if there were no effect of suring the phenotypic variance within each heterozygous
the parental environment on children. If the phenotype genotype. Because all individuals within each group have
is the sum of a genetic and an environmental effect, the same genotype and therefore there is no genetic
p ϭ g ϩ e, then the variance of the phenotype is, accord- variance within groups, these variances will (when aver-
ing to the formula on page 672, the sum of the genetic aged) provide an estimate of s2e. This value can then be
variance, the environmental variance, and twice the subtracted from the value of s2p in the original popula-
covariance between the genotypic and environmental tion to give s2g. With the use of this method, any covari-
effects: ance between genotype and environment in the original
population will be hidden in the estimate of genetic
sp2 ϭ s2g ϩ se2 ϩ 2 cov ge variance and will inflate it. So, for example, if individuals
with genotypes that would make them taller on average
If genotypes are not distributed randomly across envi- over random environments were also given better nutri-
ronments but this is not taken into account, there will tion than individuals with genotypes that would make
be some covariance between genotypic and environmen- them shorter, then the observed difference in heights be-
tal values, and that covariance will be hidden in the tween the two genotypic groups would be exaggerated.
genetic and environmental variances.
Other estimates of genetic variance can be obtained
The quantitative measure of heritability of a charac- by considering the genetic similarities between relatives.
ter is that part of the total phenotypic variance that is By using simple Mendelian principles, we can see that
due to genetic variance: half the genes of two full siblings will (on average) be
identical. For simplicity, we can label the alleles at a lo-
H2 ϭ s2g ϭ sg2 cus carried by the parents uniquely — say, as A1/A2 and
sp2 s2g ϩ se2 A3/A4. The older sibling has a probability of 1/2 of get-
ting A1 from its father, as does the younger sibling, and
H2, so defined, is called the broad heritability of the so the two siblings have a chance of 1/2 ϫ 1/2 ϭ 1/4
character. of both carrying A1. On the other hand, they might both
receive A2 from their father; so, again, they have a prob-
It must be stressed that this measure of “genetic in- ability of 1/4 of carrying that allele. Thus, the chance is
fluence” tells us what part of the population’s variation 1/4 ϩ 1/4 ϭ 1/2 that both siblings will inherit the same
in phenotype can be attributed to variation in genotype. allele (either A1 or A2) from their father. The other half
It does not tell us what parts of an individual’s pheno- of the time, one sibling will inherit an A1 and the other
type can be ascribed to its genotype and to its environ- will inherit an A2. So, as far as paternally inherited genes
ment. This latter distinction is not a reasonable one. An are concerned, full siblings have a 50 percent chance of
individual’s phenotype is a consequence of the interac- carrying the same allele. But the same reasoning applies
tion between its genes and the sequence of environ- to their maternally inherited allele. Averaging over their
ments that it experiences as it develops. It would be silly paternally and maternally inherited genes [(1/2 ϩ
to say that 60 inches of your height were produced by 1/2)/2 ϭ 1/2], half the genes of full siblings will be
your genes and 10 inches were then added by your envi- identical between them. Their genetic correlation,
ronment. All measures of the “importance” of genes are which is equal to the chance that they carry the same al-
framed in terms of the proportion of phenotypic vari- lele, will be 1/2, or 0.5.
ance ascribable to their variation. This approach is a spe-
cial application of the more general technique of analy- If we apply this reasoning to half-siblings, say, with a
sis of variance, used for apportioning relative weight to common father but with different mothers, we get a dif-
contributing causes. The technique was, in fact, invented ferent result. Again, the two siblings have a 50 percent
originally to deal with experiments in which different chance of inheriting an identical gene from their father,
environmental and genetic factors were influencing the but this time they have no way of inheriting the same
growth of plants. (For a sophisticated but accessible gene from their mothers because they have two differ-
treatment of the analysis of variance written for biolo- ent mothers. Averaging the maternally inherited and pa-
gists, see R. Sokal and J. Rohlf, Biometry, 3d ed., W. H. ternally inherited genes thus gives a probability of
Freeman and Company, 1995.) (1/2 ϩ 0)/2 ϭ 1/4 that these half-siblings will carry the
same gene.
Methods of estimating H 2
We might be tempted to use this theoretical correla-
Heritability in a population can be estimated in several tion between relatives to estimate H2. If the observed
ways. Most directly, we can obtain an estimate of the en- phenotypic correlation between siblings were, for exam-
vironmental variance in the population, s2e, by making a ple, 0.4, and we expected, on purely genetic grounds, a


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658 Chapter 20 • Quantitative Genetics

correlation of 0.5, then our estimate of heritability human genetics to estimate H2 for cognitive or person-
would be 0.4/0.5 ϭ 0.8. But such an estimate fails to ality traits. Here, the problem of degree of environmen-
take into account the fact that the environments of sib- tal similarity is very severe. Monozygotic (identical)
lings also may be correlated. Unless we are careful twins are generally treated more similarly to each other
to raise the siblings in independent environments, our than are dizygotic (fraternal) twins. Parents often
estimate of H2 will be too large and could even exceed give their identical twins names that are similar, dress
1 if the observed phenotypic correlation were greater them alike, treat them in the same way, and, in general,
than 0.5. accentuate their similarities. As a result, heritability is
overestimated.
To get around this problem, we use the differences
between phenotypic correlations of different relatives. The meaning of H2
For example, the difference in genetic correlation be-
tween full and half-siblings is 1/2 Ϫ 1/4 ϭ 1/4. Let’s Attention to the problems of estimating broad heritabil-
contrast this with their phenotypic correlations. If the ity distracts from the deeper questions about the mean-
environmental similarity is the same for half- and full ing of the ratio even when it can be estimated. Despite
siblings — a very important condition for estimating her- its widespread use as a measure of how “important”
itability — then environmental similarities will cancel genes are in influencing a character, H2 actually has a
out if we take the difference in correlation between the special and limited meaning.
two kinds of siblings. This difference in phenotypic cor-
relation will then be proportional to how much of the Two alternative conclusions can be drawn from the
variance is genetic. Thus: results of a properly designed heritability study. First, if
there is a nonzero heritability, we can conclude that, in
΂ ΃ ΂ ΃genetic correlation the population measured and in the environments in
of full siblings which the organisms have developed, genetic differences
Ϫ genetic correlation ϭ 1 have influenced the phenotypic variation among individ-
of half-siblings 4 uals, and so genetic differences do matter to the trait.
This finding is not trivial, and it is a first step in a more
but detailed investigation of the role of genes.

΂ ΃ ΂ ΃phenotypic It is important to notice that the reverse is not true.
phenotypic If zero heritability for the trait is found, this finding is
not a demonstration that genes are irrelevant to the trait;
correlation Ϫ correlation ϭ H2 ϫ 1 rather, it demonstrates only that, in the particular popu-
4 lation and environment studied, either there is no ge-
netic variation at the relevant loci or different genotypes
of full siblings of half-siblings have the same phenotype. In other populations or other
environments, the character might be heritable.
and so an estimate of H2 is:
MESSAGE The heritability of a character difference is
correlation correlation different in each population and in each set of
΄΂ ΃ ΂ ΃΅H2 ϭ 4 environments; it cannot be extrapolated from one population
of full siblings Ϫ of half-siblings and set of environments to another.

where the correlation here is the phenotypic correlation. Moreover, we must distinguish between genes con-
This estimate, as well as others based on correlations tributing to a trait and genetic differences contributing to
differences in a trait. The natural experiment of immigra-
between relatives, depends critically on the assumption tion to North America has proved that the ability to
that environmental correlations between individuals are pronounce the sounds of North American English,
the same for all degrees of relationship — which is un- rather than French, Swedish, or Russian, is not a conse-
likely to be the case. Full sibs, for example, are usually quence of genetic differences between our immigrant
raised by the same pair of parents, whereas half-sibs are ancestors. But, without the appropriate genes, we could
likely to be raised in circumstances with only one parent not speak any language at all.
in common. If closer relatives have more similar envi-
ronments, as they do among humans, these estimates of Second, the value of H2 provides a limited predic-
heritability will be biased. It is reasonable to assume that tion of how much a character can be modified by chang-
most environmental correlations between relatives are ing the environment. If all the relevant environmental
positive, in which case the heritabilities would be over- variation is eliminated and the new constant environ-
estimated. But negative environmental correlations also ment is the same as the mean environment in the original
can exist. For example, if the members of a litter must
compete for food that is in short supply, there could be
negative correlations in growth rates among siblings.

The difference in phenotypic correlation between
monozygotic and dizygotic twins is commonly used in


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20.7 Quantifying heritability 659

population, then H2 estimates how much phenotypic All that high heritability means is that, for the par-
variation will still be present. So, if the heritability of per- ticular population developing in the particular distribu-
formance on an IQ test were found to be, say, 0.4, then tion of environments in which the heritability was mea-
we could predict that, if all children had the same devel- sured, average differences between genotypes are large
opmental and social environment as the “average child,” compared with environmental variation within geno-
about 60 percent of the variation in IQ test performance types. If the environment is changed, there may be large
would disappear and 40 percent would remain. differences in phenotype.

The requirement that the new constant environ- Perhaps the best-known example of the erroneous
ment be at the mean of the old environmental distribu- use of heritability arguments to make claims about the
tion is absolutely essential to this prediction. If the envi- changeability of a trait is that of human IQ performance
ronment is shifted toward one end or the other of the and social success. Many studies have been made of the
environmental distribution present in the population heritability of IQ performance in the belief that, if heri-
used to determine H2 or if a new environment is intro- tability is high, then various programs of education de-
duced, nothing at all can be predicted. In the example of signed to increase intellectual performance are a waste
IQ test performance, the heritability gives us no infor- of time. The argument is that, if a trait is highly herita-
mation at all about how variable performance would be ble, then it cannot be changed much by environmental
if the developmental and social environments of all chil- changes. But, irrespective of the value of H2 for IQ test
dren were enriched. To understand why this is so, we performance, the real error of the argument lies in
must return to the concept of the norm of reaction. equating high heritability with unchangeability. In fact,
the heritability of IQ is irrelevant to the question of how
The separation of phenotypic variance into genetic changeable it is.
and environmental components, s2g and se2, does not really
separate the genetic and environmental causes of varia- To see why this is so, let us consider the usual results
tion. Consider the results presented in Figure 20-9b. of IQ studies on children who have been separated from
When the environment is poor (an environmental qual- their biological parents in infancy and reared by adoptive
ity of 50), corn variety 2 has a much higher yield than parents. Although these results vary quantitatively from
variety 1, and so a population made up of a mixture of study to study, they have three characteristics in com-
the two varieties would have a lot of genetic variance for mon. First, because adoptive parents usually come from a
yield in that environment. But, in a richer environment better-educated population than do the biological par-
(scoring 75), there is no difference in yield between vari- ents who offer their children for adoption, they generally
eties 1 and 2, and so a mixed population would have no have higher IQ scores than those of the biological par-
genetic variance at all for yield in that environment. ents. Second, the adopted children have higher IQ scores
Thus, genetic variance has been changed by changing the than those of their biological parents. Third, the adopted
environment. On the other hand, variety 2 is less sensi- children show a higher correlation of IQ scores with
tive to environment than variety 1, as shown by the their biological parents than with their adoptive parents.
slopes of the two lines. So a population made up mostly The following table is a hypothetical data set that shows
of variety 2 would have a lower environmental variance all these characteristics, in idealized form, to illustrate
than one made up mostly of variety 1. So, environmental these concepts. The scores given for parents are meant to
variance in the population is changed by changing the be the average of mother and father.
proportion of genotypes.
Mean Children Biological Adoptive
As a consequence of the argument just given, we parents parents
cannot predict just from knowing the heritability of a 110
character difference how the distribution of variation in 112 90 118
the character will change if either genotypic frequencies 114 92 114
or environmental factors change markedly. So, for exam- 116 94 110
ple, in regard to IQ test performance, knowing that the 118 96 120
heritability is 0.4 in one environment does not allow us 120 98 112
to predict how IQ test performance will vary among 115 100 116
children in a different environment. 95 115

MESSAGE A high heritability does not mean that a First, we can see that the scores of the children have
character is unaffected by the environment. Because a high correlation with those of their biological parents
but a low correlation with those of their adoptive par-
genotype and environment interact to produce phenotype, ents. In fact, in our hypothetical example, the correlation

no partition of variation into its genetic and environmental

components can actually separate causes of variation.


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660 Chapter 20 • Quantitative Genetics

of children with biological parents is r ϭ 1.00, but with to the amount of active gene product, we would expect
adoptive parents it is r ϭ 0. (Remember that a correla- the heterozygote phenotype to be exactly intermediate
tion between two sets of numbers does not mean that between the homozygotes (show no dominance).
the two sets are identical, but that, for each unit of in-
crease in one set, there is a constant proportional in- For many quantitative traits, however, neither of
crease in the other set — see the Statistical Appendix on these simple cases is the rule. In general, heterozygotes
statistical analysis at the end of this chapter.) This per- are not exactly intermediate between the two homozy-
fect correlation with biological parents and zero correla- gotes but are closer to one or the other (show partial
tion with adoptive parents means that H2 ϭ 1, given dominance), even though there is an equal mixture of
the arguments just developed. All the variation in IQ the primary products of the two alleles in the heterozy-
score among the children is explained by the variation in gote. Suppose that two alleles, a and A, segregate at a lo-
IQ score among the biological parents, who have had no cus influencing height. In the environments encountered
chance to influence the environments of their children. by the population, the mean phenotypes (heights) and
frequencies of the three genotypes might be:
Second, however, we notice that the IQ score of
each child is 20 points higher than that of its biological a/a A/a A/A
parents and that the mean IQ of the children is equal to
the mean IQ of the adoptive parents. Thus, adoption has Phenotype 10 18 20
raised the average IQ of the children 20 points above Frequency 0.36 0.48 0.16
the average IQ of their biological parents, and so, as a
group, the children resemble their adoptive parents. So There is genetic variance in the population; the pheno-
we have perfect heritability, yet high plasticity in re- typic means of the three genotypic classes are different.
sponse to environmental modification. Some of the variance arises because there is an average
effect on phenotype of substituting an allele A for an al-
An investigator who is seriously interested in know- lele a; that is, the average height of all individuals with
ing how genes might constrain or influence the course of A alleles is greater than that of all individuals with a
development of any character in any organism must alleles. By defining the average effect of an allele as the
study directly the norms of reaction of the various geno- average phenotype of all individuals that carry it, we
types in the population over the range of projected envi- necessarily make the average effect of the allele depend
ronments. No less detailed information will do. on the frequencies of the genotypes.
Summary measures such as H 2 are not valuable in
themselves. The average effect is calculated by simply counting
the a and A alleles and multiplying them by the heights
MESSAGE Heritability is not the opposite of phenotypic of the individuals in which they appear. Thus, 0.36 of all
plasticity. A character may have perfect heritability in a the individuals are homozygous a/a, each a/a individual
population and still be subject to great changes resulting from has two a alleles, and the average height of a/a individu-
environmental variation. als is 10 cm. Heterozygotes make up 0.48 of the popula-
tion, each has only one a allele, and the average pheno-
Narrow heritability typic measurement of A/a individuals is 18 cm. The
total “number” of a alleles is 2(0.36) ϩ 1(0.48). Thus,
Knowledge of the broad heritability (H2) of a character the average effect of all the a alleles is:
in a population is not very useful in itself, but a finer
subdivision of phenotypic variance can provide impor- a ϭaverage effect of a ϭ 2(0.36)(10) ϩ1(0.48)(18)
tant information for plant and animal breeders. The 2(0.36) ϩ1(0.48)
genetic variance can itself be subdivided into two com-
ponents to provide information about gene action and ϭ 13.20 cm
the possibility of shaping the genetic composition of a
population. and, by a similar argument,

Our previous consideration of gene action suggests A ϭ average effect of A ϭ 2(0.16)(20) ϩ 1(0.48)(18)
that the phenotypes of homozygotes and heterozygotes 2(0.16) ϩ 1(0.48)
ought to have a simple relation. If one of the alleles en-
coded a less active gene product or one with no activity ϭ 18.80 cm
at all and if one unit of gene product were sufficient to
allow full physiological activity of the organism, then we This average difference in effect between A and a
would expect complete dominance of one allele over the alleles, the additive effect, of 5.60 cm accounts for some
other, as Mendel observed for flower color in peas. If, on of the variance in phenotype — but not for all of it. The
the other hand, physiological activity were proportional heterozygote is not exactly intermediate between the
homozygotes; there is some dominance.


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20.7 Quantifying heritability 661

We would like to separate the so-called additive ef- greater the h2 is, the greater the fraction of the differ-
fect caused by substituting a alleles for A alleles from ence between selected parents and the population as a
the variation caused by dominance. The reason is that whole that will be preserved in the offspring of the se-
the effect of selective breeding depends on the additive lected parents.
variation and not on the variation caused by dominance.
Thus, for purposes of plant and animal breeding or for MESSAGE The effect of selection depends on the amount
making predictions about evolution by natural selection, of additive genetic variance and not on the genetic variance
we must determine the additive variation. An extreme in general. Therefore, it is the narrow heritability, h 2, not the
example will illustrate the principle. Suppose that plant broad heritability, H 2, that predicts response to selection.
height is influenced by variation in a gene and that the
phenotypic means and frequencies of three genotypes Estimating the components
are: of genetic variance

A/A A/a a/a The different components of genetic variance can be es-
timated from covariance between relatives — the degree
Phenotype 10 12 10 to which the phenotypes of pairs of relatives are corre-
Frequency 0.25 0.50 0.25 lated with each other — but the derivation of these esti-
mates is beyond the scope of this text. There is, how-
It is apparent (and a calculation like the preceding one ever, another way to estimate narrow heritability h2 that
will confirm) that there is no average difference between reveals its real meaning. If, in two generations of a popu-
the a and A alleles, because each has an effect of 11 lation, we plot the phenotype — say, height — of off-
units. So there is no additive variation, although there is spring against the average phenotype of their two par-
obviously genetic variation because there is variation in ents (the midparent value), we may observe a relation
phenotype between the genotypes. The tallest plants are like the one illustrated by the red line in Figure 20-11.
heterozygotes. If a breeder attempts to increase height in The regression line will pass through the mean height of
this population by selective breeding, mating these het- all the parents and the mean height of all the offspring,
erozygotes together will simply reconstitute the original which will be equal to each other because no change has
population. Selection will be totally ineffective. This ex- taken place in the population between generations.
ample illustrates the general law that the effect of selec- Moreover, taller parents have taller children and shorter
tion depends on the additive genetic variation and not parents have shorter children, and so the slope of
on genetic variation in general. the line is positive. But the slope is not unity; very short

The total genetic variance in a population can be Slope = 1.0 = h 2
subdivided into two components: additive genetic varia-
tion (s2a), the variance that arises because there is an Slope = 0.5 = h 2
average difference between the carriers of a alleles and
the carriers of A alleles, and dominance variance (s2d), y = mean of offspring
the variance that results from the fact that heterozy-
gotes are not exactly intermediate between the
monozygotes. Thus:

s2g ϭ sa2 ϩ s2d

The total phenotypic variance can now be written as (y–, x–) Slope = 0.0
y– = x–

sp2 ϭ s2g ϩ s2e ϭ sa2 ϩ sd2 ϩ s2e

We define a new kind of heritability, the heritability in
the narrow sense (h2), as

h2 ϭ s2a ϭ sa2 x = midparent = father + mother
s2p sa2 ϩ sd2 ϩ s2e 2

It is this heritability, not to be confused with H2, that is Figure 20-11 The regression (red line) of offspring
useful in determining whether a program of selective measurements (y) on midparent values (x) for a trait with
breeding will succeed in changing the population. The narrow heritability (h 2) of 0.5. The blue line would be the
regression slope if the trait were perfectly heritable.


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662 Chapter 20 • Quantitative Genetics

parents on average have children who are somewhat Size and Body weight
taller, and very tall parents on average have children who conformation Shank length
are somewhat shorter, than they themselves are. This Keel length
slope of less than unity arises because heritability is less Egg Body depth
than perfect. If the phenotype were additively inherited production Breast width and angle
with complete fidelity, then the heights of the offspring
would be identical with the midparent values and the Egg Production of survivors
slope of the regression line would be 1. On the other quality Rate
hand, if the offspring had no heritable similarity to their Sexual maturity
parents, all parents would have offspring of the same av- Viability Pauses in laying
erage height and the slope of the line would be 0. This Miscellaneous Hen-housed production
reasoning suggests that the slope of the regression line Persistency
relating offspring value to the midparent value provides
an estimate of additive heritability. In fact, the slope of Egg weight
the line can be shown mathematically to be a correct es- Blood-spot incidence
timate of h2. Shell color
Albumen weight
The fact that the slope of the regression line esti- Egg shape
mates additive heritability allows us to use h2 to predict Albumen quality
the effects of artificial selection. Suppose that we select Shell texture
parents for the next generation who are, on average, 2 Shell thickness
units above the general mean of the population from Yolk weight
which they were chosen. If h2 ϭ 0.5, then the offspring
of those selected parents will lie 0.5(2.0) ϭ 1.0 unit Total mortality
above the mean of the parental population, because the Hatchability
slope of the regression line predicts how much increase Respiratory diseases
in y will result from a unit increase in x. We can define Reproductive disorders
the selection differential as the difference between the
selected parents and the mean of the entire population Weight of some internal organs
in their generation, and the selection response as the dif- Rate of feathering
ference between the offspring of the selected parents
and the mean of the parental generation. Thus 0 0.5 1.0
Heritability (h 2)

Figure 20-12 Ranges of heritabilities (h2) reported for a
variety of characters in chickens. [From I. M. Lerner and W. J.

Libby, Heredity, Evolution, and Society. Copyright 1976 by W. H.
Freeman and Company. Photograph copyright by Kenneth
Thomas/Photo Researchers.]

selection response ϭ h2 ϫ selection differential most traits for which a substantial heritability has been
or reported, there are big differences from study to study,
presumably because different populations have different
h2 ϭ selection response amounts of genetic variation and because the different
selection differential studies were carried out in different environments. Thus,
breeders who want to know whether selection will be
The second expression provides us with yet another way effective in changing some character in their chickens
to estimate h2: by carrying out selective breeding for one cannot count on the heritabilities found in earlier stud-
generation and comparing the selection response with ies but must estimate the heritability in the particular
the selection differential. Usually this process is carried population and particular environment in which the se-
out for several generations with the use of the same se- lection program is to be carried out.
lection differential, and the average response is used as
an estimate of h2. Artificial selection

Remember that any estimate of h2, just as for H 2, A vast record demonstrates the effectiveness of artificial
depends on the assumption of no correlation between selection in changing phenotypes within a population.
the similarity of the individuals’ environments and the Animal and plant breeding has, for example, increased
similarity of their genotypes. Moreover, h2 in one popu- milk production in cows and rust resistance in wheat.
lation in one set of environments will not be the same as Selection experiments in the laboratory have made large
h2 in a different population in a different set of environ- changes in the physiology and morphology of many or-
ments. To illustrate this principle, Figure 20-12 shows ganisms including microorganisms, plants, and animals.
the range of narrow-sense heritabilities reported in vari- No analysis of these experiments in terms of allelic fre-
ous studies for a number of characters in chickens. For quencies is possible, because individual loci have not
been identified and followed. Nevertheless, it is clear
that genetic changes have taken place because the popu-
lations maintain their characteristics even after the selec-
tion has been terminated. Figure 20-13 shows, as an ex-
ample, that a selection experiment achieved large
changes in average bristle number in a population of D.


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20.7 Quantifying heritability 663

56Mean bristle number the character, because the selected individuals do not re-
produce. The loss of fitness may be a direct phenotypic
52 Average egg production effect of the genes for the selected character, in which
case nothing much can be done to improve the popula-
48 tion further. Often, however, the loss of fitness is tied
Upwardly selected line not to the genes that are under selection but to linked
sterility genes that are carried along with them. In such
44 cases, a number of generations are allowed to breed
without selection until recombinants form by chance,
40 freeing the genes under selection from their association
with the sterility. Selection can then be continued, as in
36 the upwardly selected line in Figure 20-13.
32 Downwardly selected line
We must be very careful in our interpretation of
28 long-term agricultural selection programs. In the real
world of agriculture, changes in cultivation methods,
24 machinery, fertilizers, insecticides, herbicides, and so
0 5 10 15 20 25 30 35 40 45 50 forth, are taking place along with the production of ge-
Generations netically improved varieties. Increases in average yields
are consequences of all of these changes. For example,
Figure 20-13 Effect of selection on bristle number. Changes the average yield of corn in the United States increased
in average bristle number obtained in two laboratory from 40 bushels to 80 bushels per acre between 1940
populations of Drosophila melanogaster through artificial and 1970. But experiments comparing old and new vari-
selection for high bristle number in one population and low eties of corn in common environments show that only
bristle number in the other. The dashed line shows five about half this increase is a direct result of new corn va-
generations during which no selection was practiced. [From rieties (the other half being a result of improved farming
techniques). Furthermore, the new varieties are superior
K. Mather and B. J. Harrison, “The Manifold Effects of Selection,” to the old ones only at the high densities of modern
Heredity 3, 1949, 1.] planting for which they were selected.

melanogaster. Figure 20-14 shows the increase in the The use of h 2 in breeding
number of eggs laid per chicken as a consequence of 30
years of selection. Even though h2 is a number that applies only to a par-
ticular population and a given set of environments, it is
The usual method of selection for a continuously still of great practical importance to breeders. A poultry
varying trait is truncation selection. The individuals in a geneticist interested in increasing, say, the growth rate
given generation are pooled (irrespective of their fami- of chickens is not concerned with the genetic variance
lies), a sample is measured, and only those individuals over all possible flocks and all environmental distribu-
above (or below) a given phenotypic value (the trunca- tions. Given a particular flock (or a choice between a
tion point) are chosen as parents for the next generation. few particular flocks) under the environmental condi-
tions approximating present husbandry practice, the
A common experience in artificial selection pro- question becomes, Can a selection scheme be devised to
grams is that, as the population becomes more and more increase growth rate and, if so, how rapidly can it be in-
extreme, its viability and fertility decrease. As a result, creased? If one flock has a lot of genetic variance for
eventually no further progress under selection is possi- growth rate and another only a little, the breeder will
ble, despite the presence of additive genetic variance for choose the former flock to carry out selection. If the
heritability in the chosen flock is very high, then the
100 mean of the population will respond quickly to the se-
lection imposed, because most of the superiority of the
80 selected parents will appear in the offspring. The higher
the h2 is, the higher the parent–offspring correlation is.
60 If, on the other hand, h2 is low, then only a small frac-
tion of the superiority of the selected parents will ap-
40 pear in the next generation.

20 If h2 is very low, some alternative scheme of se-
0 lection or husbandry may be needed. In this case, H 2
1933 1938 1943 1948 1953 1958 1963 1965

Year

Figure 20-14 Effect of selection on egg production. Changes
in average egg production in a chicken population selected for
its increase in egg-laying rate over a period of 30 years. [From

I. M. Lerner and W. J. Libby, Heredity, Evolution, and Society, 2d ed.
Copyright 1976 by W. H. Freeman and Company. Data courtesy of
D. C. Lowry.]


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664 Chapter 20 • Quantitative Genetics

together with h2 can be of use to the breeder. Suppose 20.8 Locating genes
that h2 and H 2 are both low, which means that there is a
large proportion of environmental variance compared It is not possible to identify all the genes that influence
with genetic variance. Some scheme of reducing s2e must the development of a given character by using purely ge-
be used. One method is to change the husbandry condi- netic techniques. In a given population, only a subset of
tions so that environmental variance is lowered. Another the genes that contribute to the development of any
is to use family selection. Rather than selecting the best given character will be genetically variable. Hence, only
individuals, the breeder allows pairs to produce several some of the possible variation will be observed. This is
trial progeny, and parental pairs are selected to produce true even for genes that determine simple qualitative
the next generation on the basis of the average perfor- traits — for example, the genes that determine the total
mance of those progeny. Averaging over progeny allows antigenic configuration of the membrane of the human
uncontrolled environmental variation and developmen- red blood cell. About 40 loci determining human blood
tal noise to be canceled out, and a better estimate of groups are known at present; each has been discovered
the genotypic difference between pairs can be made so by finding at least one person with an immunological
that the best pairs can be chosen as parents of the next specificity that differs from the specificities of other peo-
generation. ple. Many other loci that determine red blood cell mem-
brane structure may remain undiscovered because all
If, on the other hand, h2 is low but H 2 is high, then the people studied are genetically identical. Genetic
there is not much environmental variance. The low h2 is analysis detects genes only when there is some allelic
the result of a small proportion of additive genetic vari- variation. In contrast, molecular analysis deals directly
ance compared with dominance variance. Such a situa- with DNA and its translated information and so can
tion calls for special breeding schemes that make use identify genes as stretches of DNA coding for certain
of nonadditive variance. One such scheme is the products, even when they do not vary — provided that
hybrid – inbred method, which is used almost univer- the gene products can be identified.
sally for corn. A large number of inbred lines are cre-
ated by selfing. These inbred lines are then crossed in Even though a character may show continuous phe-
many different combinations (all possible combinations, notypic variation, the genetic basis for the differences
if it is economically feasible), and the cross that gives may be allelic variation at a single locus. Most of the clas-
the best hybrid is chosen. Then new inbred lines are de- sic mutations in Drosophila are phenotypically variable in
veloped from this best hybrid, and again crosses are their expression, and in many cases the mutant class dif-
made to find the best hybrid cross. This process is con- fers little from wild type, and so many flies that carry the
tinued cycle after cycle. This scheme selects not only for mutation are indistinguishable from normal flies. Even the
additive effects but also for dominance effects, because genes of the bithorax complex, which have dramatic
it selects the best heterozygotes as parents for the next homeotic mutations that turn halteres into wings (see
cycle; it has been the basis of major genetic advances in Figure 18-24), also have weak alleles that increase the size
hybrid maize yield in North America since 1930. Yield of the halteres only slightly on average, and so flies of the
in corn does not appear to have large amounts of non- mutant genotype may appear to be wild type.
additive genetic variance, however, and so it is debatable
whether this technique ultimately produces higher- It is sometimes possible to use prior knowledge of
yielding varieties than those that would have resulted the biochemistry and development of an organism to
from years of simple selection techniques based on ad- guess that variation at a known locus is responsible for at
ditive variance. least some of the variation in a certain character. Such
a locus is a candidate gene for the investigation of
The hybrid – inbred method has been introduced continuous phenotypic variation. The variation in ac-
into the breeding of all kinds of plants and animals. tivity of the enzyme acid phosphatase in human red
Tomatoes and chickens, for example, are now almost ex- blood cells was investigated in this way. Because we are
clusively hybrids. Attempts also have been made to dealing with variation in enzyme activity, a good
breed hybrid wheat, but thus far the wheat hybrids ob- hypothesis would be that there is allelic variation at the
tained do not yield consistently better than do the non- locus that codes for this enzyme. When H. Harris and
hybrid varieties now used. D. Hopkinson sampled an English population, they
found that there were, indeed, three allelic forms, A, B,
MESSAGE The subdivision of genetic variation and and C, that resulted in enzymes with different activity
environmental variation provides important information levels. Table 20-2 shows the mean activity, the variance
in activity, and the population frequency of the six geno-
about gene action that can be used in plant and animal types. Figure 20-15 shows the distribution of activity
for the entire population and how it is composed of the
breeding.


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20.8 Locating genes 665

TABLE 20-2 Red Blood Cell Activity of Different Genotypes of Red-Cell
Acid Phosphatase in the English Population

Genotype Mean activity Variance of activity Frequency in population

A/A 122.4 282.4 0.13
A/B 153.9 229.3 0.43
B/B 188.3 380.3 0.36
A/C 183.8 392.0 0.03
B/C 212.3 533.6 0.05
C/C 240 0.002
Grand average 166.0 —
Total distribution 166.0 310.7
607.8

Note: Averages are weighted by frequency in population.
Source: H. Harris, The Principles of Human Biochemical Genetics, 3d ed. North-Holland, 1980.

distributions of the different genotypes. As Table 20-2 to different alleles at a single locus, but the proportion of
shows, of the variance in activity in the total distribution variance associated with the single locus is usually less
(607.8), about half is explained by the average variance than what was found for acid phosphatase activity. For
within genotypes (310.7); so half (607.8 Ϫ 310.7 ϭ example, the three common alleles for the gene apoE,
297.1) must be accounted for by the variance between which encodes the protein apolipoprotein E, account for
the means of the six genotypes. Although so much of only about 16 percent of the variance in blood levels of
the variation in activity is explained by the mean differ- the low-density lipoproteins that carry cholesterol and
ences between the genotypes, there remains variation are implicated in excess cholesterol levels. The remain-
within each genotype that may be the result of environ- ing variance is a consequence of some unknown combi-
mental influences or of the segregation of other, as yet nation of genetic variation at other loci and environmen-
unidentified genes. tal variation.

By using the candidate-gene method, one often finds Marker-gene segregation
that part of the variation in a population is attributable
The genes segregating for a quantitative trait — so-called
Relative frequency A/B General quantitative trait loci, or QTLs — cannot be individually
population identified in most cases. It is possible, however, to locate
regions of the genome in which the relevant loci lie and
B/B to estimate how much of the total variation is accounted
for by QTL variation in each region. This analysis can be
A /A done in experimental organisms by crossing two lines
that differ markedly in the quantitative trait and that
A /C B /C also differ in alleles at well-known loci, called marker
genes. The marker genes used for such analyses are ones
100 140 180 220 260 for which the different genotypes can be distinguished
by some visible phenotype that cannot be confused with
Acid phosphatase activity the quantitative trait (for example, eye color in
Drosophila) or by the electrophoretic mobility of the
Figure 20-15 Distribution of enzyme activity. Acid proteins that they encode or by the DNA sequence of
phosphatase activity in red cells for different genotypes (red the genes themselves. A typical experiment entails cross-
curves) and the distribution of activity in an English ing two lines that differ markedly in the quantitative
population made up of a mixture of these genotypes (green character and that also differ in marker alleles. The F1 re-
curve). [H. Harris, The Principles of Human Biochemical Genetics, sulting from the cross between the two lines may then
be crossed with itself to make a segregating F2, or it may
3d ed. Copyright 1970 by North-Holland.] be backcrossed to one of the parental lines. If there are
QTLs closely linked to a marker gene, then the different
marker genotypes and the QTLs will be inherited


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666 Chapter 20 • Quantitative Genetics

together, and the different marker genotypes in the F2 or rieties or family groups that differ markedly in the trait.
backcross will have different average phenotypes for the These lines must then be surveyed for marker loci that
quantitative character. differ between them. A cross is made between the two
lines, and the F1 is then crossed with itself to produce a
Quantitative linkage analysis segregating F2 or is crossed with one of the parental lines
to produce a segregating backcross. A large number of
The localization of QTLs to small regions within chro- offspring from the segregating generation are then mea-
mosomes requires the presence of closely spaced marker sured for the quantitative phenotype and characterized
loci along the chromosome. Moreover, it must be possi- for their genotype at the marker loci. A marker locus
ble to create parental lines that differ from each other in that is unlinked or very loosely linked to any QTLs af-
the alleles carried at these marker loci. With the advent fecting the quantitative trait of interest will have the
of molecular techniques that can detect genetic poly- same average value of the quantitative trait for all its
morphism at the DNA level, a very high density of vari- genotypes, whereas one that is closely linked to some
ant loci has been discovered along the chromosomes of QTLs will differ in its mean quantitative phenotype
all species. Especially useful are restriction fragment from one marker genotype to another.
length polymorphisms (RFLPs), tandem repeats, and sin-
gle nucleotide polymorphisms (SNPs) in DNA. Such How much difference there is in the mean quantita-
polymorphisms are so common that any two lines se- tive phenotype between the different marker genotypes
lected for a difference in quantitative traits are also sure depends both on the strength of the effect of the QTL
to differ from each other at some known molecular and on the tightness of linkage between the QTL and
marker loci spaced a few crossover units from each the marker locus. Suppose, for example, that two se-
other along each chromosome. lected lines differ by a total of 100 units in some quanti-
tative character. The line with the high value is homozy-
An experimental protocol for localizing genes, gous 1/1 at a particular QTL, whereas the line with the
shown in Figure 20-16, uses groups of individuals that low value is homozygous –/–, and each 1allele at this
differ markedly in the quantitative character of interest QTL accounts for 5 units of the total difference between
as well as at marker loci. These groups may be created the lines. Further, suppose that the high line is M/M and
by several generations of divergent selection to create the low line is m/m at a marker locus 10 crossover units
extreme lines, or advantage may be taken of existing va- away from the QTL. Then, as shown in Figure 20-16,
there are 4 units of difference between the average ga-
+M × –m mete carrying an M allele and the average gamete carry-
ing an m allele in the segregating F2. We can therefore
Selected lines +M –m calculate that 8 units of the difference between an M/M
homozygote and an m/m homozygote are attributable to
F1 +M that QTL. Thus, we have accounted for 8 percent of the
Gamete production average difference between the original selected lines.
RF = 0.10 The QTL actually accounts for 10 percent of the differ-
–m ence; the discrepancy comes from the recombination be-
tween the marker gene and the QTL. We could then re-
Frequency + M– M + m– m peat this process by using marker loci at other locations
along the chromosome and on different chromosomes to
0.45 0.05 0.05 0.45 account for yet further fractions of the quantitative dif-
(0.9 : 0.1) (0.1 : 0.9) ference between the original selected lines.

Contribution to 50 50 This technique has been used to locate chromoso-
phenotype in F2 mal segments associated with such characters as fruit
weight in tomatoes, bristle number in Drosophila, and
Average phenotypic effect of M class = 5 (0.9) + 0 (0.1) = 4.5 vegetative characters in maize. In the maize case, 82 veg-
Average phenotypic effect of m class = 5 (0.1) + 0 (0.9) = 0.5 etative characters were examined in a cross between
lines that differed in 20 DNA markers. On the average,
Difference between M-carrying gametes and m-carrying gametes = each character was significantly associated with 14 dif-
4.5 –0.5 = 4 ferent markers, but the proportion of the character dif-
ference between the two lines that was associated with
Difference between average F2 M /M homozygotes and average any particular marker was usually very small. Figure
F2 m /m homozygotes = 8 20-17 shows the proportion of the statistically signifi-
cant marker – character associations (on the y-axis) that
Figure 20-16 Results of a cross between two selected lines accounted for different proportions of character differ-
that differ at a QTL and at a molecular marker locus 10 crossover
units away from the QTL. The QTL 1allele adds 5 units of
difference to the phenotype.


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Statistical appendix 667

y
30

Percentage of QTLs identified 25

20

15

10

5

x
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

Percentage of difference explained

Figure 20-17 Distribution of associations of the trait differences between two lines of maize
with an array of DNA markers. The x-axis shows the percentage of the difference explained
between the two lines in a given trait that could be associated with any marker gene. The
y-axis shows the proportion of all the identified QTLs that had the corresponding
percentage of its difference explained. Note that 55 percent of all the associations (first
two columns) account for less than 1 percent of their trait differences. [After M. Lynch and

B. Walsh, Genetics and Analysis of Quantitative Traits. Sinauer Associates, 1998. Data from
M. D. Edwards, C. W. Stuber, and J. F. Wendel, Genetics 116, 1987, 113-125.]

ence between the lines. As Figure 20-17 shows, most as- have not been very successful, although the marker seg-
sociations accounted for less than 1 percent of the char- regation technique has been a success in finding loci
acter difference. Unfortunately, in human genetics, al- whose mutations are responsible for single-gene disor-
though marker-gene segregation can be used to localize ders or for quantitative characters whose variation is
single-gene disorders, the small size of human pedigree strongly influenced by variation at one locus. For exam-
groups makes the marker segregation technique inap- ple, people vary in their ability to taste the substance
plicable for quantitative trait loci because there are too phenylthiocarbamate (PTC). Some can detect quite low
few progeny from any particular marker cross to provide concentrations, whereas others can detect only high con-
any accuracy. centrations or are unable to taste PTC at all. Linkage
analysis using single nucleotide polymorphisms located a
For many organisms (for example, humans), it is not region on human chromsome 7q that accounted for
possible to make homozygous lines differing in some about 75 percent of the variation in taste sensitivity. This
trait and then cross them to produce a segregating gen- chromosomal region was already known to contain sev-
eration. For such organisms, one can use the differences eral genes coding for bitter taste receptor proteins. When
among sibs carrying different marker alleles from het- the DNA of these genes was sequenced, three amino
erozygous parents. This method has much less power to acid polymorphisms in one of the genes were found to
find QTLs especially when the number of sibs in any be strongly associated with the difference between the
family is small, as it is in human families. As a conse- taster and the nontaster phenotypes.
quence, the attempts to map QTLs for human traits

STATISTICAL APPENDIX vidual measurements of height for male graduates tend to
cluster around 100 cm or 200 cm?) Second, we need
Complete information about the distribution of a pheno- some measure of the amount of variation within the distri-
type in a population can be given only by specifying the bution. (For example, are the heights of the male under-
frequency of each measured class, but a great deal of infor- graduates all concentrated around the central measure-
mation can be summarized in just two statistics. First, we ment or do they vary widely across a large range?)
need some measure of the location of the distribution
along the axis of measurement. (For example, do the indi-


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668 Chapter 20 • Quantitative Genetics

Measures of central tendency will have the same value within the accuracy of the

The mode Most distributions of phenotypes look measuring instrument. In such a case, x can be rewritten
roughly like those in Figure 20-3: a single mode is lo-
cated near the middle of the distribution, with frequen- as the sum of all measurement values, each weighted by
cies decreasing on either side. There are exceptions to
this pattern, however. Figure 20-18a shows the very how frequently it occurs in the population. From a total
asymmetrical distribution of seed weights in the plant
Crinum longifolium. Figure 20-18b shows a bimodal of N individuals measured, suppose that n1 fall in the
(two-mode) distribution of larval survival probabili- class with value x1, that n2 fall in the class with value x2,
ties for different second-chromosome homozygotes in and so forth, so that ͚ni ϭ N. If we let fi be the relative
Drosophila willistoni. frequency of the ith measurement class, so that

A bimodal distribution may indicate that the popu- fi ϭ ni
lation being studied could be better considered a mix- N,
ture of two populations, each with its own mode. In Fig-
ure 20-18b, the left-hand mode probably represents a then we can rewrite the mean as
subpopulation of severe single-locus mutations that are
extremely deleterious when homozygous but whose ef- x ϭ f1x1 ϩ f2x2 ϩ и и и ϩ fkxk ϭ ͚fi xi
fects are not felt in the heterozygous state in which they
usually exist in natural populations. The right-hand where xi equals the value of the ith measurement class.
mode is part of the distribution of “normal” viability Let us apply these calculation methods to the data
modifiers of small effect.
of Table 20-3, which gives the numbers of toothlike bris-
tles in the sex combs on the right (x) and left (y) front
legs and on both legs (T ϭ x ϩ y) of 20 Drosophila.
Looking for the moment only at the sum of the two legs
T, we find the mean number of sex comb teeth T to be:

The mean A more common measure of central ten- Tϭ 11 ϩ 12 ϩ 12 ϩ 12 ϩ 13 ϩ иии ϩ 15 ϩ 16 ϩ 16
20
dency is the arithmetic average, or the mean. The mean
ϭ 274
of the measurement ( x) is simply the sum of all the in- 20
dividual measurements ( xi ) divided by the number of
measurements in the sample (N):

ϭ 13.7

mean ϭ x ϭ x1 ϩ x2 ϩ x3 ϩ иии ϩ xN ϭ 1 ͚xi Alternatively, by using the relative frequencies of the
N N different measurement values, we find that

where ͚ represents the operation of summing over all T ϭ 0.05(11) ϩ 0.15(12) ϩ 0.20(13) ϩ 0.35(14)
values of i from 1 to N, and xi is the ith measurement. ϩ 0.15(15) ϩ 0.10(16)

In a typical large sample, the same measured value ϭ 13.7

will appear more than once, because several individuals

Distribution function
Distribution function

0123456789 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
(a) Seed weight (g) (b) Standard viability (%)

Figure 20-18 Asymmetrical distribution functions. (a) Asymmetrical distribution of seed
weight in Crinum longifolium; (b) bimodal distribution of survival of Drosophila willistoni
expressed as a percentage of standard survival. [After S. Wright, Evolution and the Genetics of

Populations, vol. 1. Copyright 1968 by University of Chicago Press. Photograph: Earth
Scenes/Copyright Thompson GOSF.]


44200_20_p643-678 3/23/04 14:48 Page 669

Statistical appendix 669

TABLE 20-3 Number of Teeth in the Sex Comb on the Right (x) and Left
(y) Legs and the Sum of the Two (T) for 20 Drosophila Males

x y T ni fi ϭ ni/N
1
6 5 11 3 1 ϭ 0.05
6 6 4 20
5 7 ·12
6 6 7 3 ϭ 0.15
7 6 12 20
5 8 12 3
6 7 2 4 ϭ 0.20
7 6 ·13 20
8 6
6 8 13 7 ϭ 0.35
7 7 13 20
7 7 13
7 7 14 3 ϭ 0.15
6 8 20
8 6 ·14
8 7 2 ϭ 0.10
7 8 14 20
6 9 14
8 8 14
7 9 14
N ϭ 20 14
x ϭ 6.25 sx ϭ 0.9096
y ϭ 7.05 ·15 sy ϭ 1.0722
sT ϭ 1.308
T ϭ 13.70 15
15

·16

16
s2x ϭ 0.8275
sy2 ϭ 1.1475
s2T ϭ 1.71

cov xy ϭ Ϫ0.1325
rxy ϭ Ϫ0.1360

Measures of dispersion: the variance the mean, we can use an alternative computing formula
that is algebraically identical with the preceding equation:
A second characteristic of a distribution is the width of
its spread around the central class. Two distributions ΂ ΃͚s2 ϭ1 x 2 Ϫ x2
with the same mean might differ very much in how N i
closely the measurements are concentrated around the
mean. The most common measure of variation around Because the variance is in squared units (square centime-
the center is the variance, which is defined as the aver- ters, for example), it is common to take the square root
age squared deviation of the observations from the of the variance, which then has the same units as the
mean, or measurement itself. This square-root measure of variation
is called the standard deviation of the distribution:
variance ϭ s2

ϭ (x1 Ϫ x)2(x2 Ϫ x)2 ϩ иии ϩ (xN Ϫ x)2 standard deviation ϭ s ϭ √variance ϭ √s2
N

ϭ 1 ͚ (xi Ϫ x )2 The data for sex-comb teeth in Table 20-3 can be used
N to exemplify these calculations:

When more than one individual has the same measured sT2 ϭ (11 Ϫ 13.7)2 ϩ (12 Ϫ 13.7)2 ϩ (12 Ϫ 13.7)2
value, the variance can be written as 20

s2 ϭ f1(x1 Ϫ x)2 ϩ f2(x2 Ϫ x)2 ϩ и и и ϩ fk(xk Ϫ x)2 ϩ и и и ϩ (15 Ϫ 13.7)2 ϩ (16 Ϫ 13.7)2
ϭ ͚ fi(xi Ϫ x)2
20

To avoid subtracting every value of x separately from ϭ 34.20 ϭ 1.71
20


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670 Chapter 20 • Quantitative Genetics

We can also use the computing formula that avoids tak- 14.0
ing individual deviations:
13.5
sT2 ϭ 1 ͚T 2 Ϫ T 2 ϭ 3788 Ϫ 187.69 ϭ 1.71
N i 20 13.0

and Length, M2 (mm)12.5

s ϭ √1.71 ϭ 1.308 12.0

Figure 20-19 shows two distributions having the same Body length (mm)11.5
mean but different standard deviations (curves A and B)
and two distributions having the same standard devia- 11.0
tion but different means (curves A and C).
10.5
The mean and the variance of a distribution do not
describe it completely. They do not distinguish a sym- 10.0
metrical distribution from an asymmetrical one, for ex-
ample. There are even symmetrical distributions that 9.5
have the same mean and variance but still have some-
what different shapes. Nevertheless, for the purposes of 9.0
dealing with most quantitative genetic problems, the 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0
mean and variance suffice to characterize a distribution. Length, M1 (mm)
(a)
Measures of relationship
1400
Covariance and correlation Another statistical notion
that is of use in the study of quantitative genetics is the 1300
association, or correlation, between variables. As a result
of complex paths of causation, many variables in nature 1200
vary together but in an imperfect or approximate way.
Figure 20-20a provides an example, showing the lengths 1100
of two particular teeth in several individual specimens of
a fossil mammal, Phenacodus primaevis. There is a rough 1000
trend such that individuals with longer first molars tend
to have longer second molars, but there is considerable 900
scatter of data points around this trend. In contrast, Fig-
ure 20-20b shows that the body length and tail length 800
in individual snakes (Lampropeltis polyzona) are quite
closely related to each other, with all the points falling 700
close to a straight line that could be drawn through them
from the lower left of the graph to the upper right. 600

0.45 500

0.40 A C 400
0.35 x–= 0 x–= 1
s =1 300
0.30 s =1
200
0.25 x–B= 0 20 40 60 80 100 120 140 160 180 200
y s =2 Tail length (mm)
(b)
0.20
0.15 Figure 20-20 Scatter diagrams of relations between pairs of
variables. (a) Relation between the lengths of the first and
0.10 second lower molars (M1 and M2) in the extinct mammal
Phenacodus primaevis. Each point gives the M1 and M2
0.05 measurements for one individual. (b) Tail length and body
length of 18 Lampropeltis polyzona snakes. [Image: Negative
0.00
– 4.0 –3.0 –2.0 –1.0 0 1.0 2.0 3.0 4.0 no. 2430, Phenacodus, painting by Charles Knight; courtesy of
Department of Library Services, American Museum of Natural History.
x Photograph: Animals Animals/Copyright Zig Leszczynski.]

Figure 20-19 Three distribution functions, two of which have
the same mean (A and B) and two of which have the same
standard deviation (B and C).


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Statistical appendix 671

The usual measure of the precision of a relation be- Table 20-3, the correlation between left and right legs is:
tween two variables x and y is the correlation coefficient
(rxy). It is calculated in part from the product of the de- rxy ϭ cov xy ϭ Ϫ0.1325 ϭ Ϫ0.1360
viation of each observation of x from the mean of the x
values and the deviation of each observation of y from √s2x s2y √(0.8275)(1.1475)
the mean of the y values — a quantity called the covari-
ance of x and y (cov xy): a very small value. It is important to notice, however,
that sometimes when there is no linear relation between
cov xy ϭ (x1 Ϫ x)(y1 Ϫ y) ϩ (x2 Ϫ x)(y2 Ϫ y) ϩ иии two variables, but there is a regular nonlinear relation be-
N tween them, one variable may be perfectly predicted
from the other. Consider, for example, the parabola
ϩ (xN Ϫ x)(yN Ϫ y) shown in Figure 20-21. The values of y are perfectly pre-
dictable from the values of x; yet rxy ϭ 0, because, on av-
N erage over the whole range of x values, larger x values
are not associated with either larger or smaller y values.
ϭ 1 ͚ (xi Ϫ x)(yi Ϫ y)
N

A formula that is exactly algebraically equivalent Correlation and equality It is important to notice that
but that makes computation easier is: correlation between two sets of numbers is not the same
as numerical identity. For example, two sets of values
΂ ΃cov xy ϭ 1 can be perfectly correlated, even though the values in
N ͚ xi yi Ϫ xy one set are very much larger than the values in the other
set. Consider the following pairs of values:
By using this formula, we can calculate the covariance
between the right (x) and the left (y) leg counts in xy
Table 20-3. 1 22
2 24
΂ ΃cov xy ϭ 1 3 26
N ͚ xy Ϫ xy
The variables x and y in the pairs are perfectly correlated
ϭ (6)(5) ϩ (6)(6) ϩ иии ϩ (8)(8) ϩ (7)(9) (r ϭ 1.0), although each value of y is about 20 units
20 greater than the corresponding value of x. Two variables
are perfectly correlated if, for a unit increase in one,
Ϫ (6.65)(7.05) there is a constant increase in the other (or a constant
decrease if r is negative).
ϭ Ϫ0.1325
The importance of the difference between correla-
The correlation, rxy, is defined as: tion and identity arises when we consider the effect of
environment on heritable characters. Parents and off-
correlation ϭ rxy ϭ cov xy spring might be perfectly correlated in some character
sx sy
y
In the formula for correlation, the products of the
x
deviations are divided by the product of the standard
Figure 20-21 A parabola. Each value of y is perfectly
deviations of x and y (sx and sy). This normalization by predictable from the value of x, but there is no linear
the standard deviations has the effect of making rxy a di- correlation.
mensionless number that is independent of the units in

which x and y are measured. So defined, rxy will vary
from Ϫ1, which signifies a perfectly linear negative rela-
tion between x and y, to ϩ1, which indicates a perfectly
linear positive relation between x and y. If rxy ϭ 0, there
is no linear relation between the variables. Intermediate

values between 0 and ϩ1 or Ϫ1 indicate intermediate
degrees of relation between the variables. The data in

Figure 20-20a and b have rxy values of 0.82 and 0.99, re-
spectively. In the example of the sex-comb teeth of


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672 Chapter 20 • Quantitative Genetics

such as height, yet, because of an environmental differ- y
ence between generations, every child might be taller
than its parents. This phenomenon appears in adoption y = 0.5x+3
studies, in which children may be correlated with their
biological parents but, on the average, may be quite dif- ∆y ∆y
ferent from the parents as a result of a change in their
social situation. 2 (x–, y–) ∆y
2
Covariance and the variance of a sum In Table 20-3, Slope = 4
the variances of the left and right legs are 0.8275 and
1.1475, which adds up to 1.975, but the variance of the 4
sum of the two legs T is only 1.71. That is, the variance
of the whole is less than the sum of the variances of the y intercept = 3
parts. This discrepancy is a consequence of the negative
correlation between left and right sides. Larger left sides x
are associated with smaller right sides and vice versa,
and so the sum of the two sides varies less than each side Figure 20-22 A scatter diagram showing the relation between
separately. If, on the other hand, there were a positive two variables, x and y, with the regression line of y on x.
correlation between sides, then larger left and right sides This line, with a slope of 42, minimizes the squares of the
would go together and the variation of the sum of the deviations (⌬y).
two sides would be larger than the sum of the two sepa-
rate variances. In general, if x ϩ y ϭ T, then bϭ cov xy
sx2
s2T ϭ s2x ϩ sy2 ϩ 2 cov xy
and if a is then calculated from
For the data of Table 20-3,
a ϭ y Ϫ bx
sT2 ϭ 1.71 ϭ 0.8275 ϩ 1.1475 Ϫ 2(0.1325)
so that the line passes through the point x, y, then these
Regression The correlation coefficient provides us with values of b and a will yield the linear equation of the
only an estimate of the precision of relation between two least-squares regression line.
variables. A related problem is predicting the value of
one variable given the value of the other. If x increases Note that the preceding prediction equation cannot
by two units, by how much will y increase? If the two predict y exactly for a given x, because there is scatter
variables are linearly related, then that relation can be around the least-squares regression line. The equation
expressed as predicts the average y for a given x if large enough sam-
ples are taken.
y ϭ bx ϩ a
Samples and populations The preceding sections have
where b is the slope of the line relating y to x and a is described the distributions of, and some statistics for, par-
the y intercept of that line. ticular assemblages of individuals that have been col-
lected in some experiments or sets of observations. For
Figure 20-22 shows a scatter diagram of points for some purposes, however, we are not really interested in
two variables, y and x, together with a straight line ex- the particular 100 undergraduates or 18 snakes that have
pressing the general linear trend of y with increasing x. been measured. Instead, we are interested in the wider
This line, called the regression line of y on x, has been world of phenomena of which those particular individu-
positioned so that the deviations of the points from the als are representative. For example, we might want to
line are as small as possible. Specifically, if ⌬y is the dis- know the average height, in general, of male undergradu-
tance of any point from the line in the y direction, then ates in the United States. That is, we are interested in the
the line has been chosen so that the sum of (⌬y)2 equals characteristics of a universe, of which our small collec-
a minimum. Any other straight line passed through the tion of observations is only a sample. The characteristics
points on the scatter diagram will have a larger total of any particular sample are not identical with those of
squared deviation of the points from it. the universe but vary from sample to sample.

Obviously, we cannot find this least-squares regres- We can use the sample mean to estimate the true
sion line by trial and error. It turns out, however, that, if mean of the universe, but the sample variance and
slope b of the line is calculated by covariance will be on the average a little smaller than


44200_20_p643-678 3/23/04 3:43 PM Page 673

Key questions revisited 673

the true value in the universe. That is because the devia- squared deviations by N Ϫ 1 instead of N in the first
tions from the sample mean are not all independent of place, so
one another. In fact, by definition, the sum of all the de-
viations of the observations from the mean is 0! (Try to N 1
prove it as an exercise.) Therefore, if we are told N Ϫ 1 NϪ1 N
of the deviations from the mean in a sample of N obser- ΂ ΃ ΂ ΃N
vations, we can calculate the missing deviation, because NϪ1
all the deviations must add up to zero. s2 ϭ ͚ (xi Ϫ x)2

It is simple to correct for this bias in our estimate of ϭ 1 ͚ (xi Ϫ x)2
variance. Whenever we are interested in the variance of NϪ1
a set of measurements — not as a characteristic of the
particular sample but as an estimate of a universe that All these considerations about bias also apply to the
the sample represents — then the appropriate quantity sample covariance. In the preceding formula for the cor-
to use, rather than s2 itself, is [N/(N Ϫ 1)]s2. Note that relation coefficient, however, the factor N/(N Ϫ 1)
this new quantity is equivalent to dividing the sum of would appear in both the numerator and the denomina-
tor and therefore cancel out, and so we can ignore it for
the purposes of computation.

KEY QUESTIONS REVISITED gous lines of individuals in a few generations, or by
cloning techniques. The genetically identical individu-
• Is the observed variation in a character influenced at als are then allowed to develop in a set of controlled
all by genetic variation? Are there alleles segregating environments differing by some identifiable environ-
in the population that produce some differential mental variable, and the phenotype in each environment
effect on the character or is all the variation simply is measured. These measurements, when plotted against
the result of environmental variation and the environmental variable, give the norm of reaction of
developmental noise (see Chapter 1)? the genotype.

One form of evidence that the observed phenotypic • How important is genetic variation as a source of total
variation is influenced by genotype comes from the re- phenotypic variation? Are the norms of reaction and
sults of studies of related individuals. If close relatives re- the environments such that nearly all the variation is a
semble one another more than distant relatives or than consequence of environmental difference and
unrelated individuals this resemblance is evidence of ge- developmental instabilities or does genetic variation
netic effects on variation only if the groups being com- predominate?
pared have developed and are living in the same envi-
ronment. Otherwise, it is not possible to distinguish To obtain a quantitative estimate of the amount of varia-
genetic similarity from environmental similarity. An- tion in a population that is associated with genetic differ-
other form of evidence can be obtained by comparing ences, environmental differences, and developmental in-
individuals with known alternative genotypes for one or stabilities, it is necessary to carry out a heritability study.
more well-defined genes. If there is an association be- One form of such a study is to measure the character in
tween the marker genotype and the phenotypic charac- groups of individuals that differ by a known amount in
ter, then there is evidence for a genetic component to their degree of genetic relationship, as, for example, com-
the phenotypic variation. The marker gene may be one paring the similarity of identical twin and nonidentical
that is thought to take part in the development of the twins or sibs and half-sibs. The heritability can then be
character or it may simply be a functionally unrelated estimated by comparing the observed difference in simi-
marker that happens to lie near a relevant functional larity between individuals with the amount predicted
gene on the chromosome. Again, the environments must from their degree of relationship. This comparison is only
be the same for the different genotypes in order to dis- valid if the different relationship groups have developed
tinguish genetic from environmental causes of similarity. in the same environment. A second method is to deter-
mine the realized heritability of a characteristic by a se-
• If there is genetic variation, what are the norms of lection experiment. A population is selected to change
reaction of the various genotypes? the character measurement by producing offspring from
a group of selected parents. The amount of measured dif-
To carry out norm of reaction studies, it is necessary to ference between the selected parents and the unselected
have many individuals of the same genotype. They can population (selection differential) is then compared with
be produced by a long succession of matings between
close relatives (inbreeding), by crosses involving ge-
netic markers that allow the production of homozy-


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674 Chapter 20 • Quantitative Genetics

the amount of difference between the offspring and the An estimate of the number of loci that influence the ob-
unselected parents (realized selection progress). If there served variation in a character is made from the results
is no selection progress, the heritability is zero. If the se- of linkage studies with known genetic markers distrib-
lection progress is equal to the selection differential, the uted across the genome. If a detectable proportion of the
heritability is unity. differences between individuals in the quantitative char-
acter segregates together with the allelic differences at a
• Do many loci (or only a few) vary with respect to the marker gene, then a quantitative trait locus (QTL) has
character? How are they distributed over the been detected near the marker gene.
genome?

SUMMARY very difficult to determine whether a particular trait is
heritable. Norm of reaction studies show only small dif-
Many — perhaps most — of the phenotypic traits that we ferences between genotypes, and these differences are
observe in organisms vary continuously. In many cases, not consistent over a wide range of environments. Thus,
the variation of the trait is determined by more than a “superior” genotypes in domesticated animals and culti-
single segregating locus. Each of these loci may con- vated plants may be superior only in certain environ-
tribute equally to a particular phenotype, but it is more ments. If it should turn out that humans exhibit genetic
likely that they contribute unequally. The measurement variation for various mental and emotional traits, this
of these phenotypes and the determination of the con- variation is unlikely to favor one genotype over another
tributions of specific alleles to the distribution must be across a range of environments.
made on a statistical basis in these cases. Some of these
variations of phenotype (such as height in some plants) The attempt to quantify the influence of genes on a
may show a normal distribution around a mean value; particular trait has led to the determination of heritabil-
others (such as seed weight in some plants) will illus- ity in the broad sense (H2). In general, the heritability of
trate a skewed distribution around a mean value. a trait is different in each population and each set of en-
vironments, and so heritability cannot be extrapolated
A quantitative character is one for which the aver- from one population and set of environments to another.
age phenotypic differences between genotypes are small Because H2 characterizes present populations in present
compared with the variation between the individuals environments only, it is fundamentally flawed as a pre-
within the genotypes. This situation may be true even dictive device. Heritability in the narrow sense (h2) mea-
for characters that are influenced by alleles at one locus. sures the proportion of phenotypic variation that results
The distribution of environments is reflected biologically from substituting one allele for another. This quantity,
as a distribution of phenotypes. The transformation of if large, predicts that selection for a trait will succeed
environmental distribution into phenotypic distribution rapidly. If h2 is small, special forms of selection are
is determined by the norm of reaction. Norms of reac- required.
tion can be characterized in organisms in which large
numbers of genetically identical individuals can be pro- With the use of genetically marked chromosomes, it
duced. Traits are familial if they are common to mem- is possible to determine the relative contributions of dif-
bers of the same family, for whatever reason. Traits are ferent chromosomes to variation in a quantitative trait,
heritable, however, only if the similarity arises from to observe dominance and epistasis from whole chromo-
common genotypes. In experimental organisms, environ- somes, and, in some cases, to map genes that are segre-
mental similarities may be readily distinguished from ge- gating for a trait.
netic similarities, or heritability. In humans, however, it is

KEY TERMS candidate gene (p. 664) distribution function (p. 647)
central tendency (p. 648) dominance variance (p. 661)
additive effect (p. 660) correlation (p. 648, 670) environmental variance (p. 656)
additive genetic correlation coefficient (p. 671) familial (p. 655)
covariance (p. 671) family selection (p. 664)
variation (p. 661) dispersion (p. 648) frequency histogram (p. 647)
analysis of variance (p. 657)
bimodal distribution (p. 668)
broad heritability (H2) (p. 657)


44200_20_p643-678 3/23/04 3:43 PM Page 675

Solved problems 675

genetic correlation (p. 657) midparent value (p. 661) relative frequency (p. 668)
genetic variance (p. 656) mode (p. 648) sample (p. 672)
heritability in the narrow multiple-factor hypothesis (p. 650) segregating line (p. 652)
norm of reaction (p. 651) selection differential (p. 662)
sense (h2) (p. 661) phenotypic correlation (p. 658) selection response (p. 662)
heritable (p. 654) quantitative genetics (p. 647) standard deviation (p. 669)
hybrid – inbred method (p. 664) quantitative trait locus statistical distribution (p. 647)
inbreeding (p. 650) truncation selection (p. 663)
least-squares regression line (p. 672) (QTL) (p. 665) universe (p. 672)
marker gene (p. 664) regression line of y on x (p. 672) variance (p. 648, also 669)
mean (p. 648, 668) relation (p. 648)

SOLVED PROBLEMS a. To determine whether there is any genetic difference
underlying the observed phenotypic difference in dialect
1. In some species of songbirds, populations living in between the populations, we need to raise birds of each
different geographical regions sing different “local di- population, from the egg, in the absence of auditory in-
alects” of the species song. Some people believe that put from their own ancestors and in various combina-
this difference in dialect is the result of genetic tions of auditory environments of other populations. We
differences between populations, whereas others can do so by raising birds from the egg that have been
believe that these differences arose from purely indi- grouped as follows:
vidual idiosyncracies in the founders of these popula-
tions and have been passed on from generation (1) In isolation
to generation by learning. Outline an experimental
program that would determine the importance of (2) Surrounded by hatchlings consisting only of birds
genetic and nongenetic factors and their interaction derived from the same population
in this dialect variation. If there is evidence of ge-
netic difference, what experiments could be done to (3) Surrounded by hatchlings consisting of birds de-
provide a detailed description of the genetic system, rived from other populations
including the number of segregating genes, their link-
age relations, and their additive and nonadditive phe- (4) In the presence of singing adults from other popu-
notypic effects? lations

Solution (5) In the presence of singing adults from their own
population (as a control on the rearing conditions)
This example has been chosen because it illustrates the
very considerable experimental difficulties that arise If there are no genotypic differences and all dialect dif-
when we try to examine claims that observed differ- ferences are learned, then birds from group 5 will sing
ences in quantitative characters in some species have a their population dialect and those from group 4 will sing
genetic basis. To be able to say anything at all about the the foreign dialect. Groups 1, 2, and 3 may not sing at
roles of genes and developmental environment requires, all; they may sing a generalized song not corresponding
at minimum, that the organisms can be raised from fer- to any of the dialects; or they may all sing the same song
tilized eggs in a controlled laboratory environment. To dialect — this dialect would then represent the “intrinsic”
be able to make more detailed statements about the developmental program unmodified by learning.
genotypes underlying variation in the character requires,
further, that the results of crosses between parents of If dialect differences are totally determined by ge-
known phenotype and known ancestry be observable netic differences, birds from groups 4 and 5 will sing the
and that the offspring of some of those crosses be, in same dialect, that of their parents. Birds from groups 1,
turn, crossed with other individuals of known phenotype 2, and 3, if they sing at all, will each sing the song dialect
and ancestry. Very few animal species can satisfy this re- of their parent population, irrespective of the other
quirement, although it is much easier to carry out con- birds in their group. There are then the possibilities of
trolled crosses in plants. We will assume that the song- less-clear-cut results, indicating that both genetic and
bird species in question can indeed be raised and crossed learned differences influence the trait. For example,
in captivity, but that is a big assumption. birds in group 4 might sing a song with both population
elements. Note that, if the birds in the control group 5
do not sing their normal dialect, the rest of the results


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676 Chapter 20 • Quantitative Genetics

are uninterpretable, because the conditions of artificial 6.1. Estimate the broad heritability of bean weight in
rearing are interfering with the normal developmental the F2 population of this experiment.
program.
Solution
b. If the results of the first experiments show some her-
itability in the broad sense, then a further analysis is The key here is to recognize that all the variance in the
possible. This analysis requires a genetically segregating F1 population must be environmental because all indi-
population, made from a cross between two dialect viduals must be of identical genotype. Furthermore, the
populations — say, A and B. A cross between males F2 variance must be a combination of environmental and
from population A and females from population B and genetic components, because all the genes that are het-
the reciprocal cross will give an estimate of the average erozygous in the F1 will segregate in the F2 to give an ar-
degree of dominance of genes influencing the trait and ray of different genotypes that relate to bean weight.
whether there is any sex linkage. (Remember that, in Hence, we can estimate
birds, the female is the heterogametic sex.) The off-
spring of this cross and all subsequent crosses must be s2e ϭ 1.5
raised in conditions that do not confuse the learned
and the genetic components of the differences, as re- se2 ϩ sg2 ϭ 6.1
vealed in the experiments in part a. If learned effects
cannot be separated out, this further genetic analysis is Therefore
impossible.
sg2 ϭ 6.1 Ϫ 1.5 ϭ 4.6
c. To localize genes influencing dialect differences would
require a large number of segregating genetic markers. and broad heritability is
These markers could be morphological mutants or mo-
lecular variants such as restriction-site polymorphisms. H2 ϭ 4.6 ϭ 0.75 (75%)
Families segregating for the quantitative trait differences 6.1
would be examined to see if there were cosegregation of
any of the marker loci with the quantitative trait. These 3. In an experimental population of Tribolium (flour
cosegregated loci would then be candidates for loci beetles), the body length shows a continuous distri-
linked to the quantitative trait loci. Further crosses be- bution with a mean of 6 mm. A group of males and
tween individuals with and without mutant markers and females with body lengths of 9 mm are removed and
measure of the quantitative trait values in F2 individuals interbred. The body lengths of their offspring average
would establish whether there was actual linkage be- 7.2 mm. From these data, calculate the heritability in
tween the marker and the quantitative trait loci. In prac- the narrow sense for body length in this population.
tice, it is very unlikely that such experiments could be
carried out on a songbird species, because of the im- Solution
mense time and effort required to establish lines carry-
ing the large number of different marker genes and mo- The selection differential is 9 Ϫ 6 ϭ 3 mm, and the se-
lecular polymorphisms. lection response is 7.2 Ϫ 6 ϭ 1.2 mm. Therefore, the
heritability in the narrow sense is:
2. Two inbred lines of beans are intercrossed. In the F1,
the variance in bean weight is measured at 1.5. The h2 ϭ 1.2 ϭ 0.4 (40%)
F1 is selfed; in the F2, the variance in bean weight is 3

PROBLEMS Bristle number Number of
individuals
BASIC PROBLEMS 1
1. Distinguish between continuous and discontinuous 2 1
3 4
variation in a population, and give some examples of 4 7
each. 5 31
6 56
2. The table at the right shows a distribution of bristle 7 17
number in Drosophila. Calculate the mean, variance, 4
and standard deviation of this distribution.


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Problems 677

3. A book on the problem of heritability of IQ makes mean fat content can be expected in the descen-
the following three statements. Discuss the validity dants of these animals?
of each statement and its implications about the au-
thors’ understanding of h2 and H2. 6. Suppose that two triple heterozygotes A/a ; B/b ;
C/c are crossed. Assume that the three loci are in
a. “The interesting question then is . . . ‘How her- different chromosomes.
itable?’ The answer [0.01] has a very different theo-
retical and practical application from the answer a. What proportions of the offspring are homozy-
[0.99].” (The authors are talking about H2.) gous at one, two, and three loci, respectively?

b. “As a rule of thumb, when education is at issue, b. What proportions of the offspring carry 0, 1, 2, 3,
H2 is usually the more relevant coefficient, and, 4, 5, and 6 alleles (represented by capital letters),
when eugenics and dysgenics (reproduction of se- respectively?
lected individuals) are being discussed, h2 is ordinar-
ily what is called for.” 7. In Problem 6, suppose that the average phenotypic
effect of the three genotypes at the A locus is A/A ϭ
c. “But whether the different ability patterns derive 4, A/a ϭ 3, and a/a ϭ 1 and that similar effects exist
from differences in genes . . . is not relevant to as- for the B and C loci. Moreover, suppose that the ef-
sessing discrimination in hiring. Where it could be fects of loci add to each other. Calculate and graph
relevant is in deciding what, in the long run, might the distribution of phenotypes in the population (as-
be done to change the situation.” suming no environmental variance).

(From J. C. Loehlin, G. Lindzey, and J. N. Spuhler, Race 8. In Problem 7, suppose that there is a threshold in
Differences in Intelligence. Copyright 1975 by W. H. Free- the phenotypic character so that, when the pheno-
man and Company.) typic value is above 9, an individual Drosophila has
three bristles; when it is between 5 and 9, the indi-
4. Using the concepts of norms of reaction, environ- vidual has two bristles; and when the value is 4 or
mental distribution, genotypic distribution, and phe- less, the individual has one bristle. Describe the out-
notypic distribution, try to restate the following come of crosses within and between bristle classes.
statement in more exact terms: “80 percent of the Given the result, could you infer the underlying ge-
difference in IQ performance between the two netic situation?
groups is genetic.” What would it mean to talk about
the heritability of a difference between two groups? 9. Suppose that the general form of a distribution of a
trait for a given genotype is:

CHALLENGING PROBLEMS fϭ1Ϫ (x Ϫ x)2
se2
5. In a large herd of cattle, three different characters
showing continuous distribution are measured, and over the range of x where f is positive.
the variances in the following table are calculated:
a. On the same scale, plot the distributions for three
Characters genotypes with the following means and environ-
mental variances:
Shank Neck Fat
Variance length length content Approximate range
se2 of phenotype
Phenotypic 310.2 730.4 106.0 Genotype x
Environmental 248.1 292.2 53.0
Additive genetic 42.4 1 0.20 0.3 x ϭ 0.03 to x ϭ 0.37
Dominance genetic 46.5 73.0 10.6 2 0.22 0.1 x ϭ 0.12 to x ϭ 0.24
15.6 365.2 3 0.24 0.2 x ϭ 0.10 to x ϭ 0.38

a. Calculate the broad- and narrow-sense heritabili- b. Plot the phenotypic distribution that would re-
ties for each character. sult if the three genotypes were equally frequent in
a population. Can you see distinct modes? If so,
b. In the population of animals studied, which char- what are they?
acter would respond best to selection? Why?
10. The following sets of hypothetical data represent
c. A project is undertaken to decrease mean fat con- paired observations on two variables (x, y). Plot each
tent in the herd. The mean fat content is currently set of data pairs as a scatter diagram. Look at the
10.5 percent. Animals of 6.5 percent fat content are plot of the points, and make an intuitive guess about
interbred as parents of the next generation. What


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678 Chapter 20 • Quantitative Genetics

the correlation between x and y. Then calculate the Son’s height (inches)d. An increase in temperature variance changes a
correlation coefficient for each set of data pairs, and unimodal into a bimodal phenotypic distribution
compare this value with your estimate. (one norm of reaction is sufficient here).
14. Francis Galton compared the heights of male under-
a. (1, 1); (2, 2); (3, 3); (4, 4); (5, 5); (6, 6). graduates with the heights of their fathers, with the
results shown in the following graph.
b. (1, 2); (2, 1); (3, 4); (4, 3); (5, 6); (6, 5).
76
c. (1, 3); (2, 1); (3, 2); (4, 6); (5, 4); (6, 5).
74
d. (1, 5); (2, 3); (3, 1); (4, 6); (5, 4); (6, 2).
72
11. Describe an experimental protocol for studies of rel-
atives that could estimate the broad heritability of 70
alcoholism. Remember that you must make an ade-
quate observational definition of the trait itself. 68

12. A line selected for high bristle number in Drosophila 66
has a mean of 25 sternopleural bristles, whereas a
low-selected line has a mean of only 2. Marker 64
stocks involving the two large autosomes II and III
are used to create stocks with various mixtures of 62
chromosomes from the high (h) and low (l) lines. 62 64 66 68 70 72 74 76
The mean number of bristles for each chromosomal Father’s height (inches)
combination is as follows:
The average height of all fathers is the same as
h h 25.1 h h 22.2 l h 19.0 the average height of all sons, but the individual
h h l h l h height classes are not equal across generations. The
very tall fathers had somewhat shorter sons, whereas
h h 23.0 h h 19.9 l h 14.7 the very short fathers had somewhat taller sons. As a
h l l l l l result, the best line that can be drawn through the
points on the scatter diagram has a slope of about
h l 11.8 h l 9.1 l l 2.3 0.67 (solid line) rather than 1.00 (dashed line). Gal-
h l l l l l ton used the term regression to describe this ten-
dency for the phenotype of the sons to be closer
What conclusions can you reach about the distribu- than the phenotype of their fathers to the popula-
tion of genetic factors and their actions from these tion mean.
data? a. Propose an explanation for this regression.
b. How are regression and heritability related here?
13. Suppose that number of eye facets is measured in a (Graph after W. F. Bodmer and L. L. Cavalli-Sforza, Genet-
population of Drosophila under various temperature ics, Evolution, and Man. Copyright 1976 by W. H. Freeman
conditions. Further suppose that it is possible to es- and Company.)
timate total genetic variance (s2g) as well as the phe-
notypic distribution. Finally, suppose that there are
only two genotypes in the population. Draw pairs of
norms of reaction that would lead to the following
results:

a. An increase in mean temperature decreases the
phenotypic variance.

b. An increase in mean temperature increases H 2.

c. An increase in mean temperature increases sg2 but
decreases H 2.


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21

EVOLUTIONARY GENETICS

Charles Darwin. [Corbis/Bettmann.] KEY QUESTIONS

• What are the basic principles of the
Darwinian mechanism of evolution?

• What are the roles of natural selection and
other processes in evolution and how do
they interact with one another?

• How do different species arise?

• How different are the genomes of different
kinds of organisms?

• How do evolutionary novelties arise?

OUTLINE

21.1 A synthesis of forces:
variation and divergence of populations

21.2 Multiple adaptive peaks
21.3 Heritability of variation
21.4 Observed variation within

and between populations
21.5 The process of speciation
21.6 Origin of new genes
21.7 Rate of molecular evolution
21.8 Genetic evidence

of common ancestry in evolution
21.9 Comparative genomics and proteomics

679


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680 Chapter 21 • Evolutionary Genetics

CHAPTER OVERVIEW evolved, but that is certainly not the case. Most scholars
had abandoned the notion of fixed species, unchanged
The modern theory of evolution is so completely since their origin in a grand creation of life, long before
identified with the name of Charles Darwin publication of Darwin’s Origin of Species in 1859. By
(1809 – 1882) that many people think that it was Dar- that time, most biologists agreed that new species arise
win who first proposed the concept that organisms have through some process of evolution from older species;

CHAPTER OVERVIEW Figure

Figure 21-1 Overview of Population of original species
the processes leading to
evolution within populations, AB /AB AB /AB
the divergence of populations
from one another, and the AB /AB
formation of new species.
AB /AB

Variation due to
mutation
duplication
recombination

AB /AB AB /AB
aB /AB Ab /AB

A B B´ / A B ab /AB

Founder effect Geographical split of population Founder effect

AB /AB AB /AB AB /AB AB /AB

Ab /AB aB /AB aB /AB

A B B´/ A B ab /AB

Selection in local environment and genetic drift

AB /AB aB /aB aB /Ab
AB /AB
aB /aB
A B B´ / A B aB /aB
A B B´ / A B

Migration

AB /AB Ab /AB A B B´ / a B aB /AB
aB /aB aB /aB
A B B´ / A B aB /AB

A B B´/ A B

Further divergence due to selection and drift

A B B´ / A b B´ Reproductive isolation aB /aB aB /aB
A B B´ / A B B´ ab /aB aB /aB

A B B´ / A B B´ New species 2

New species 1


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Chapter overview 681

the problem was to explain how this evolution could Clearly, a selective process can produce change
occur. in the population composition only if there are some
variations among which to select. If all individuals are
Darwin provided a detailed explanation of the identical, no amount of differential reproduction of indi-
mechanism of the evolutionary process. Darwin’s theory viduals will alter the composition of the population.
of the mechanism of evolution begins with the variation Furthermore, the variation must be in some part herita-
that exists among organisms within a species. Individuals ble if differential reproduction is to alter the popula-
of one generation are qualitatively different from one tion’s genetic composition. If large animals within a
another. Evolution of the species as a whole results from population have more offspring than do small ones but
the fact that the various types differ in their rates of sur- their offspring are no larger on average than those of
vival and reproduction, and so the relative frequencies of small animals, then there will be no change in popula-
the types change over time. Evolution, in this view, is a tion composition from one generation to another. Fi-
sorting process. nally, if all variant types leave, on average, the same
number of offspring, then we can expect the population
For Darwin, evolution of the group resulted from to remain unchanged.
the differential survival and reproduction of individual
variants already existing in the group — variants arising MESSAGE Darwin’s principles of variation, heredity, and
in a way unrelated to the environment but whose sur- selection must hold true if there is to be evolution by a
vival and reproduction do depend on the environment variational mechanism.
(Figure 21-1).
The Darwinian explanation of evolution must be
MESSAGE Darwin proposed a new explanation to account able to account for two different aspects of the history
for the accepted phenomenon of evolution. He argued that of life. One is the successive change of form and func-
the population of a given species at a given time includes tion that occurs in a single continuous line of descent,
individuals of varying characteristics. The population of the phyletic evolution. Figure 21-2 shows such a continuous
next generation will contain a higher frequency of those types change over a period of 40 million years in the size and
that most successfully survive and reproduce under the curvature of the left shell of the oyster, Gryphea. The
existing environmental conditions. Thus, the frequencies of other is the diversification that occurs among species: in
various types within the species will change over time. the history of life on earth, there have existed many dif-
ferent contemporaneous species having quite different
There is an obvious similarity between the process forms and living in different ways. Figure 21-3 shows
of evolution as Darwin described it and the process by some of the variety of bivalve mollusc forms that existed
which the plant or animal breeder improves a domestic at various times in the past 300 million years. Every
stock. The plant breeder selects the highest-yielding species eventually becomes extinct and more than 99.9
plants from the current population and (as far as possi- percent of all the species that have ever existed are al-
ble) uses them as the parents of the next generation. If ready extinct, yet the number of species and the diver-
the characteristics causing the higher yield are heritable, sity of their forms and functions have increased in the
then the next generation should produce a higher yield. past billion years. Thus species not only must be chang-
It was no accident that Darwin chose the term natural ing, but must give rise to new and different species in
selection to describe his model of evolution through dif- the course of evolution.
ferential rates of reproduction of different variants in the
population. As a model for this evolutionary process, he Both these processes — phyletic evolution and diver-
had in mind the selection that breeders exercise on suc- sification — are the consequences of heritable variation
cessive generations of domestic plants and animals. within populations. Heritable variation provides the raw
material for successive changes within a species and for
We can summarize Darwin’s theory of evolution the multiplication of new species. The basic mechanisms
through natural selection in three principles: of those changes (as discussed in Chapter 19) are the
origin of new variation by mutation and chromosomal
1. Principle of variation. Among individuals within any rearrangements, the change in frequency of alleles
population, there is variation in morphology, within populations by selective and random processes,
physiology, and behavior. the divergence of different populations because the se-
lective forces are different or because of random drift,
2. Principle of heredity. Offspring resemble their parents and the reduction of variation between populations
more than they resemble unrelated individuals. by migration. From those basic mechanisms, a set of

3. Principle of selection. Some forms are more successful
at surviving and reproducing than other forms in a
given environment.


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682 Chapter 21 • Evolutionary Genetics

G. gigantea ϫ3

Martesia ovalis (Say). Exogyra arietina Roemer.
Shell and shell in tube. Late Cretaceous
Miocene
Gryphaea arcuata
ϫ 1.5 Lamarci. Early Jurassic

ϫ 0.5 ϫ 0.5 ϫ 0.5

Exogyra ponderosa Roemer. Venericardia planicosta Lamarck. Myalina subquadrata
Late Cretaceous
Eocene Shumard

Figure 21-3 A variety of bivalve mollusc shell forms that have
appeared in the past 300 million years of evolution. [After C. L.

Fenton and M. A. Fenton, The Fossil Book. Doubleday, 1958.]

G. mccullochii 21.1 A synthesis of forces:
variation and divergence
G. arcuata incurva of populations

G. arcuata obliquata When Darwin arrived in the Galapagos Islands in 1835,
he found a remarkable group of finchlike birds that pro-
Figure 21-2 Changes in shell size and curvature in the bivalve vided a very suggestive case for the development of his
mollusc Gryphaea in the course of its phyletic evolution in the theory of evolution. The Galapagos archipelago is a clus-
early Jurassic. Only the left shell is shown. In each case, the ter of 29 islands and islets of different sizes lying on the
shell back and a longitudinal section through it are illustrated. equator about 600 miles off the coast of Ecuador.
Finches are generally ground-feeding seed eaters with
[After A. Hallam, “Morphology, Palaeoecology and Evolution of the stout bills for cracking the tough outer coats of the
Genus Gryphaea in the British Lias,” Philosophical Transactions of the seeds. Figure 21-4 shows the 13 Galapagos finch species.
Royal Society of London Series B 254, 1968, 124.] The Galapagos species, though clearly finches, exhibit an
immense variation in feeding behavior and in the bill
principles governing changes in the genetic composition shape that corresponds to their food sources. For exam-
of populations can be derived. The application of these ple, the vegetarian tree finch uses its heavy bill to eat
principles of population genetics provides a detailed fruits and leaves, the insectivorous finch has a bill with a
genetic theory of evolution. biting tip for eating large insects, and, most remarkable
of all, the woodpecker finch grasps a twig in its bill and
MESSAGE Evolution, under the Darwinian scheme, is the uses it to obtain insect prey by probing holes in trees.
conversion of heritable variation between individuals within This diversity of species arose from an original popula-
populations into heritable differences between populations in tion of a seed-eating finch that arrived in the Galapagos
time and in space, by population genetic mechanisms. from the mainland of South America and populated the
islands. The descendants of the original colonizers spread
to the different islands and to different parts of large is-
lands and formed local populations that diverged from
one another and eventually formed different species.
The finches illustrate the two aspects of evolution that
need to be explained. How does one original species
with a particular set of characteristics give rise to a di-
versity of species, each with its own form and function?
How do the characteristics of species come to be so


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21.1 A synthesis of forces: variation and divergence of populations 683

Seed eaters Large-billed finches can
Bills of seed eaters are adapted crush large, hard seeds.
for harvesting and crushing seeds.
Small-billed finches cannot crush
Large ground finch large seeds as well, but are more
(Geospiza magnitrostis) adept at handling small seeds.

Medium ground finch Cactus finches are adapted
(G. fortis) to opening cactus fruits and
extracting the seeds.
Small ground finch
(G. fuliginosa) The large tree finch uses its heavy
bill to twist apart wood to reach
Sharp-billed ground finch larvae inside.
(G. difficilis) The small and medium tree finches
and mangrove finches pick insects
Large cactus finch from leaves and branches and
(G. conirostris) explore crevices for hidden prey.
The woodpecker finch uses its long
Cactus finch beak to probe into dead wood,
(G. scandens) crevices, and bark for insects.
The warbler finch uses quick
ANCESTOR FINCH Bud eater motions to capture insects on
from South American The bud eater‘s heavy bill is adapted for plant surfaces.
mainland. grasping and wrenching buds from branches.

Vegetarian finch
(Platyspiza crassirostris)

Insect eaters
The bills of insect eaters vary because they eat
different types and sizes of insects and they
capture them in different ways.

Small tree finch
(Camarhynchus parvulus)

Large tree finch
(C. psittacula)

Medium tree finch
(C. pauper)

Mangrove finch
(C. heliobates)

Woodpecker finch
(C. pallidus)

Warbler finch
(Certhidea olivacea)

Figure 21-4 The thirteen species of finches found in the Galapagos Islands. [After W. K.

Purves, G. H. Orians, and H. C. Heller, Life: The Science of Biology, 4th ed. Sinauer Associates/
W. H. Freeman and Company, 1995, Figure 20.3, p. 450.]


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684 Chapter 21 • Evolutionary Genetics

Mutation a A Mutation A a within populations prevent populations from diverging
from one another, whereas forces that make each popu-
Genetic drift Genetic drift lation homozygous cause populations to diverge. Thus,
Migration Migration random drift (or inbreeding) produces homozygosity
while causing different populations to diverge. This
Balanced polymorphism trend toward divergence and homozygosity is counter-
acted by the constant flux of mutation and the migra-
Directional selection tion of individuals between populations, both of which
introduce variation into the populations, making them
Selection against heterozygotes more alike.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Consider the situation at a genetically variable locus
with two alleles, say A and a, in frequencies p and 1 Ϫ p,
Allelic frequency of A respectively in a large population. Suppose that a group
of isolated island populations were founded by migrants
Figure 21-5 The effects on gene frequency of various forces of from that single population. The original founders of
evolution. The blue arrows show a tendency toward increased each population are small samples from the donor popu-
variation within the population; the red arrows, decreased lation and so differ from one another in allele frequen-
variation. cies because of a random sampling effect. This initial
variation is called the founder effect. In succeeding gen-
suited to the environments in which the species live? erations, random genetic drift further alters allelic fre-
These are the problems of the origin of diversity and the quencies within each population. The frequency of each
origin of adaptation. of the alleles will move toward either 1 or 0 in each
population, but average allelic frequency over all the
In evolution, the various forces of breeding struc- populations remains constant. As time goes on, the gene
ture, mutation, migration, and selection are all acting si- frequencies among the populations diverge and some
multaneously in populations. We need to consider how become fixed for one of the alleles. By the time 4N gen-
these forces, operating together, mold the genetic com- erations have gone by, 80 percent of the populations are
position of populations to produce both variation within fixed, a proportion p being homozygous A/A and pro-
local populations and differences between them. portion 1 Ϫ p being homozygous a/a. Eventually, all
populations would become fixed at A/A or a/a in these
The genetic variation within and between popula- proportions.
tions is a result of the interplay of the various evolution-
ary forces just listed (Figure 21-5). Generally, as Table The process of differentiation by inbreeding in is-
21-1 shows, forces that increase or maintain variation land populations is slow, but not on an evolutionary or
geological time scale. If an island can support, say,
10,000 individuals of a rodent species, then, after 20,000
generations (about 7000 years, assuming 3 generations
per year), the population will be homozygous for about
half of all the loci that were initially at the maximum of

TABLE 21-1 How the Forces of Evolution Increase (ϩ)
or Decrease (Ϫ) Variation Within
and Between Populations

Force Variation within Variation between
populations populations
Inbreeding or
genetic drift Ϫ ϩ
ϩ Ϫ
Mutation ϩ Ϫ
Migration
Directional Ϫ ϩ/Ϫ
ϩ Ϫ
selection Ϫ ϩ
Balancing
Incompatible


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21.2 Multiple adaptive peaks 685

heterozygosity. Moreover, the island will be differenti- irrespective of population size. For many populations,
ated from other similar islands in two ways: (1) loci that more than a single migrant individual per generation is
are fixed on that island will either still be segregating on quite likely. Human populations (even isolated tribal
many of the other islands or be fixed at a different allele populations) have a higher migration rate than this mini-
and (2) loci that are still segregating in all the islands mal value, and, as a result, no locus is known in humans
will vary in allele frequency from island to island. for which one allele is fixed in some populations and an
alternative allele is fixed in others.
Every population of every species is finite in size,
and so all populations should eventually become homo- The effects of selection are more variable than those
zygous and differentiated from one another as a result of of random genetic drift because selection may or may
inbreeding. All variation would be eliminated and evolu- not push a population toward homozygosity. Directional
tion would cease. In nature, however, new variation is al- selection pushes a population toward homozygosity, re-
ways being introduced into populations by mutation and jecting most new mutations as they are introduced but
by some migration between localities. Thus, the actual occasionally (if the mutation is advantageous) spreading
variation available for natural selection is a balance be- a new allele through the population to create a new
tween the introduction of new variation and its loss homozygous state. Whether such directional selection
through local inbreeding. Recall from Chapter 19 that promotes differentiation of populations depends on the
the rate of loss of heterozygosity in a closed population environment and on chance events. Two populations liv-
is 1/(2N) per generation, and so any effective differenti- ing in very similar environments may be kept genetically
ation between populations that occurs because of drift similar by directional selection, but, if there are environ-
will be negated if new variation is introduced at this rate mental differences, selection may direct the populations
or a higher rate. If m is the migration rate into a given toward different compositions.
population and ␮ is the rate of mutation to new alleles
per generation, then roughly (to an order of magnitude) Selection favoring heterozygotes (balancing selec-
a population will retain most of its heterozygosity and tion) will, for the most part, maintain more or less similar
will not differentiate much from other populations by polymorphisms in different populations. However, again,
local inbreeding if if the environments are different enough, then the popu-
lations will show some divergence. The opposite of bal-
mՆ 1 or 1 ancing selection is selection against heterozygotes, which
N ␮Ն N produces unstable equilibria. Such selection will cause
homozygosity and divergence between populations.
or, in other words, if
21.2 Multiple adaptive peaks
Nm Ն 1 or N␮ Ն 1
We must avoid taking an overly simplified view of the
For populations of intermediate and even fairly large consequences of selection. At the level of the gene — or
size, it is unlikely that N␮ Ն 1. For example, if the pop- even at the level of the partial phenotype — there is
ulation size is 100,000, then, to prevent loss of variation, more than one possible outcome of selection for a trait
the mutation rate must exceed 10Ϫ5, which is somewhat in a given environment. Selection to alter a trait (say, to
on the high side for known mutation rates, although it is increase size) may be successful in a number of ways. In
not an unknown rate. On the other hand, a migration 1952, F. Robertson and E. Reeve successfully selected to
rate of 10Ϫ5 per generation is not unreasonably large. change wing size in two different populations of
In fact Drosophila. However, in one case, the number of cells in
the wing changed, whereas, in the other case, the size of
mϭ number of migrants ϭ number of migrants the wing cells changed. Two different genotypes had
total population size N been selected, both causing a change in wing size. The
initial state of the population at the outset of selection
Thus, the requirement that Nm Ն 1 is equivalent to the determined which of these selections occurred.
requirement that
A simple hypothetical case illustrates how the same
Nm ϭ N ϫ number of migrants Ն1 selection can lead to different outcomes. Suppose that
N the variation of two loci (there will usually be many
more) influences a character and that (in a particular en-
or that vironment) intermediate phenotypes have the highest
fitness. (For example, newborn babies have a higher
number of migrant individuals Ն 1 chance of surviving birth if they are neither too big nor
too small.) If the alleles act in a simple way in influenc-
ing the phenotype, then the three genetic constitutions


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686 Chapter 21 • Evolutionary Genetics

AB/ab, Ab/Ab, and aB/aB will produce a high fitness be- netic composition will be — depends on whether the ini-
cause they will all be intermediate in phenotype. On the tial genetic composition of the population is on one side
other hand, very low fitness will characterize the double or the other of the dashed “fall line” shown in the figure.
homozygotes AB/AB and ab/ab. What will the result of
selection be? We can predict the result by using the MESSAGE Under identical conditions of natural selection,
mean fitness W of a population. As previously discussed, two populations may arrive at two different genetic
selection acts in most simple cases to increase W . There- compositions as a direct result of natural selection.
fore, if we calculate W for every possible combination of
gene frequencies at the two loci, we can determine It is important to note that nothing in the theory of
which combinations yield high values of W . Then we selection requires that the different adaptive peaks be of
should be able to predict the course of selection by fol- the same height. The kinetics of selection dictate only
lowing a curve of increasing W . that W increases, not that it necessarily reaches the
highest possible peak in the field of gene frequencies.
The surface of mean fitness for all possible combina- Suppose, for example, that a population is near the peak
tions of allelic frequency is called an adaptive surface or aB/aB in Figure 21-6 and that this peak is lower than
an adaptive landscape (Figure 21-6). The figure is like a the Ab/Ab peak. Selection alone cannot carry the pop-
topographic map. The frequency of allele A at one locus ulation to Ab/Ab, because that would require a tempo-
is plotted on one axis, and the frequency of allele B at rary decrease in W as the population descended the
the other locus is plotted on the other axis. The height aB/aB slope, crossed the saddle, and ascended the other
above the plane (represented by topographic lines) is slope. Thus, the force of selection is myopic. It drives the
the value of W that the population would have for a population to a local maximum of W in the field of gene
particular combination of frequencies of A and B. Ac- frequencies — not to a global one.
cording to the rule of increasing fitness, selection should
carry the population from a low-fitness “valley” to a The existence of multiple adaptive peaks for a selec-
high-fitness “peak.” However, Figure 21-6 shows that tive process means that some differences between
there are two adaptive peaks, corresponding to a fixed species are the result of history and not of environmen-
population of Ab/Ab and a fixed population of aB/aB, tal differences. For example, African rhinoceroses have
with an adaptive valley between them. Which peak the two horns on their noses, whereas Indian rhinoceroses
population will ascend — and therefore what its final ge- have one. We need not invent a special story to explain

Ab /Ab AB /AB Ab /Ab aB/aB
+ −
1.0 + −

0.9

0.8

0.7

Frequency of A 0.6 ab/ab
(b)
0.5 Fall line
0.4

0.3

0.2

0.1

−+

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

ab/ab Frequency of B aB/aB

(a)

Figure 21-6 An adaptive landscape with two adaptive peaks (red), two adaptive valleys
(blue), and a topographic saddle in the center of the landscape. The topographic lines are lines
of equal mean fitness. If the genetic composition of a population always changes in such a
way as to move the population “uphill” in the landscape (to increasing fitness), then the
final composition will depend on where the population began with respect to the fall
(dashed) line. (a) Topographic map of the adaptive landscape. (b) A perspective sketch of
the surface shown in the map.


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21.3 Heritability of variation 687

why it is better to have two horns on the African plains the random fixation of less fit alleles are integral features
and one in India. It is much more plausible that the trait of the evolutionary process. Natural selection cannot be
of having horns was selected but that two long, slender relied on to produce the best of all possible worlds.
horns and one short, stout horn are simply alternative
adaptive features, and the differences between them are Pathway II in Figure 21-7, on the other hand, shows
a result of historical accident. Explanations of adapta- how random drift may improve adaptation. The popula-
tions by natural selection do not require that every dif- tion was originally in the sphere of influence of the
ference between species be an adaptive difference. lower adaptive peak; however, by random fluctuation in
gene frequency, its composition passed over the adaptive
Exploration of adaptive peaks saddle, and the population was captured by the higher,
steeper adaptive peak. This passage from a lower to a
Random and selective forces should not be thought of as higher adaptive stable state could never have occurred
simple antagonists. Random drift may counteract the by selection in an infinite population, because, by selec-
force of selection, but it can enhance it as well. The out- tion alone, W could never decrease temporarily to cross
come of the evolutionary process is a result of the simul- from one slope to another.
taneous operation of these two forces. Figure 21-7 illus-
trates these possibilities. Note that there are multiple Another important source of indeterminacy in the
adaptive peaks in this landscape. Because of random outcome of a long selective process is the randomness of
drift, a population under selection does not ascend an the mutational process. After the initial genetic variation
adaptive peak smoothly. Instead, it takes an erratic is exhausted by the selective and random fixation of al-
course in the field of gene frequencies, like an oxygen- leles, new variation arising from mutation can be the
starved mountain climber. Pathway I shows a population source of yet further evolutionary change. The particular
history where adaptation has failed. The random fluctua- direction of this further evolution depends on the par-
tions of gene frequency were sufficiently great that the ticular mutations that occur and the time order in which
population by chance became fixed at an unfit genotype. they take place. A very clear illustration of this historical
In any population, some proportion of loci are fixed at a contingency of the evolutionary process is a selection ex-
selectively unfavorable allele because the intensity of se- periment carried out by H. Wichman and her colleagues.
lection is insufficient to overcome the random drift to They forced the bacteriophage ⌽X174 to reproduce at
fixation. The existence of multiple adaptive peaks and high temperatures and on the host Salmonella typhi-
murium instead of its normal host Escherichia coli. Two
A b /A b A B /A B independent selection lines were established, labeled TX
and ID, and both evolved the ability to reproduce at
1.0 + – high temperatures in the new host. In one of the two
lines, the ability to reproduce on E. coli still existed, but,
0.9 in the other line, the ability was lost. The bacteriophage
has only 11 genes, and so the experimenters were able to
0.8 record the successive changes in the DNA for all these
genes and in the proteins encoded by them during the
Frequency of A0.7 selection process. There were 15 DNA changes in strain
Pathway II TX, located in 6 different genes; in strain ID, there were
Pathway I0.6 14 changes located in 4 different genes. In only 7 cases
were the changes to the two strains identical, including a
0.5 large deletion, but even these identical changes appeared
in each line in a different order. So, for example, the
0.4 change at DNA site 1533, causing a substitution of
isoleucine for threonine, was the third change in the ID
0.3 strain, but the fourteenth change in the TX strain.

0.2 21.3 Heritability of variation

0.1 + The first rule of any reconstruction or prediction of evo-
lutionary change is that the phenotypic variation must
– be heritable. It is easy to construct stories of the possible
selective advantage of one form of a trait over another,
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 but it is a matter of considerable experimental difficulty
to show that the variation in the trait corresponds to
a b /a b Frequency of B a B /a B genotypic differences (see Chapter 20).

Figure 21-7 Interaction of selection and random drift.
Selection and random drift can interact to produce different
changes in gene frequency in an adaptive landscape. Without
random drift, both populations would have moved toward
aB / aB as a result of selection alone.


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688 Chapter 21 • Evolutionary Genetics

It should not be supposed that all variable traits are duced, but, in addition, there is variation from fly to fly.
heritable. Certain metabolic traits (such as resistance to This variation is heritable, and lines with zero or one
high salt concentrations in Drosophila) show individual bristle and lines with three or four bristles can be ob-
variation but no heritability. In general, behavioral traits tained by selection of flies carrying the scute mutation.
have lower heritabilities than morphological traits, espe- When the mutation is removed, these lines now have
cially in organisms with more complex nervous systems two and six bristles, respectively. Similar experiments
that exhibit immense individual flexibility in central with similar results have been performed by using ex-
nervous states. Before any prediction is made about the tremely stressful environments in place of mutants. A
evolution of a particular quantitative trait, it is essential consequence of such hidden genetic variation is that a
to determine if there is genetic variance for it in the character that is phenotypically uniform in a species
population whose evolution is to be predicted. Thus, may nevertheless undergo rapid evolution if a stressful
suggestions that such traits in the human species as per- environment uncovers the genetic variation.
formance on IQ tests, temperament, and social organiza-
tion are in the process of evolving or have evolved at 21.4 Observed variation within
particular epochs in human history depend critically on and between populations
evidence about whether there is genetic variation for
these traits. Reciprocally, traits that appear to be com- In Chapter 19, we saw that genetic variation exists
pletely phenotypically invariant in a species may never- within populations at the levels of morphology, kary-
theless evolve. otype, proteins, and DNA. The general conclusion is that
about one-third of all protein-encoding loci are polymor-
One of the most important findings in evolutionary phic and that all classes of DNA, including exons, in-
genetics has been the discovery that substantial genetic trons, regulatory sequences, and flanking sequences, show
variation may underly characters that show no morpho- nucleotide diversity among individuals within popula-
logical variation. They are called canalized characters, tions. Several of these examples also documented some
because the final outcome of their development is held differences in genotype frequencies between populations
within narrow bounds despite disturbing forces. Differ- (see Tables 19-1 through 19-3 and 19-5). The relative
ent genotypes for canalized characters have the same amounts of variation within and between populations
constant phenotype over the range of environments that vary from species to species, depending on history and
is usual for the species. The genetic differences are re- environment. In humans, some gene frequencies (for ex-
vealed if the organisms are put in a stressful environ- ample, those for skin color or hair form) are well differ-
ment or if a severe mutation stresses the developmental entiated between populations and major geographical
system. For example, all wild-type Drosophila have ex- groups (so-called geographical races). If, however, we
actly four scutellar bristles (Figure 21-8). If the recessive look at single structural genes identified immunologically
mutant scute is present, the number of bristles is re- or by electrophoresis rather than by these outward
phenotypic characters, the situation is rather different.
Scutellar Table 21-2 shows the three loci for which Caucasians,
bristles Negroids, and Mongoloids are known to be most differ-
ent from one another (Duffy and Rhesus blood groups
Figure 21-8 The scutellar bristles of the adult Drosophila, and the P antigen). Even for the most divergent loci, no
shown in blue. This illustration shows an example of a major geographical group is homozygous for one allele
canalized character; all wild-type Drosophila have four that is absent in the other two groups.
scutellar bristles in a very wide range of environments.
In general, different human populations show rather
similar frequencies for polymorphic genes. Findings from
studies of polymorphic blood groups, enzyme-coding
loci, and DNA polymorphisms in a variety of human
populations have shown that about 85 percent of total
human genetic diversity is found within local popula-
tions, about 6 percent is found among local populations
within major geographical races, and the remaining 9
percent is found among major geographical races.
Clearly, the genes influencing skin color, hair form, and
facial form that are well differentiated among “races” are
not a random sample of structural gene loci.


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21.5 The process of speciation 689

TABLE 21-2 Examples of Extreme Differentiation
in Blood-Group Allelic Frequencies
in Three Major Geographical Groups

Geographical group

Gene Allele Caucasoid Negroid Mongoloid
Duffy
Rhesus Fy 0.0300 0.9393 0.0985
Fya 0.4208 0.0000 0.9015
P antigen Fyb 0.5492 0.0607 0.0000
R0 0.0186 0.7395 0.0409
R1 0.4036 0.0256 0.7591
R2 0.1670 0.0427 0.1951
r 0.3820 0.1184 0.0049
rЈ 0.0049 0.0707 0.0000
Others 0.0239 0.0021 0.0000
P1 0.5161 0.8911 0.1677
P2 0.4839 0.1089 0.8323

Source: A summary is provided in L. L. Cavalli-Sforza and W. F. Bodmer, The Genetics of Human
Populations (W. H. Freeman and Company, 1971), pp. 724 – 731. See L. L. Cavalli-Sforza,
P. Menozzi, and A. Piazza, The History and Geography of Human Genes (Princeton University Press,
1994), for detailed data.

21.5 The process of speciation of a particular population as a distinct race is arbitrary
and, as a consequence, the concept of race is no longer
When we examine the living world, we see that individ- much used in biology.
ual organisms are usually clustered into collections that
resemble one another more or less closely and are clearly MESSAGE A species is a group of organisms that can
distinct from other clusters. A close examination of a exchange genes among themselves but are genetically
sibship of Drosophila will show differences in bristle unable to exchange genes in nature with individuals in other
number, eye size, and details of color pattern from fly to such groups. A geographical race is a phenotypically
fly, but an entomologist has no difficulty whatsoever distinguishable local population within a species that is
in distinguishing Drosophila melanogaster from, say, capable of exchanging genes with other races within that
Drosophila pseudoobscura. One never sees a fly that is species. Because nearly all geographical populations are
halfway between these two kinds. Clearly, in nature at different from others in the frequencies of some genes, race is
least, there is no effective interbreeding between these a concept that makes no clear biological distinction.
two forms. A group of organisms that exchanges genes
within the group but cannot do so with other groups is All the species now existing are related to each
what is meant by a species. Within a species there may other, having had a common ancestor at some time in
exist local populations that are also easily distinguished the evolutionary past. That means that each of these
from one another by some phenotypic characters, but it species has separated out from a previously existing
is also the case that genes can easily be exchanged be- species and has become genetically distinct and geneti-
tween them. For example, no one has any difficulty dis- cally isolated from its ancestral line. In extraordinary cir-
tinguishing a “typical” Senegalese from a “typical” Swede, cumstances, a single mutation might be enough to found
but such people are able to mate with each other and such a genetically isolated group, but the carrier of that
produce progeny. In fact, there have been many such mutation would need to be capable of self-fertilization
matings in North America in the past 300 years, creating or vegetative reproduction. Moreover, that mutation
an immense number of people of every degree of inter- would have to cause complete mating incompatibility
mediacy between these local geographical types. They between its carrier and the original species and to allow
are not separate species. In general, there is some differ- the new line to compete successfully with the previously
ence in the frequency of various genes in different geo- established group. Although not impossible, such events
graphical populations of any species; so the marking out must be rare.


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690 Chapter 21 • Evolutionary Genetics

More commonly, new species form as a result of ge- Examples of prezygotic isolating mechanisms are
ographical isolation. We have already seen how popula- well known in plants and animals. The two species of
tions that are geographically separated will diverge from pine growing on the Monterey peninsula, Pinus radiata
one another genetically as a consequence of unique mu- and P. muricata, shed their pollen in February and April
tations, selection, and genetic drift. Migration between and so do not exchange genes. The light signals that are
populations will prevent them from diverging too far, emitted by male fireflies and attract females differ in in-
however. As shown on page 685, even a single migrant tensity and timing between species. In the tsetse fly,
per generation is sufficient to prevent populations from Glossina, mechanical incompatibilities cause severe in-
fixing at alternative alleles by genetic drift alone, and jury and even death if males of one species mate with
even selection toward different adaptive peaks will not females of another. The pollen of different species of
succeed in causing complete divergence unless it is ex- Nicotiana, the genus to which tobacco belongs, either
tremely strong. As a consequence, populations that di- fails to germinate or cannot grow down the style of other
verge enough to become new, reproductively isolated species. Postzygotic isolation results from the failure of
species must first be virtually totally isolated from one fertilized zygotes to contribute gametes to future genera-
another by some mechanical barrier. This isolation al- tions. Hybrids may fail to develop or have a lower proba-
most always requires some spatial separation, and the bility of survival than that of the parental species or the
separation must be great enough or the natural barriers hybrids may be partly or completely sterile. Postzygotic
to the passage of migrants must be strong enough to isolation is more common in animals than in plants, ap-
prevent any effective migration. Such spatially isolated parently because the development of many plants is
populations are referred to as allopatric. The isolating much more tolerant to genetic incompatibilities and
barrier might be, for example, the extending tongue of a chromosomal variations. When the eggs of the leopard
continental glacier during glacial epochs that forces frog, Rana pipiens, are fertilized by sperm of the wood
apart a previously continuously distributed population frog, R. sylvatica, the embryos do not succeed in devel-
or the drifting apart of continents that become separated oping. Horses and asses can be easily crossed to produce
by water or the infrequent colonization of islands that mules, but, as is well known, these hybrids are sterile.
are far from shore. The critical point is that these barri-
ers must make further migration between the separated Genetics of species isolation
populations a very rare event. If so, then the populations
are now genetically independent and will continue to di- Usually, it is not possible to carry out any genetic analy-
verge by mutation, selection, and genetic drift. Eventu- sis of the isolating mechanisms between two species for
ally, the genetic differentiation between the populations the simple reason that, by definition, they cannot be
becomes so great that the formation of hybrids between crossed with each other. It is possible, however, to make
them would be physiologically, developmentally, or be- use of very closely related species in which the isolating
haviorally impossible even if the geographical separation mechanism has not produced complete hybrid sterility
were abolished. These biologically isolated populations and hybrid breakdown. These species can be crossed and
are now new species, formed by the process of allopatric the segregating progeny of hybrid F2 or backcross gener-
speciation. ations can be analyzed by using genetic markers and the
technique of locating quantitative trait loci (QTLs) dis-
MESSAGE Allopatric speciation occurs through an initial cussed in Chapter 20. When such marker experiments
geographical and mechanical isolation of populations that have been performed on other species, mostly in the
prevents any gene flow between them, followed by genetic genus Drosophila, the general conclusions are that gene
divergence of the isolated populations sufficient to make it differences responsible for hybrid inviability are on all
biologically impossible for them to exchange genes in the the chromosomes more or less equally and that, for hy-
future. brid sterility, there is some added effect of the X chro-
mosome. For behavioral sexual isolation, the results are
There are two main biological isolating mechanisms: variable. In Drosophila, all the chromosomes are in-
prezygotic isolating mechanisms and postzygotic mecha- volved, but, in Lepidoptera, the genes are much more
nisms. Prezygotic isolation occurs when there is failure localized, apparently because of the involvement of spe-
to form zygotes. The cause of this failure may be that cific pheromones whose scent is important in species
the different species mate at different seasons or in dif- recognition. The sex chromosome has a very strong
ferent habitats. It may also be that the species are not effect in butterflies; in the European corn borer, for
sexually attractive to each other or their genitalia do not example, only three loci, one of which is on the sex
match or male gametes are physiologically incompatable chromosome, account for the entire isolation between
with the female. pheromonal types within the species.


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21.6 Origin of new genes 691

21.6 Origin of new genes Polyploidy

It is clear that evolution consists of more than the sub- One process for the provision of new DNA is the dupli-
stitution of one allele for another at loci of defined func- cation of the entire genome by polyploidization, which
tion. New functions have arisen that have resulted in is much more common in plants than in animals (Chap-
major new ways of making a living. Many of these new ter 15). Evidence that polyploids have played a major
functions — for example, the development of the mam- role in the evolution of plant species is presented in
malian inner ear from a transformation of the reptilian Figure 21-9, which shows the frequency distribution of
jaw bones — result from continuous transformations of haploid chromosome numbers among dicotyledonous
shape and do not require totally new genes and proteins. plant species. Above a chromosome number of about
But new genes and proteins are necessary to produce 12, even numbers are much more common than odd
qualitative novelties, such as photosynthesis and cell numbers — a consequence of frequent polyploidy.
walls in plants, contractile proteins, new cell and tissue
types, oxygenation molecules such as hemoglobin, the Duplications
immune system, chemical detoxification cycles, and di-
gestive enzymes. Older metabolic functions must have A second way to increase DNA is by the duplication of
been maintained while new ones were being developed, small sections of the genome. Such duplication may be a
which in turn means that old genes had to be preserved consequence of misreplication of DNA. Alternatively, a
while new genes with new functions had to evolve. transposable element may insert a copy of one part of
Where does the DNA for new genes come from? the genome into another location (see Chapter 11).
After a duplicated segment has arisen, one of three

1100 8
11

1000

900

800 14
700

Number of species 600
500 16 18

400

20
24

300 22

200
28

26
100 30 32 34 36

38 40

01 5 10 20 30 40 50 60

Haploid number

Figure 21-9 Frequency distribution of haploid chromosome numbers in dicotyledonous plants.

[After Verne Grant, The Origin of Adaptations. Columbia University Press, 1963.]


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692 Chapter 21 • Evolutionary Genetics

Percentage of total globin synthesis 50 α α TABLE 21-3 Percentage of Similarity
γ β in Amino Acid Sequences
Among Human Globin Chains
40

30 ␣␨ ␤␥ ⑀

⑀ ␣ 58 42 39 37

20 ␨ 34 38 37

ζ ␤ 73 75

10 γ ␥ 80
δ
β

6 12 18 24 30 36 6 12 18 24 30 36 42 48

Postconceptual age (weeks) Birth Postnatal age (weeks)

Figure 21-10 Developmental changes in the synthesis of the Table 21-3 shows the percentage of amino acid
␣-like and ␤-like globins that make up human hemoglobin. identity among these chains, and Figure 21-11 shows the
chromosomal locations and intron — exon structures of
things can happen: (1) the production of the polypep- the genes encoding them. The story is remarkably con-
tide may simply increase; (2) the general function of the sistent. The ␤, ␦, ␥, and ⑀ chains all belong to a “␤-like”
original sequence is maintained in the new DNA, but group; they have very similar amino acid sequences and
there is some differentiation of the sequences by accu- are encoded by genes of identical intron — exon struc-
mulated mutations so that variations on the same pro- ture that are all contained in a 60-kb stretch of DNA on
tein theme are produced, allowing a somewhat more chromosome 11. The ␣ and ␨ chains belong to an “␣-
complex molecular structure; or (3) the new segment like” group and are encoded by genes contained in a 40-
may diverge more dramatically and take a whole new kb region on chromosome 16. In addition, Figure 21-11
function. shows that on both chromosome 11 and chromosome
16 are pseudogenes, labeled ␺␣ and ␺␤. These pseudo-
A classic example of the second case is the set of gene genes are duplicate copies of the genes that did not ac-
duplications and divergences that underlie the production quire new functions but accumulated random mutations
of human hemoglobin. Adult hemoglobin is a tetramer that render them nonfunctional. What is remarkable is
consisting of two ␣ polypeptide chains and two ␤ chains, that the order of genes on each chromosome is the same
each with its bound heme molecule. The gene encoding as the temporal order of appearance of the globin chains
the ␣ chain is on chromosome 16 and the gene for the ␤ in the course of development.
chain is on chromosome 11, but the two chains are about
49 percent identical in their amino acid sequences, an In regard to hemoglobin, the duplicated DNA en-
identity that clearly points to the common origin. How- codes a new protein that performs a function closely re-
ever, in fetuses, until birth, about 80 percent of ␤ chains lated to the function encoded by the original gene. But
are substituted by a related ␥ chain. These ␤ and ␥ duplicated DNA can diverge dramatically in function.
polypeptide chains are 75 percent identical. Furthermore, An example of such a divergence is shown in Figure
the gene for the ␥ chain is close to the ␤-chain gene on 21-12. Birds and mammals, like other eukaryotic organ-
chromosome 11 and has an identical intron – exon isms, have a gene encoding lysozyme, a protective en-
structure. This developmental change in globin synthesis zyme that breaks down the bacterial cell wall. This gene
is part of a larger set of developmental changes that are has been duplicated in mammals to produce a second
shown in Figure 21-10. The early embryo begins with sequence that encodes a completely different, nonenzy-
␣, ␥, ⑀, and ␨ chains and, after about 10 weeks, the ⑀ and ␨ matic protein, ␣-lactalbumin, a nutritional component
chains are replaced by ␣, ␤, and ␥. Near birth, ␤ replaces of milk. Figure 21-12 shows that the duplicated gene has
␥ and a small amount of yet a sixth globin, ␦, is produced. the same intron – exon structure as that of the lysozyme
gene, whose array of four exons and three introns itself

Figure 21-11 60 50 40 30 20 10 kb
Chromosomal distribution of
the genes for the ␣ family of Chromosome 11 Chromosome 16 ζ1 ψα1 α2 α1
globins on chromosome 16 ⑀ ζ2 ψβ1 3′
and the ␤ family of globins on
chromosome 11 in humans. 5′ 5′ δβ
Gene structure is shown by 3′
black bars (exons) and Gγ Aγ
colored bars (introns).


44200_21_p679-706 3/12/04 3:58 PM Page 693

21.6 Origin of new genes 693

Goat α-lactalbumin gene

Exon 1 Intron 1 Exon 2 Intron 2 Exon 3 Intron 3 Exon 4
159 GTGAG AG 76 GTGAG CAG 58
GTGAGT TAG
474 2303
76 327

Hen lysozyme gene

Exon 1 Intron 1 Exon 2 Intron 2 Exon 3 Intron 3 Exon 4
162 GTGAG AG 79 GTGAG CAG 69
GTAAGT CAG
1810 79
82 1270

Figure 21-12 Structural homology of the gene for hen lysozyme and mammalian
␣-lactalbumin. Exons and introns are indicated by dark green bars and light green bars,
respectively. Nucleotide sequences at the beginning and end of each intron are indicated,
and the numbers refer to the nucleotide lengths of each segment. [After I. Kumagai,

S. Takeda, and K.-I. Miura, “Functional Conversion of the Homologous Proteins ␣-Lactalbumin and
Lysozyme by Exon Exchange,” Proceedings of the National Academy of Sciences USA 89, 1992,

5887 – 5891.]

suggests an earlier multiple duplication event in the ori- chloroplasts of photosynthetic organisms and mitochon-
gin of lysozyme. dria are the descendants of prokaryotes that entered the
eukaryotic cells either as infections or by being ingested.
Imported DNA These prokaryotes became symbionts, transferring much
of their genomes to the nuclei of their eukaryotic hosts
DNA duplications are not the only source of new DNA but retaining genes that are essential to cellular func-
that is the basis of new functions; it can also be im- tions. Mitochondria have retained about three dozen
ported. Repeatedly in evolution, extra DNA has been genes concerned with cellular respiration as well as some
imported into the genome from outside sources by tRNA genes, whereas chloroplast genomes have about
mechanisms other than normal sexual reproduction. 130 genes encoding enzymes of the photosynthetic cycle
DNA can be inserted into chromosomes from other as well as ribosomal proteins and tRNAs.
chromosomal locations and even from other species. In
some cases, genes from totally unrelated organisms can Important evidence for the extracellular origin of
become incorporated into cells to become a functional mitochondria is to be found in their genetic code. The
part of the recipient cell’s genome. “universal” DNA – RNA code of nuclear genes is not, in
fact, universal and differs in some respects from that in
CELLULAR ORGANELLES Eukaryotic cells have ob- mitochondria. Table 21-4 shows that, for 5 of the 64
tained some of their organelles in this way. Both the RNA triplets, mitochondria differ in their coding from
the nuclear genome. Moreover, mitochondria in different

TABLE 21-4 Comparison of the Universal Nuclear DNA Code
with Several Mitochondrial Codes
for Five Triplets in Which They Differ

Nuclear TGA ATA Triplet code AGG AAA
Mitochondrial
Stop Ile AGA Arg Lys
Mammalia
Aves Trp Met Arg Stop Lys
Amphibia Trp Met Stop Lys
Echinoderms Trp Met Stop Stop Lys
Insecta Trp Ile Stop Ser Asn
Nematodes Trp Met Stop Stop Lys
Platyhelminth Trp Met Ser Ser Lys
Cnidaria Trp Met Ser Ser Asn
Trp Ile Ser Arg Lys
Ser
Arg


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694 Chapter 21 • Evolutionary Genetics

organisms differ from one another for these coding ele- from an ancient common ancestor; so an alignment of
ments, providing evidence that eukaryotic cells must their two protein or DNA sequences would not reveal
have been invaded by prokaryotes at least five times, any similarity. The evidence that yeast and human
each time by a prokaryote with a different coding sys- lysozyme genes are descended from an original common
tem. For the vertebrates, worms, and insects, the mito- ancestral gene comes from comparisons of evolutionarily
chondrial code is more regular than the universal intermediate forms that show more and more diver-
nuclear code. In the nuclear genome, for example, gence of sequence as species are more divergent. The en-
isoleucine is the only amino acid redundantly encoded zyme has maintained its function despite the replace-
by precisely three triplets: ATT, ATC, and ATA. The ment of the amino acids because just the right amino
transition of the third base from A to G yields the fourth acids were substituted to maintain the enzyme’s three-
member of this codon group, ATG, but it codes for me- dimensional structure.
thionine. In contrast, in mitochondria, this codon group
contains two codons for methionine and two for In contrast, it is possible to change the function of an
isoleucine, separated by a transversion. enzyme by a single amino acid substitution. The sheep
blow fly, Lucilia cuprina, has developed resistance to
HORIZONTAL TRANSFER It is now clear that the nu- organophosphate insecticides used widely to control it.
clear genome is open to the insertion of DNA both from R. Newcombe, P. Campbell, and their colleagues showed
other parts of the same genome and from outside. that this resistance is the consequence of a single substitu-
Within a genome, DNA can be transferred through the tion of an aspartic acid for a glycine residue in the active
action of transposable elements (see Chapter 13). The site of an enzyme that is ordinarily a carboxylesterase. The
chromosomes of an individual Drosophila, for example, mutation causes complete loss of the carboxylesterase ac-
contain a large variety of families of transposable ele- tivity and its replacement by esterase specificity. Three-
ments with multiple copies of each distributed through- dimensional modeling of the molecule indicates that the
out the genome. As much as 25 percent of the DNA of substituted protein gains the ability to bind a water mole-
Drosophila may be of transposable origin. What role this cule close to the site of attachment of the organophos-
mobile DNA plays in functional evolution is not clear. phate, which is then hydrolyzed by the water.
When transposable elements are introduced into zygotes
at mating, such as the P elements of Drosophila (see MESSAGE There is no regular relation between how
Chapter 11, page 371), the result is an explosive prolif- much DNA change takes place in evolution and how much
eration of the elements in the recipient genome. When a functional change results.
mobile element is inserted into a gene, the effect on the
organism is usually drastic and deleterious, but this ef- When more than one mutation is required for a new
fect may be an artifact of the methods used to detect function to arise, the order in which these mutations oc-
the presence of such elements. The results of laboratory cur in the evolution of the molecule may be critical.
selection experiments on quantitative characters have B. Hall has experimentally changed a gene to a new
shown that transposition can act as an added source of function in E. coli by a succession of mutations and se-
selectable variation. There is also the possibility that lection. In addition to the lacZ genes specifying the usual
genes are transferred from the nuclear genome of one lactose-fermenting activity in E. coli, another structural
species to the nuclear genome of another by retroviruses gene locus, ebg, specifies another ␤-galactosidase that
(see Chapter 13). Retroviruses can be carried between does not ferment lactose, although it is induced by lac-
very distantly related species by common disease vectors tose. The natural function of this second gene is un-
such as insects or by bacterial infections; so any foreign known. Hall was able to select mutations of this extra
genetic material carried by a retrovirus could be a pow- gene to enable E. coli to live, without any lactose, on a
erful source of new functions. wholly new substrate, galactobionate. To do so, he first
had to mutate the regulatory sequence of ebg so that it
Relation of genetic to functional change became constitutive and no longer required lactose to
induce its translation. Next, he tried to select mutants
There is no simple relation between the amount of that would ferment lactobionate, but he failed. First, it
change in a gene’s DNA and the amount of change in was necessary to select a form that would ferment a re-
the encoded protein’s function. At one extreme, almost lated substrate, lactulose, and then he could mutagenize
the entire amino acid sequence of a protein can be re- the lactulose fermenters and select from among the mu-
placed while maintaining the original function. Eukary- tants those able to operate on lactobionate. Moreover,
otes, from yeast to humans, produce lysozyme, an en- only some of the independent mutants from lactose fer-
zyme that breaks down bacterial cell walls, as mentioned mentation to lactulose utilization could be further mu-
earlier. Virtually every amino acid in this protein has tated and selected to operate on lactobionate. The others
been replaced since yeast and vertebrate lines diverged were dead ends. Thus, the sequence of evolution had to
be (1) from an inducible to a constitutive enzyme,


44200_21_p679-706 3/23/04 10:54 AM Page 695

21.7 Rate of molecular evolution 695

followed by (2) just the right mutation from lactose to are effectively deleterious need not be considered, be-Number of substitutions per nucleotide
lactulose fermentation, followed by (3) a mutation to cause they will be kept at low frequencies in popula-
ferment lactobionate. tions and will not contribute to evolutionary change.
If a newly arisen mutation is effectively neutral, then,
MESSAGE In the evolution of new functions by mutation as pointed out in Chapter 19, there is a probability
and selection, particular pathways through the array of of 1/(2N ) that it will replace the previous allele because
mutations must be followed. Other pathways come to dead of random genetic drift. If ␮ is the rate of appearance of
ends that do not allow further evolution. new effectively neutral mutations at a locus per gene
copy per generation, then the absolute number of new
21.7 Rate of mutational copies that will appear in a population of N
molecular evolution diploid individuals is 2N␮. Each one of these new copies
has a probability of 1/(2N ) of eventually taking over the
There is no simple relation between the number of mu- population. Thus, the absolute rate of replacement of
tations in DNA or substitutions of amino acids in pro- old alleles by new ones at a locus per generation is their
teins and the amount of functional change in those pro- rate of appearance multiplied by the probability that any
teins. Although it is possible that only one or a few one of them will eventually take over by drift:
mutations can lead to a major change in the function of
a protein, the more usual situation is that DNA accumu- rate of neutral replacement ϭ 2N␮ ϫ 1/(2N ) ϭ ␮
lates substitutions over long periods of evolution with-
out any qualitative change to the functional properties That is, we expect that in every generation there will be
of the encoded proteins. Some of the substitutions may, ␮ substitutions of a new allele for an old one at each lo-
however, have smaller effects, influencing the kinetic cus in the population, purely from genetic drift of effec-
properties, timing of production, or quantities of the en- tively neutral mutations.
coded proteins that, in turn, will affect the fitness of the
organism that carries them. Mutations of DNA can have MESSAGE The rate of replacement in evolution resulting
three effects on fitness. First, they may be deleterious, re- from the random genetic drift of effectively neutral
ducing the probability of survival and reproduction of mutations is equal to the mutation rate to such alleles, ␮.
their carriers. All of the laboratory mutants used by the
experimental geneticist have some deleterious effect on The constant rate of neutral substitution predicts
fitness. Second, they may increase fitness by increasing that, if the number of nucleotide differences between
efficiency or by expanding the range of environmental two species is plotted against the time since their diver-
conditions in which the species can make a living or by gence from a common ancestor, the result should be a
enabling the organism to track changes in the environ- straight line with slope equal to ␮. That is, evolution
ment. Third, they may have no effect on fitness, leaving should proceed according to a molecular clock that is
the probability of survival and reproduction unchanged; ticking at the rate ␮. Figure 21-13 shows such a plot for
they are the so-called neutral mutations. For the pur-
poses of understanding the rate of molecular evolution, Synonymous
however, we need to make a slightly different distinc- sites
tion — that between effectively neutral and effectively se-
lected mutations. It is possible to prove that, in a finite 3.0
population of N individuals, the process of random ge-
netic drift will not be materially altered if the intensity 2.0
of selection, s, on an allele is of lower order than 1/N.
Thus the class of evolutionarily neutral mutations in- 1.0
cludes both those that have absolutely no effect on fit- Nonsynonymous
ness and those whose effects on fitness are less than the sites
reciprocal of population size, so small as to be effectively
neutral. On the other hand, if the intensity of selection, 0 12345
s, is of a greater order than 1/N, then the mutation will Divergence time (× 108)
be effectively selected.
Figure 21-13 The amount of nucleotide divergence at
We would like to know how much of molecular synonymous and nonsynonymous sites of the ␤-globin gene as a
evolution is a consequence of new, favorable adaptive function of time since divergence.
mutations sweeping through a species, the picture pre-
sented by a simplistic Darwinian view of evolution, and
how much is simply the accumulation of effectively
neutral mutations by random fixation. Mutations that


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