JOURNAL OF EXPERIMENTAL ZOOLOGY (MOL DEV EVOL) 302B:424–435 (2004)
Pleiotropic Effects on Mandibular Morphology II:
Differential Epistasis and Genetic Variation in
Morphological Integration
JAMES M. CHEVERUD*, THOMAS H. EHRICH, TY T. VAUGHN,
SAFINA F. KOREISHI, ROBIN B. LINSEY, AND L. SUSAN PLETSCHER
Department of Anatomy & Neurobiology, Washington University School of
Medicine, St. Louis, Missouri 63110
ABSTRACT
The evolution of morphological modularity through the sequestration of pleiotropy
to sets of functionally and developmentally related traits requires genetic variation in the
relationships between traits. Genetic variation in relationships between traits can result from
differential epistasis, where epistatic relationships for pairs of loci are different for different traits.
This study maps relationship quantitative trait loci (QTLs), specifically QTLs that affect the
relationship between individual mandibular traits and mandible length, across the genome in an F2
intercross of the LG/J and SM/J inbred mouse strains (N ¼ 1045). We discovered 23 relationship
QTLs scattered throughout the genome. All mandibular traits were involved in one or more
relationship QTL. When multiple traits were affected at a relationship QTL, the traits tended to
come from a developmentally restricted region of the mandible, either the muscular processes or the
alveolus. About one-third of the relationship QTLs correspond to previously located trait QTLs
affecting the same traits. These results comprise examples of genetic variation necessary for an
evolutionary response to selection on the range of pleiotropic effects. J. Exp. Zool. (Mol. Dev. Evol.)
302B:424–435, 2004. r 2004 Wiley-Liss, Inc.
INTRODUCTION
The principle of evolutionary morphological
integration (Cheverud, ’82, ’84; Olson and Miller,
’58; Chernoff and Magwene, ’99) states that
functionally and developmentally related traits
will evolve as an integrated unit. Lande (’79, ’80,
’84) provided a genetic basis for this theory by
showing that various traits should evolve genetic
correlations consistent with the patterns of stabilizing selection produced by their functional and
developmental relationships. Hence, functionally
and developmentally related traits should evolve
higher correlations than unrelated traits (Cheverud, ’84) and should evolve in a coordinated
fashion. These predictions have been confirmed
by a wide array of studies in a variety of plant and
animal systems, such as floral morphology (Berg,
’60), plant architecture (Venable and Burquez,
’90), butterfly wings (Kingsolver and Wiernasz,
’91; Holloway et al., ’95), and primate cranial
morphology (Cheverud, ’82, ’96; Marriog and
Cheverud, 2001).
Until recently, however, the pleiotropic patterns
supporting the relatively high correlation among
r 2004 WILEY-LISS, INC.
functionally and developmentally related traits
have not been well understood. Correlation among
traits may be due to ubiquitous pleiotropy with a
balance of positive and negative pleiotropy determining correlation magnitudes. Another model
holds that pleiotropy itself is modular, with
pleiotropic effects restricted to modules of functionally and developmentally related traits (see
Fig. 1).
Pleiotropy and morphological integration
Under the ubiquitous pleiotropy model, most
loci are pleiotropic over a wide range of traits with
individual loci displaying either positive or negative pleiotropy. The evolved correlation between
the traits would then be due to a balance between
positive and negative pleiotropy. This balance
Grant sponsor: NSF; Grant number: DEB–9726433; Grant sponsor:
NIH; Grant number: RR15116.
n
Correspondence to: James M. Cheverud, Department of Anatomy
and Neurobiology, Box 8108, Washington University School of
Medicine, 660 S. Euclid Avenue, St. Louis, Missouri 63110. E-mail:
[email protected]
Received 1 March 2004; Accepted 9 April 2004
Published online 28 July 2004 in Wiley InterScience (www.
interscience.wiley.com). DOI: 10.1002/jez.b.21008
425
GENETIC VARIATION IN MANDIBULAR PLEIOTROPY
systems. Recent studies have supported the
modular pleiotropy model. In a series of quantitative trait locus (QTL) studies, Cheverud and
colleagues (2004) have found a modular structure
to pleiotropy for body size and growth (Cheverud
et al., ’96; Vaughn et al., ’99), body composition
(Cheverud et al., 2001), skull morphology (Leamy
et al. ’99), and mandibular morphology (Ehrich
et al., 2003).
Differential epistasis
Fig. 1. Idealized pleiotropic patterns for multiple loci (L)
affecting multiple phenotypes (P). In modular pleiotropy traits
are affected by different sets of loci resulting in genetic
correlation (r) among phenotypes belonging to a trait set and
no correlation between sets. In ubiquitous pleiotropy all loci
affect all traits, but some loci have opposite effects on traits
belonging to different trait sets, again resulting in genetic
correlation (r) within trait sets and no correlation between
sets.
would depend on the relative allele frequencies
present at the positively and negatively pleiotropic
loci (Cheverud, ’84). A pair of traits selected for a
high degree of correlation would have intermediate allele frequencies at positively pleiotropic loci
and extreme frequencies at negatively pleiotropic
loci. Traits selected for low correlations would
have intermediate frequencies at both kinds of
loci. Wright (’80) favored a model of ubiquitous
pleiotropy and polygeny. In its admittedly extreme
form, he suggested that each trait is affected by
every gene and that every gene potentially affects
every trait. Wright supported this view of pleiotropy with examples of pleiotropic effects of
mutations on diverse and apparently unrelated
phenotypes.
Under the modular pleiotropy model, pleiotropic
effects are often restricted to sets of functionally
and developmentally related traits, such that the
level of evolved intertrait correlation depends on
the relative sequestration of pleiotropy. Taking
ubiquitous pleiotropy as the primitive state
(Riska, ’86; Wagner and Altenberg, ’96), modularity would evolve by the sequestration of pleiotropy, restricting the effects of individual genes to a
reduced set of traits. Reidl (’78) and Wagner and
Altenberg (’96) have argued that modular pleiotropy is critical for adaptive evolution in complex
In order for pleiotropy to evolve, it must be
genetically variable. One mechanism by which
genetic variability in pleiotropy can be achieved is
by means of differential epistasis (Cheverud, 2001,
2004). Differential epistasis occurs when epistatic
interactions between pairs of loci are different for
different traits. It is a multilocus version of the
differential dominance discussed by Ehrich et al.
(2003). In this hypothetical example, loci X and Y
have potential effects on traits A and B (see
Table 1). The two locus genotypic values for trait
A illustrate additive effects at both loci, X and Y,
and an absence of epistasis. However, there is
strong epistasis between these loci for trait B
because locus X affects trait B when the Y locus is
‘‘yy’’ or ‘‘Yy’’ but not when the genotype is ‘‘YY.’’
In this example epistatic patterns are different for
different traits at the same pair of loci. The X locus
has pleiotropic effects on both traits A and B when
the ’y’ allele is in moderate to high frequency but
its effect is limited to trait A when the ’Y’ allele is
common. Thus, evolution at the Y locus causes the
evolution of pleiotropy expressed at the X locus. As
is true for any interaction, the relationship
between traits A and B also varies among
genotypes at the alternate X locus, being strongest
for the ‘‘xx’’ genotype, intermediate for the ‘‘Xx’’
genotype, and weakest for the ‘‘XX’’ genotype.
TABLE 1. Di¡erential epistasis at loci X and Y for traits A and B
xx
Xx
XX
xx
Xx
XX
yy
Trait A
Yy
YY
2
1
0
1
0
1
0
1
2
yy
Trait B
Yy
YY
2
1
0
1
0
1
0
0
0
426
J.M. CHEVERUD ET AL.
Therefore, evolution at the X locus also results in
evolution of Y locus pleiotropy.
Some examples serve to illustrate the phenomenon of differential epistasis. The abnormal abdomen (aa) gene in Drosophila mercatorum was
found to have a wide variety of pleiotropic effects
on morphological and life history traits (Templeton and Johnston, ’88; Templeton et al., ’85, ’93;
Hollocher et al. ’92). Relative to the wild-type
allele, ‘aa’ results in a juvenilized cuticle, slow
development time, high early fecundity, and low
adult survivorship in laboratory stocks (Templeton et al., ’85). However, ’aa’ animals collected
from the wild rarely showed the juvenilized cuticle
that is the hallmark of this syndrome, even though
the life history effects were still evident. Templeton et al. (’93) found that this difference was due
to modifier genes at other loci present in the wild
population but not in the laboratory. These other
genes modified the range of pleiotropic effects
displayed by the ‘aa’ allele by differential epistasis
on the morphological and life history effects of
abnormal abdomen.
In maize, the mutant opaque–2 came to the
attention of geneticists because it caused a high
level of the essential amino acid lysine in the
endosperm (Moro et al. ’96). However, this mutant
had pleiotropic effects on the kernel, making it soft
and easily damaged in harvesting and treatment.
Crosses into other maize stocks followed by
selection uncovered other loci that modified the
pleiotropic effects of opaque–2, eliminating the
undesirable effects on kernel structure while
maintaining the high lysine level (Burnett and
Larkins, ’99; Geetha et al., ’91). Again, this was
due to the differential epistatic interaction of the
loci for the different traits.
Boerwinkle et al. (’87) investigated the effects of
the apolipoprotein E (apoE) polymorphism in
human populations. In addition to affecting serum
cholesterol values, the apoE locus affects the
relationship between the levels of serum cholesterol and triglycerides. Serum cholesterol and
triglyceride levels are moderate to highly intercorrelated in the general population. However, the
subsets of individuals that are either apoE3/4
heterozygotes or apoE4/4 homozygotes exhibit no
correlation between serum cholesterol and triglyceride levels. Thus, apoE locus genotypes affect
the relationship between these two traits. As with
the examples above, this can be accomplished by
differential epistatic relationships between apoE
and other loci. Genetic variation in pleiotropy has
long been recognized as playing an important role
in evolutionary processes. Mayr (’63) noted the
importance of epistatic interactions in ameliorating the deleterious pleiotropic effects of alleles on
fitness and enhancing their positive fitness effects.
Mayr (’63) saw this selection as producing a
coadapted gene complex that resulted in the unity
of the genotype. Wright (’68, p. 105) stated that
‘‘Evolution depends on the fitting together of
favorable complexes from genes that cannot be
described in themselves as either favorable or
unfavorable’’ because the pleiotropic effects of any
given gene will have both favorable and unfavorable consequences and the balance between these
effects is subject to evolution. Baatz and Wagner
(’97) also note that deleterious pleiotropic effects
can inhibit adaptive evolution, independent of any
genetic correlation between the traits. Variants
that limit these ‘‘hidden’’ pleiotropic effects will be
favored by natural selection.
This report examines the genetic basis of
variation in the relationships among mandibular
traits. Specifically, we consider the relationships
between local regions of the mandible and total
mandibular length, or mandibular allometry.
Allometry is a special form of intertrait relationship of a part to the whole (Gould, ’66). We will
map quantitative trait loci that have effects on the
relationship between specific parts of the mandible and total mandibular length, illustrating
genetic variation in the allometric relationships
and pleiotropy displayed by a locus.
MATERIALS AND METHODS
Population and measurements
The population of mice used for this study
comes from an F2 intercross of Large (LG/J) and
Small (SM/J) inbred mouse strains and is described in detail by Ehrich et al. (2003). Briefly,
the Small (MacArthur, ’44) and Large (Goodale,
’38) strains were selected for low and high 60–day
body weight, respectively, in separate experiments. Both strains have been systematically
inbred by brother-sister mating for over 100
generations (Festing, ’96), making them genetically homozygous aside from spontaneous mutations. Additionally, variation is maintained in the
SM/J strain at the agouti locus (Chai ’56). Animals
used in this study were drawn from two independent, replicate intercross experiments. In Intercross I, 10 SM/J males were mated with 10 LG/J
females, resulting in 41 F1 progeny. Intercrossing
the F1 hybrids resulted in 535 F2 offspring.
Intercross II replicated the conditions of
427
GENETIC VARIATION IN MANDIBULAR PLEIOTROPY
Fig 2.
Measurements of specific mandibular regions. Measurement names are given in Table 2.
Intercross I, resulting in an additional 510 F2
animals for a total of 1045 specimens. Results
from the replicate experiments were comparable
(Ehrich et al., 2003) and are pooled in the analyses
described here.
Animals were weaned at three weeks, after
which they were housed separately by sex, no
more than five animals to a cage. Animals were fed
a standard mouse chow diet ad libitum (Purina
PicoLab Rodent Chow 20 #5353, St. Louis, MO),
an irradiated diet with 20% protein and 4.5% fat.
See Cheverud and colleagues (’96) and other
studies (Kramer, et al. ’98; Vaughn et al. ’99) for
details of animal husbandry. Animals were
sacrificed by CO2 asphyxiation. Following sacrifice
and necropsy, carcasses were skinned and macerated by dermestid beetles. Skeletons were then
cleaned, and the right and left mandibles were
separated for measurement.
Details of mandible measurement have been
described by Ehrich et al. (2003). A total of twenty
interlandmark distances were obtained from 2D
coordinate values of right hemimandibles (see
Figure 2, Table 2). In addition to these measurements, mandible length was defined as the
distance between the most posterior-inferior point
on the mandibular condyle and the superior
incisor alveolus. The effects of individual QTLs
became more apparent once the statistical effects
due to dam, litter size, experimental block, and sex
were removed from the data as described in
Ehrich et al. (2003). Correction for covariates
reduces the error variance in the gene mapping
analyses, resulting in greater statistical power to
detect QTL effects.
TABLE 2. Individual mandibular measurements. Numbers correspond to measurements in Figure 2
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Measurements
Posterior coronoid height
Superior condyloid length
Posterior condyloid length
Inferior condyloid length
Condyloid neck length
Posterior angular length
Inferior angular length
Anterior angular length
Angular neck length
Posterior mandibular corpus height
Inferior coronoid length
Posterior-inferior corpus length
Anterior-inferior corpus length
Inferior incisor alveolar length
Incisor alveolar width
Superior incisor alveolar length
Anterior mandibular corpus height
Molar alveolar height
Molar alveolar length
Superior corpus length
Anterior coronoid length
Molecular markers
For Intercross I, 76 microsatellite markers were
scored across the 19 mouse autosomes (Dietrich
et al., ’92; Cheverud et al., ’96). Markers polymorphic for the parental strains were chosen to
cover the autosomes as evenly as possible. Increased marker availability facilitated an increase
to 96 polymorphic loci in 72 intervals for Intercross II, with correspondingly greater coverage
428
J.M. CHEVERUD ET AL.
Fig. 3. Positions of molecular markers mapped in the F2
generation.
density (Dietrich et al. ’92, ’96) as shown in
Figure 3. Three markers were used in Intercross I
that were not repeated in Intercross II due to
difficulty in scoring the genotypes. Together,
Intercross I and II define a total map distance of
about 1780 cM, with an average intermarker
interval of about 23 cM (Vaughn et al., ’99).
All 1045 animals and 96 microsatellite markers
were used to generate map distances using MAPMAKER 3.0b software program (Lander et al., ’87;
Lincoln et al., ’92). The microsatellite map positions were obtained from a combined analysis of
intercrosses I and II, as described in Ehrich et al.
(2003).
Interval mapping
QTL gene effects and positions were determined
using a multivariate interval mapping approach
based on Haley and Knott’s least squares regression method (Cheverud, 2001a; Haley and Knott,
’92). In this method traits of interest are regressed
on genotype scores imputed for positions every 2
cM along each chromosome. Additive genotype
scores (Xa) at markers are 1.0 for SM/J homozygotes, 0.0 for heterozygotes, and þ1.0 for LG/J
homozygotes. Dominance genotype scores (Xd) at
markers are 0.0 for both homozygotes and 1.0 for
heterozygotes. In a F2 intercross population, the
regression coefficients are estimates of the additive (a) and dominance (d) genotypic values
(Falconer and Mackay, ’96). Genotype scores for
positions in the intervals between markers are
imputed using the genotype scores for the flanking
markers and the recombination rates between the
flanking markers and the location of interest, as
described by Haley and Knott (’92). Multivariate
analysis was undertaken using the ‘‘Set Correlation’’ feature of the SYSTAT 8.0 statistical
analysis program (Cohen and Wilkinson, ’96)
which performs a canonical correlation analysis
between phenotypes and genotype scores. This
program provides Wilk’s Lambda, F, and w2
statistics for the full multivariate trait set and
for each trait separately, analyzed every 2 cM
along the map (Cheverud, 2001a).
Statistical significances at both the chromosomal and genome-wide levels were calculated using
the Bonferroni correction based on an estimate of
the number of independent tests performed
(Cheverud, 2001b). Briefly, significance thresholds
were derived by first calculating the number of
independently assorting markers on each chromosome or the effective marker number, Meff
(Cheverud, 2001b),
Meff ¼ Mð1 ððM 1ÞVl =M 2 ÞÞ;
in which M equals the actual number of markers
scored and Vl is the variance of the eigenvalues of
the intermarker correlation matrix for each
chromosome. The 5% chromosome and genome
significance levels were then calculated by dividing
0.05 by the Meff for the given chromosome or the
whole genome, respectively.
QTLs affecting mandible length were located
using a simple univariate model regressing mandible length (MLi) on the additive and dominance
genotype scores
MLi ¼ a þ aXai þ dXdi þ ei
where a is the regression constant, a and d are the
regression coefficients estimating the additive and
dominance genotypic values, Xai and Xdi are the
additive and dominance genotype scores, and ei is
the residual.
The model for detecting genetic variation in
allometry regresses the specific mandible traits on
the interactions between mandible length and the
additive and dominance genotype scores at each
chromosomal location, holding mandible length,
and the two genotype scores constant
Yi ¼ m þ aml MLi Xai þ dml MLi Xdi
þ ei jMLi Xai Xdi
where aml and dml are the regression coefficients
for the additive and dominance interactions with
mandible length and the other terms are as given
above. The operator ‘‘|’’ indicates that the variables to the right of the symbol are controlled for
in this model and do not contribute to significance
testing. Significant interactions indicate that the
429
GENETIC VARIATION IN MANDIBULAR PLEIOTROPY
allometric relationship between a specific trait and
mandible length varies by genotype at the locus.
Alternatively, a significant interaction can be
interpreted as meaning that the effect of the
QTL on the specific mandible traits varies depending on mandibular length.
The results of QTL mapping for these specific
traits have already been reported in Ehrich et al.
(2003). This study will consider the degree to
which that mapping depends on overall mandible
length.
A multivariate test for interaction was performed first, on each chromosome, by comparing
the multivariate probability of no interaction with
thresholds based on Bonferroni correction for
multiple independent tests separately for each
chromosome (Cheverud, 2001b). Probabilities
were also evaluated relative to a genome-wide
threshold correcting for multiple comparisons
(Cheverud, 2001b). Given significant evidence of
interaction, we then located QTLs for which the
relationship between specific mandible traits and
mandible length varied significantly by genotype.
RESULTS
Mandible length QTLs
Thirteen QTLs affecting mandibular length on
12 chromosomes (see Table 3 and Figure 4) were
discovered. Typical regions of support are approximately 27 cM in width. These QTLs are each of
small effect, accounting for between 1.0% and
Fig. 4. Genomic locations of mandibular length quantitative trait loci with a bar representing the 95% support interval
for QTL position. The numerical identification (Y) to the right
of each support interval refers to the corresponding mandibular QTL (QTMANX.Y where X refers to chromosome number
and Y to the mandibular QTL previously mapped to the
location) from Ehrich et al. (2003). For example, the mandible
length QTL on chromosome 6 corresponds to QTMAN6–2
from Ehrich et al. (2003).
6.0% of the F2 phenotypic variance after adjustment for covariates. Taken together, the single
locus effects of these QTLs account for 28% of the
phenotypic variance. Average differences in mandible length between the homozygous genotypes are
0.15 to 0.34 mm or 0.30 to 0.68 phenotypic
standard deviation units. LG/J alleles produce a
longer mandible at ninety-two percent of the
QTLs. The LG/J allele is dominant to the SM/J
allele at eight loci, while in only two loci, including
TABLE 3. Mandible Length QTLs
Chromosome
Marker
1
3
4
6
7
10
11
13A
13B
14
15
17
19
D1Mit7
D3MitS4
D4Mit17
D6Mit58
D7Nds1
D10Mit133
D11Mit64
D13Mit115
D13Mit9
D14Nds1
D15Mit5
D17Mit46
D19Mit16
n
Marker
Distn
Centromeric
Distnn
Support
int.nnn
a
d
% Var
LOD
Score
QTL Name
4
34
4
0
6
12
4
14
12
16
14
8
0
48
34
36
92
50
88
50
24
74
16
38
8
0
36^52
14^56
24^52
92^96
40^56
62^88
30^72
8^44
54^92
4^28
28^46
0^18
0^40
0.132
0.095
0.099
0.080
0.084
0.096
0.167
0.076
0.113
0.173
0.148
0.112
- 0.068
0.112
0.029
0.088
0.061
0.088
0.053
0.084
0.187
0.015
0.004
0.090
0.051
0.061
4.0
1.3
2.3
1.5
1.9
2.0
5.5
1.6
1.7
3.4
3.5
2.4
1.1
8.66
2.75
4.94
3.13
4.14
4.24
11.88
3.42
3.68
7.25
7.59
4.76
2.46
QTMAN1-1
QTMAN3-4
QTMAN4-1
QTMAN6-2
QTMAN7-2
QTMAN10-2
QTMAN11-1(2,3)
QTMAN13-1B
QTMAN13-2
QTMAN14-1
QTMAN15-2
QTMAN17-1,2
QTMAN19-1
cM distance from the nearest proximal marker.
cM distance from the most proximal marker on the chromosome.
nnn
QTL support interval in cM from the most proximal marker on the chromosome.
nn
430
J.M. CHEVERUD ET AL.
the one locus where the SM/J allele produces a
larger mandible, is the SM/J allele dominant. All
mandible length QTLs map to locations corresponding to previously described mandibular
QTLs for specific mandible measurements (Table
3; Ehrich et al., 2003).
Relationship QTLs
Twenty-three QTLs were mapped on 13 chromosomes at which specific mandibular traits
were affected by mandible length by genotype
interactions (see Table 4 and Figure 5). For
eight QTLs only one specific trait was affected
while at the 15 remaining QTLs two to 10 traits
were affected for an average of four traits per
QTL. Each of the twenty traits was affected by
interaction somewhere in the genome. Superior
condylar length (2), posterior mandibular height
(10), and superior incisor alveolar length (16)
were most commonly affected. Thirty percent
of these interaction QTLs mapped to the
same location as specific trait QTLs, affecting the
same traits and 40% map to mandible length
Fig. 5. Genomic locations of QTLs affecting the relationship between specific mandibular regions and mandible length
with a bar representing the 95% support interval for QTL
position. Specific measurements showing genetic variation in
relationship to mandible length are identified by their
measurement numbers (see Figure 2 and Table 2). Numbers
in boldface indicate that this QTL also had a direct genetic
effect on the specified measurement as reported in Ehrich et al.
(2003).
QTLs. Genotype-specific regression statistics for
each trait at each QTL are provided in the
Appendix.
TABLE 4. QTLs a¡ecting the relationship between speci¢c traits and mandible length.Trait numbers are identi¢ed inTable 2 and Figure
2. Region refers to the developmental region of the mandible a¡ected by the QTL; MU for the muscle attachment regions of the ascending
ramus, AL for the alveolar processes, Total for both. QTL name refers to the corresponding trait QTL reported in Ehrich et al (2003)
Chromosome
Marker
1
1
2
2
3
3
3
4
4
6
7
7
10
10
11
11
14
14
15
16
17
18
18
D1Mit74
D1Mit17
D2Mit370
D2Mit22
D3Mit54
D3Mit22
D3Mit94
D4Mit163
D4Mit16
D6Nds5
D7Mit21
D7Nds1
D10Mit2
D10Mit133
D11Mit62
D11Mit333
D14Nds1
D14Mit7
D15Mit2
D16Mit2
D17Mit16
D18Mit17
D18Mit51
n
Masker
Distn
Centromeric
Distnn
Support
int.nnn
Traits
0
12
6
12
6
0
2
0
0
16
18
8
24
12
0
0
0
0
12
6
0
0
20
17
134
52
128
6
42
112
16
68
84
18
52
24
88
0
98
0
64
64
6
10
4
46
14^18
124^138
42^60
82^144
0^24
20^54
92^120
8^20
52^74
80^88
0^32
46^54
6^40
84^88
0^56
94^104
0^14
52^88
48^76
0^30
4^20
2^22
36^46
16
1
2,6,8,10
1,4
2
10,14,15,19
16
2,4,10,11,16
2,21
3,8,10,12,14,15,16,17,19,20
2
17
8,9,13,15
6
1,2,4
2,11,15,16
2,10,15
1,21
2,10,13,18
2,3
7,9,0,14,19
3,8
16
cM distance from the nearest proximal marker.
cM distance from the most proximal marker on the chromosome.
nnn
QTL support interval in cM from the most proximal marker on the chromosome.
nn
Region
LOD
Score
^
^
MU
MU
^AL
^
MU
MU
AL
^
^
Total
^
MU
Total
Total
MU
AL
MU
Total
MU
^
2.53
2.54
4.64
2.28
2.07
7.75
2.47
3.46
4.44
17.53
3.43
2.48
2.94
2.32
2.64
3.53
2.52
2.76
2.16
2.69
4.91
2.58
2.04
QTL Name
QTMAN2-2
QTMAN3-4
QTMAN4-1
QTMAN7-1
QTMAN11-1(2,3)
QTMAN11-4
QTMAN14-1
GENETIC VARIATION IN MANDIBULAR PLEIOTROPY
431
Fig. 6. Examples of genotype-specific regressions for local region size on total mandibular length. QTL at; (A) D10Mit2 þ 2
cM, (B) D10Mit133 þ 12 cM, (C) D11Mit62 þ 44 cM, (D) D17Mit16 þ 0 cM.
432
J.M. CHEVERUD ET AL.
The examples provided in Figure 6 illustrate the
interpretation of these interaction results. Figure
6A presents the results for the relationship QTL at
the proximal end of chromosome 10 for anteriorinferior corpus length (13). As can be clearly seen
in the figure, the allometric slope for this trait
varies with genotype, being highest for the SM/J
homozygote, intermediate for the heterozygote,
and low for the LG/J homozygote. An alternate
interpretation of this relationship is that the effect
of the QTL on anterior-inferior corpus length (13)
changes depending on mandible length. When the
mandible is short, the LG/J allele produces a
longer corpus but if the mandible is long the SM/J
allele produces a longer corpus length. Other
traits at this relationship QTL show alternate
patterns for the genotype-dependent relationship
between parts of the mandible and mandible
length. The allometry slope for anterior angular
length (8) is higher in the LG/J homozygote
and heterozygote, but relatively low in the
SM/J homozygote. Angular neck length (9) shows
overdominance for the slope, while incisor
alveolar width (15) shows a relatively strong
negative relationship with mandible length in
SM/J homozygotes. The patterns of effects at
most relationship QTL are variable from trait
to trait.
Other examples are provided in Figures 6B, 6C,
and 6D. The relationship QTL for posterior
angular height (6) on the distal portion of
chromosome 10 shows overdominance for slope
values. The relationship QTLs on proximal chromosomes 11 and 17 for inferior condylar length (4)
and posterior corpus height (10), respectively,
show additive effects on slope with the LG/J allele
leading to a stronger relationship.
Sets of traits with genetic variation in mandibular relationships at any one QTL are consistent
with a pattern of morphological integration. Of
the 15 QTLs affecting multiple traits, 11 can be
characterized as having effects primarily restricted to one of the major developmental regions
of the mandible, either the muscle attachment
region (MU; 8 QTL) or the alveolus (AL; 3 QTL)
(see Table 4). While only four of these QTLs
have enough effects restricted to one region to
show a statistically significant deviation from
random trait distribution at the 0.10 level using
a chi-square test, when the chi-square values of
all 15 QTLs are combined in a single test the
deviation from random expectation is significant
at the 0.0001 level (chi-square ¼ 48.21, 15 df).
Therefore, genetic variation in pleiotropy for
functionally and developmentally related traits
in the mandible is modular with particular loci
tending to restrict pleiotropic range within specific
trait sets.
DISCUSSION
We have mapped a substantial number of
loci spread throughout the mouse genome that
have an effect on the phenotypic relationship
between the size of local mandibular regions
and overall mandibular length. These are manifest
as differences in the allometry coefficient for
specific mandibular regions relative to overall
length for different genotypes at a locus. The
‘‘trait’’ we mapped here is not a measurement in
the usual sense but rather the relationship
between measurements. It is important to consider the meaning of these trait relationship
QTLs.
Both gene by gene and gene by environment
interactions can be responsible for the QTLs
observed in this study. The phenotypic relationship between traits is measured by their phenotypic covariance and this covariance is the sum of
separate genetic and environmental covariances
(Falconer and Mackay, ’96). Here, we have
mapped QTLs affecting the phenotypic covariance
between traits. It follows that the QTLs could
affect the phenotypic covariance by altering either
the genetic or environmental parts, or both. The
environmental covariance could be altered by
differential genotype-environment interaction for
different traits, while the genetic covariance could
be altered by differential epistasis. It is difficult to
distinguish these possibilities in a F2 intercross
population. No specific environmental factors
were measured in this experiment and all F2
individuals are equally related to one another so
that quantitative genetic methods cannot be used
to separate genetic from environmental interactions. In principle, it may be possible to map
genetic locations affecting the relationship QTLs
themselves by mapping three-way interactions
between individual loci spread across the genome,
our identified relationship QTLs, and mandible
length. However, statistical power for detecting
these effects is weak if many genomic locations
each have a small effect on the relationship QTL
and/or higher order interactions are involved.
Future studies of F3 generation animals (Kramer
et al., ’98) to analyze interactions between
relationship QTL genotype, sibship, and mandible
length, may allow for a more powerful test to
GENETIC VARIATION IN MANDIBULAR PLEIOTROPY
distinguish differential epistasis from differential
genotype by environment interaction, as could
studies of recombinant inbred strains. The
following discussion will focus on differential
epistasis as a cause of variation in pleiotropy,
although it should be kept in mind that differential gene by environment interaction can cause
the same pattern.
Differential epistasis is similar to the concept of
differential dominance, introduced in a companion
paper (Ehrich et al., 2003). Differential dominance
occurs when intralocus dominance interactions
differ among traits affected by a single pleiotropic
locus. Differential epistasis occurs when interlocus
epistatic interactions differ among traits affected
by a pair of potentially pleiotropic loci. When
differential dominance is present at a locus there
must be some linear combination of measurements for which the locus is overdominant, even if
no single trait displays overdominance. Directional selection along any of these overdominant
linear combinations results in balancing selection
and maintenance of heterozygosity at the individual locus involved.
Differential dominance caused substantial overdominance for shape at mandibular QTLs (Ehrich
et al., 2003). It is likely that differential epistasis
can produce qualitatively similar results, where
directional selection along a multivariate dimension results in balancing selection on two locus
systems. The details of this possibility remain to
be elucidated in future studies.
This study has discovered genetic variation in
pleiotropic effects associated with specific genomic
locations by mapping QTLs affecting the relationship between individual mandibular regions and
total mandibular length. This genetic variation
can serve as the basis for a response to selection on
pleiotropy itself. Riedl (’78), Wagner and Altenberg (’96), and Baatz and Wagner (’97) have
argued that selection favors the modular sequestration of sets of functionally and developmentally
related traits because evolution is most efficient in
producing adaptation if variation in unrelated
traits is controlled by separate sets of variable loci.
This pattern of modular pleiotropy is illustrated in
our companion paper on the pleiotropic effects of
mandibular trait QTLs (Ehrich et al., 2003). In
order for natural selection to produce sequestered
modules, genetic variation in modularity must be
present. Genetic variation for the sequestration of
individual mandibular regions in relation to total
mandible length, supporting the evolved modularity model has been demonstrated.
433
The relationship QTLs also showed a pattern of
morphological integration at 75% of the loci
affecting multiple traits. When multiple traits
were affected by a relationship locus, they were
typically centered in one of the two developmental
regions of the mandible, the muscle attachment
processes or the alveolus supporting the teeth.
This indicates that the standing variation in this
particular population shows variation in pleiotropic effects primarily within modules. However,
four multiple trait QTLs, on proximal chromosome 10, distal chromosome 11, proximal chromosome 14, and proximal chromosome 17, have
effects spread across both developmental regions.
These loci show variation in pleiotropic effects at
the whole mandible level and could provide
variation for further sequestration of the
muscular attachment and alveolar developmental
units.
Seven of the relationship QTLs mapped to the
same location as trait QTLs (see Table 4; Ehrich
et al., 2003). These locations not only affect the
value of the individual traits but also affect their
relationship to mandibular length. However, 16
relationship QTLs occurred at locations that had
no direct effect on the traits themselves. These
regions contain loci affecting the mandible, but
they were missed in earlier research (Ehrich et al.,
2003) because their effects were hidden by opposing effects in different segments of the population,
and canceled each other out. These loci can be
detected here by stratifying the population by
mandible length so that the opposing effects could
be separately measured.
In this study we have detected genetic variation
in the relationships among mandibular traits at
individual quantitative trait loci. This represents
variation in the range of pleiotropic effects at the
loci identified and, hence, allows for response to
selection on trait relationships in our population.
Admittedly, the study population is artificial,
being constructed from the intercross of two
inbred mouse strains. However, the alleles giving
rise to observed effects can be considered as
having been drawn at random from the range of
variability present in the ancestral ‘‘laboratory’’
mouse population (Beck et al., 2000). The selection of this kind of variation is necessary for
the evolution of modularity by restricting
pleiotropic effects to sets of functionally and
developmentally related traits. Genetic variation
in trait relationships is critical for our understanding of the co-evolution of morphological
elements.
434
J.M. CHEVERUD ET AL.
ACKNOWLEDGEMENTS
The authors thank all who helped rear the F2
mice and prepare and measure the skeletal
material, including Eric Routman, Kilinyaa Cothran, Christy Perel, Duncan Irschick, Kelly KingEllison, Emily Adams-Hunt, and Becky Rogers
Ackermann. Thanks also to Jane Kenney for
insightful comments on previous manuscript
versions.
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