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? 2004 The Society for the Study of Evolution. All rights reserved.
Evolution, 58(10), 2004, pp. 2287–2304
FROM MICRO- TO MACROEVOLUTION THROUGH QUANTITATIVE GENETIC
VARIATION: POSITIVE EVIDENCE FROM FIELD CRICKETS
MATTIEU BE´GIN1,2AND DEREK A. ROFF3
1Department of Biology, McGill University, 1205 Dr. Penfield ave., Montre ´al, Que ´bec, H3A 1B1, Canada
2E-mail: mbegin1@po-box.mcgill.ca
3Department of Biology, University of California, Riverside, California, 92521
Abstract.
could be directly linked to macroevolutionary patterns using, among other parameters, the additive genetic variance/
covariance matrix (G) which is a statistical representation of genetic constraints to evolution. However, little is known
concerning the rate and pattern of evolution of G in nature, and it is uncertain whether the constraining effect of G
is important over evolutionary time scales. To address these issues, seven species of field crickets from the genera
Gryllus and Teleogryllus were reared in the laboratory, and quantitative genetic parameters for morphological traits
were estimated from each of them using a nested full-sibling family design. We used three statistical approaches (T
method, Flury hierarchy, and Mantel test) to compare G matrices or genetic correlation matrices in a phylogenetic
framework. Results showed that G matrices were generally similar across species, with occasional differences between
some species. We suggest that G has evolved at a low rate, a conclusion strengthened by the consideration that part
of the observed across-species variation in G can be explained by the effect of a genotype by environment interaction.
The observed pattern of G matrix variation between species could not be predicted by either morphological trait values
or phylogeny. The constraint hypothesis was tested by comparing the multivariate orientation of the reconstructed
ancestral G matrix to the orientation of the across-species divergence matrix (D matrix, based on mean trait values).
The D matrix mainly revealed divergence in size and, to a much smaller extent, in a shape component related to the
ovipositor length. This pattern of species divergence was found to be predictable from the ancestral G matrix in
agreement with the expectation of the constraint hypothesis. Overall, these results suggest that the G matrix seems
to have an influence on species divergence, and that macroevolution can be predicted, at least qualitatively, from
quantitative genetic theory. Alternative explanations are discussed.
Quantitative genetics has been introduced to evolutionary biologists with the suggestion that microevolution
Key words.
signal, population divergence, quantitative traits.
Common principal components, evolutionary constraint, heritability, matrix comparison, phylogenetic
Received January 28, 2004.Accepted July 25, 2004.
Modern evolutionary biology theory rests on the assump-
tion that macroevolutionary patterns can be explained in large
part by microevolutionary processes (e.g. Simpson 1944;
Charlesworth et al. 1982). Quantitative genetics has been
introduced to evolutionary biologists with the suggestion that
it may be used as a conceptual tool to link micro- and mac-
roevolution, at least for low taxonomic levels (Lande 1979;
Steppan 1997a; Arnold et al. 2001). The basic quantitative
genetic framework available for modeling phenotypic evo-
lution is based on the interplay between natural selection and
quantitative genetic constraints (Arnold 1992), and is de-
scribed by the equation ?z ¯ ? G?, where ?z ¯ is the vector of
across-generation change in mean trait values, G is the matrix
of additive genetic variances and covariances, and ? is the
vector of selection gradients (Lande 1979; Lande and Arnold
1983). It has been demonstrated that this model provides
relatively satisfying predictions of the response to selection
in the context of a few generations of either artificial selection
in controlled environments (Falconer and Mackay 1996; Roff
1997) or natural selection in nature (Morris 1971; Grant and
Grant 1995). However, it is not known whether this model
can be successfully applied to phenotypic evolution in natural
populations over evolutionary time scales. Simulation studies
(Reeve 2000), theoretical considerations (Mitchell-Olds and
Rutledge 1986; Turelli 1988; Riska 1989; Shaw et al. 1995;
Agrawal et al. 2001) and laboratory experiments (Leroi et al.
1994; Archer et al. 2003; Phelan et al. 2003) have provided
various warnings against the systematic extension of the
model to long-term evolution, but this issue must ultimately
be answered with adequate empirical evidence from natural
populations (Turelli 1988).
A critical requirement of this model is that the G matrix
must remain constant, or at least change predictably andslow-
ly, during evolutionary time-scales, whereas the phenotype
changes in response to evolutionary forces (Lande 1979; Tur-
elli 1988). Clearly, if G fluctuates heavily and randomly, it
cannot produce a constant long-term constraint on the evo-
lution of the phenotype, and its effects cannot be modeled
with the current equations. The first step in the exploration
of the possibility of modeling long-term phenotypic evolution
is therefore to investigate the constancy of G in nature. It is
difficult to synthesize the results of the few dozen existing
papers on this subject because many of these studies exhibit
low statistical power, and most differ with respect to their
analytical approach (Roff 1997). Despite these difficulties,
the most recent review articles (Roff 2000; Steppan et al.
2002) emphasized the point that the amount and structure of
quantitative genetic variation does evolve, and that investi-
gators should now concentrate on trying to identify predict-
able patterns and causes of G matrix evolution. A possible
avenue towards this goal is to study G matrix variation using
a phylogenetic framework to test the hypothesis that G
evolves neutrally, and to estimate its rate of evolution. Thus
far, the available data seem to indicate that closely related
species often have similar G matrices while higher taxonomic
levels are often associated with differences (reviewed in Roff
2000; Steppan et al. 2002). However, this conclusion is ten-
tative because no more than three species have been com-
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M. BE´GIN AND D. A. ROFF
pared in a single study (Lofsvold 1986; Be ´gin and Roff 2003).
Denser phylogenetic sampling has been achieved at the ex-
pense of using the phenotypic variance-covariance matrix (P)
instead of G, which constitutes a potentially misleading pro-
cedure because phenotypic (co)variances are not expected to
besystematicallyproportional
(co)variances (Willis et al. 1991; but see Cheverud 1988;
Reusch and Blanckenhorn 1998; Waitt and Levin 1998).
Some of these studies have detected a weak association be-
tween phylogenetic distance and P matrix differences (Good-
in and Johnson 1992; Steppan 1997a, b; Ackermann and
Cheverud 2000; Ackermann 2002) whereas others have de-
tected none (Cheverud 1989; Badyaev and Hill 2000; Marroig
and Cheverud 2001; Baker and Wilkinson 2003). Multispe-
cies comparisons of G matrices are necessary to shed light
on this issue.
Finding a general conservation of G or a low rate of change
of G across species would be compatible with the hypothesis
that the G matrix acts as a long-term constraint. However,
quantitative genetic constraints may ultimately be inconse-
quential in a given group of organisms if the strength of the
constraint is low compared to the intensity of other evolu-
tionary factors such as natural selection and genetic drift.
One way to investigate the importance of the G matrix is to
test the hypothesis that only genetic constraints influence the
direction and rate of phenotypic evolution (Bjo ¨rklund and
Merila ¨ 1993). The expectation of the constraint hypothesis
is that a high genetic correlation between two traits in the
ancestral species translates into a high correlation of mean
trait values among daughter species, whereas a genetic cor-
relation near zero in the ancestral species does not constrain
the evolutionary possibilities of the lineage (Sokal 1978). In
other words, the matrix of across-extant-species divergence
(the D matrix, composed of (co)variances between the mean
trait values of extant species) should be proportional to the
ancestral G matrix. No empirical consensus has yet emerged
on the importance of G as a long-term constraint. Some stud-
ies have found no evidence or weak evidence for the con-
straint hypothesis (Lofsvold 1988; Venable and Burquez
1990; Andersson 1997; Merila ¨ and Bjo ¨rklund 1999; Badyaev
and Hill 2000), some have found supporting evidence (Sokal
and Riska 1981; Bond and Midgley 1988; Andersson 1996;
Schluter 1996; Roff and Fairbairn 1999; Badyaev and Fores-
man 2000; Baker and Wilkinson 2003; Blows and Higgie
2003; Hansen et al. 2003a, b; Marroig et al. 2004), and others
have concluded that the importance of G in constraining evo-
lution varies across traits (Armbruster 1991; Bjo ¨rklund and
Merila ¨ 1993; Mitchell-Olds 1996) or across taxonomic
groups or levels (Ackermann and Cheverud 2002; Marroig
and Cheverud 2004). The problem with these studies is that
the various species that make up the D matrix were not reared
under common garden conditions and/or a small number of
species were used and/or the P matrix was used instead of
the G matrix. In addition, only Baker and Wilkinson (2003)
have used the tools of the comparative method to guide the
estimation of across-species correlations and ancestral matrix
reconstruction. The current G matrix analysis is the first to
estimate the matrices of more than three species and the first
to use the tools of the comparative method.
This study uses seven species of field crickets to (1) de-
toadditivegenetic
scribe G matrix variation in a phylogenetic context (G is here
approximated by what we call the GAFmatrix to account for
our use of the full sibling breeding system, see Materials and
Methods section), and (2) investigate whether and how
strongly the ancestral GAFmatrix has constrained the phe-
notypic divergence of this group of organisms. Five size-
related linear morphological measurements were used be-
cause genetic correlations between such traits are typically
high in crickets (Be ´gin and Roff 2001), which increases the
likelihood that the across-species divergence of these traits
has been genetically constrained. This therefore constitutes
a favorable context for testing the constraint hypothesis. The
following technical issues are also investigated. Because
there is currently no consensus as to which statistical ap-
proach to matrix comparison is better (Steppan et al. 2002),
this study aims at (3) comparing the results of three available
methods; the T method, the Flury hierarchy, and the Mantel
test. A related problem is that many studies use (co)variance
matrices whereas others use correlation matrices. Therefore,
(4) this analysis provides a comparison of results obtained
with the two types of matrices. Finally, because many studies
use the P matrix as a surrogate for the G matrix, the current
study (5) empirically investigates the validity of this as-
sumption.
MATERIALS AND METHODS
Study Organisms and Measurements
Field crickets are wing-dimorphic orthopterans that typi-
cally live in ephemeral habitats (Alexander 1968; Masaki and
Walker 1987). This study uses six North American cricket
species of the genus Gryllus and one Australian species of
the related genus Teleogryllus. Huang et al. (2000) con-
structed a phylogeny of field crickets using a mitochondrial
sequence of 1536 base pairs that includes the whole cyto-
chrome b gene and a 16S rRNA fragment. Genetic distances
(sent to us in 2002 by G. Orti, University of Nebraska, Lin-
coln, NE) were estimated using maximum-likelihood and the
general time reversible model with among-site rate hetero-
geneity (Huang et al. 2000). Distances between species (Ta-
ble 1) represent average numbers of substitutions per site.
To avoid confusion with other types of distances, we used
the term phylogenetic distance throughout the text.
In the current study, natural populations were sampled
from one location per species (Table 2) and brought into the
laboratory where they were maintained for one to ten gen-
erations prior to the experiment. Full-sibling families, with
two cage replicates per family, were formed with the purpose
of estimating quantitative genetic parameters (see Table 2
for sample sizes). All crickets were reared in 4 L buckets at
a density of 40 and were fed with an unlimited supply of
rabbit chow and water. Buckets were placed in a growth
chamber at 28?C with a cycle of 15 h of light followed by
9 h of darkness (15L: 9D) and 50% humidity. The protocol
differs in the case of G. pennsylvanicus, which was reared
for another study (Simons and Roff 1994). This species was
raised at a density of 25 per bucket, and the growth chamber
conditions were set at 24?C, 17L:7D, and 50% humidity.
Gryllus pennsylvanicus is also the only species for which
micropterous individuals (short-winged) were used instead
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FROM MICRO- TO MACROEVOLUTION THROUGH G
TABLE 1.
per site.
Pairwise phylogenetic distances between Gryllus and Teleogryllus species. Values represent average numbers of substitutions
Species
G. int. G. vel.G. fir. G. pen. G. tex.G. rub.
G. veletis
G. firmus
G. pennsylvanicus
G. texensis
G. rubens
T. oceanicus
0.060
0.111
0.102
0.093
0.088
0.524
0.120
0.103
0.106
0.097
0.547
0.021
0.095
0.094
0.491
0.100
0.095
0.459
0.022
0.540 0.518
TABLE 2. Sample size and locality for Gryllus and Teleogryllus field cricket species.
Species
Sample
locality
Number of
families
Number of
individuals
G. integer
G. veletis
G. firmus
G. pennsylvanicus
G. texensis
G. rubens
T. oceanicus
Davis, California, USA
Montre ´al, Que ´bec, Canada
Gainesville, Florida, USA
Montre ´al, Que ´bec, Canada
Austin, Texas, USA
Charleston, South Carolina, USA
Mission Beach, Queensland, Australia
56
67
62
39
54
69
66
786
1096
862
505
906
1313
1031
of macropterous individuals. However, the G matrix of G.
pennsylvanicus was not found to differ from the matrices of
most other species (see Results), which implies that the dif-
ferences in rearing condition and wing morph were incon-
sequential for this species. All crickets were preserved within
three days after their final molt.
Five linear morphological measurements, which together
represent overall size and shape, were taken on each female:
femur length (FEMUR), head width (HEAD), prothorax
length (PTHL), prothorax width (PTHW), and ovipositor
length (OVIP). An analysis of measurement error using a
subsample of individuals revealed that repeatability wasclose
to 98% for each trait (measured as the proportion of the total
variance explained by the among-individual component; Fal-
coner and Mackay 1996). All measurements were ln-trans-
formed (natural logarithm), which successfully removed the
correlation between the mean and variance of each trait. De-
viations of the trait distributions from normality were min-
imal, and multivariate outliers were rare and not very distant
from the centroids. We therefore did not transform the data
further.
Quantitative Genetic Analysis
The estimation of quantitative genetic parameters for the
five morphological traits was based on a nested ANOVA/
ANCOVA, with family and cage-nested-within-family as the
two independent variables (having two cages nested within
each family allows to correct for common family environ-
mental effects; Roff 1997, pp. 41–43). Assumptions under-
lying this quantitative genetic model are discussed in the next
paragraph. A delete-one jackknife procedure (Manly 1997,
pp. 24–33), in which each family was deleted once to produce
a population of samples, was implemented to estimate var-
iances and covariances and their standard errors. A
(co)variance was therefore estimated as the average of the
corresponding Jackknife pseudovalues, and the standard error
was estimated as the standard error of these pseudovalues.
The number of jackknife iterations was equal to the number
of families. The jackknife has been shown through simula-
tions to produce accurate estimates of means and standard
errors for heritabilities (Simons and Roff 1994) and genetic
correlations (Roff and Preziosi 1994).
Predictive models in quantitative genetics are based on
additive genetic variances and covariances (the G matrix;
Lande 1979; Arnold et al. 2001). By definition (Falconer and
Mackay 1996; Roff 1997), full-sib estimates of quantitative
genetic parameters include the additive genetic component
of variance, but are also contaminated mainly by a part of
the dominance variance and by maternal effects (family en-
vironmental effects are here corrected for by our use of two
cages per family). Among-species differences in our full-sib
estimates of G could therefore reflect variation in any of these
components. However, we have several lines of evidence that
indicate that the effects of dominance and maternal effects
are low for these traits in field crickets. First, Crnokrak and
Roff (1995) have shown that morphological traits typically
express little dominance variance. In addition, Roff (1998)
has shown that, in the case of the trait femur length in G.
firmus, estimates of heritability from a full-sib design (0.37),
a half-sib design (0.34) and a parent-offspring regression
(0.45) were very similar. This suggests that the dominance
and maternal effects are low because, if they were not, the
full-sib estimate would be expected to be larger than the other
two. Similarly Roff (1998) and Re ´ale and Roff (2003) showed
that head width in G. firmus suffered very little inbreeding
depression, which implies low levels of dominance variance
(Falconer and Mackay 1996; Roff 1997; Lynch and Walsh
1998). Moreover, a diallel analysis of femur length and other
leg measurements in inbred lines of G. firmus showed that
dominance variance was significant but accounted on average
for only 5% (restricted maximum likelihood) or 11% (Griff-
ing model) of the phenotypic variance (Roff and Re ´ale 2004).
This range of value is not very large considering that our
full-sib variance components account for, on average, 43%
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M. BE´GIN AND D. A. ROFF
of the total variation. Maternal effects have also been shown
to be of minor importance in morphological traits in inbred
lines of G. firmus. Roff and Re ´ale (2004) found that maternal
effects in leg measurements were mostly nonsignificant, as
was the case with head width (Roff and Sokolovska 2004).
Taken together, these results suggest that only a small portion
of our full-sib estimates of variance is attributable to dom-
inance or maternal effects. However, the importance of these
other sources of variation could not be investigated in the
current study. We therefore decided to be conservative by
avoiding to use the term G matrix and by replacing it with
a term that reflects the full-sibling design and that does not
imply that only additive genetic variation is present; the GAF
matrix, standing for among-family genetic covariancematrix.
(Co)variance Matrix Comparisons
Because no single method to compare covariance matrices
has been shown to be optimal (Steppan et al. 2002), two
different methods were used in this study; the T method and
the Flury hierarchy. These methods were used to investigate
differences between species with respect to their P or GAF
matrices. Except where indicated, pair-wise comparisons of
species were performed.
The T method, developed by Roff et al. (1999), uses matrix
disparity as an index of difference between two matrices. It
is similar to the method suggested by Willis et al. (1991)
and discussed by Steppan (1997b). The method is based on
the sum of element by element absolute differences between
two matrices and tests the hypothesis that two matrices are
equal, by calculating
?
i?1
c
T
?
?M
? M ?,
12
i1
i2
where Mi1and Mi2are the estimates of the ith element of the
two matrices and c is the number of nonredundant elements
in the matrix (sum of the number of diagonal elements plus
the number of elements above the diagonal). The probability
that the two matrices come from the same statistical popu-
lation is estimated by a randomization procedure (4999 it-
erations) in which families are randomly assigned to the spe-
cies being compared, and quantitative genetic parameters es-
timated for each iteration. The probability is estimated as P
? (n ? 1)/(N ? 1), where n is the number of iterations in
which the T from the randomized data set is greater than or
equal to that obtained from original data set and N is the total
number of iterations (the ‘‘?1’’ is to account for the original
estimate). The randomization procedure sets the mean and
standard deviation to 0 and 1, respectively, for each trait in
each randomized data set. To provide a more intuitively in-
terpretable statistic, we present the T% statistic which esti-
mates the average difference between the elements of two
matrices as a percentage of the average size of the elements
in these matrices:
T /c
12
T%
?
100,
12
¯¯
(M ? M )/2
12
where M¯1and M¯2are the averages of the elements of the two
matrices. However, all tests of matrix equality used T, not
T%. Note that the T% statistic is unreliable when covariances
of both signs are present (Steppan 1997b), but this was not
the case in this dataset.
The second method, called the Flury hierarchy, is a prin-
cipal components approach to the comparison of matrices
that has been applied to G matrix comparison (Cowley and
Atchley 1992; Phillips and Arnold 1999). This method, based
on maximum likelihood, determines which model is the best
descriptor of the structural differences between two or more
matrices. The hierarchically nested models are (1) ‘‘unrelated
structure’’: matrices have no eigenvector in common; (2)
‘‘partial common principal components’’: matrices share
some eigenvectors; (3) ‘‘common principal components’’:
matrices share all eigenvectors; (4) ‘‘proportionality’’: ma-
trices share all eigenvectors, and eigenvalues all differ by the
same constant between matrices; and (5) ‘‘Equality’’: ma-
trices share eigenvectors and eigenvalues. For each model,
the Flury hierarchy calculates a log-likelihood statistic to
quantify the fit of that model to the observed matrices. A
likelihood ratio is then calculated for each model against the
model of ‘‘Unrelated Structure’’ (‘‘jump up’’ procedure,
Phillips and Arnold 1999). To avoid the assumption of mul-
tivariate normality in hypothesis testing and because the de-
grees of freedom are unknown under the null hypothesis,
randomization is used to determine the probability that a
model fits the data significantly better than the ‘‘Unrelated
Structure’’ model. In this analysis, 4999 randomized data sets
were created, each iteration randomly assigning whole fam-
ilies to species. The best fitting model (referred to as the
verdict in the Results section) is determined as the model
immediately under the first significant probability, going
from the bottom (‘‘Unrelated Structure’’ model) to the top
(‘‘Equality’’ model) of the hierarchy (‘‘jump up’’ procedure,
Phillips and Arnold 1999). The randomization procedure sets
the mean and standard deviation to 0 and 1, respectively, for
each trait in each randomized data set. This analysis was
performed using the program CPCrand (Phillips 1998a). Note
that because the CPCrand program does not include the op-
tion of nesting cages within families, GAFmatrix estimations
and comparisons by the Flury hierarchy were performed by
pooling the individuals of the two cages of a family. This
procedure is expected to bias the estimation of among-family
(co)variances because of common family environmental ef-
fects. However, comparisons of matrices using the T method
suggested that there is no large difference between the results
corresponding to the nested and nonnested designs (results
not shown).
Correlation Matrix Comparisons
Because many studies investigate correlation matrices in-
stead of (co)variance matrices, this study compared the re-
sults obtained through both types of matrices. Across-species
differences in phenotypic correlation matrices (rp) or in
among-family genetic correlation matrices (rAF) were per-
formed using the Mantel test (Mantel 1967; Dietz 1983; Chev-
erud et al. 1989). This test is based on estimating an unnor-
malized correlation coefficient between two matrices as
?
i?1
c
Z
?
M M ,
i1 12
i2
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FROM MICRO- TO MACROEVOLUTION THROUGH G
TABLE 3. Mean trait values (? 1 phenotypic standard deviation). Measurements are in mm and are not ln-transformed.
SpeciesFEMUR HEADPTHLPTHWOVIP
Gryllus integer
G. veletis
G. firmus
G. pennsylvanicus
G. texensis
G. rubens
Teleogryllus oceanicus
9.39 (0.47)
10.48 (0.41)
13.46 (0.69)
11.55 (0.59)
12.17 (0.76)
12.45 (0.61)
11.72 (0.66)
5.39 (0.28)
5.14 (0.20)
6.06 (0.34)
5.27 (0.29)
5.49 (0.33)
5.74 (0.29)
5.46 (0.31)
3.43 (0.21)
3.69 (0.19)
4.40 (0.27)
3.64 (0.27)
4.04 (0.31)
4.20 (0.24)
3.85 (0.25)
5.73 (0.30)
5.80 (0.23)
6.79 (0.39)
6.14 (0.35)
6.29 (0.41)
6.28 (0.33)
6.06 (0.35)
12.67 (0.85)
14.07 (0.81)
18.08 (1.34)
15.83 (1.65)
13.38 (0.99)
15.42 (1.08)
15.06 (1.00)
where Mi1and Mi2are the estimates of the ith element of the
two matrices and c is the number of nonredundant off-di-
agonal elements. The statistical significance of the Z statistic
is tested by a permutation procedure, in which the rows and
the corresponding columns of one matrix are randomly re-
ordered (4999 permutations). The null hypothesis of no as-
sociation between two matrices is rejected if less than 5% of
the permuted datasets produced a Z statistic greater than the
observed Z. For simplicity of interpretation, the Pearson prod-
uct-moment correlation (r), and not the Z statistic, is reported
in the results section. This test was performed using the pro-
gram MANTEL (Cavalcanti 2001).
Testing the Constraint Hypothesis
To test the constraint hypothesis, the ancestral GAFmatrix
and the D matrix (across-extant-species divergence matrix)
were estimated and then compared to each other. The esti-
mation of each of these two matrices requires the use of an
appropriate phylogenetic tree that will be used to account for
the nonindependence of the data points owing to the expected
resemblance of closely related species. Adequate branch
lengths must therefore be chosen based on the statistical as-
sumption of proportionality to the expected variance of trait
evolution (Felsenstein 1985; Harvey and Pagel 1991; Garland
et al. 1992; Garland and Ives 2000). In the current study, a
star phylogeny (i.e., all internal branch lengths are equal to
0 and all external branches are of equal length), and not the
published phylogeny, has been found to meet this assumption
for both the trait values and GAFmatrices because no phy-
logenetic signal was found in either cases (see Results). We
therefore use a star phylogeny, which is equivalent to not
using any phylogenetic correction, in all analyses.
The ancestral GAFmatrix was reconstructed by using max-
imum likelihood to compute the best pooled matrix given the
constraint that all extant GAFmatrices are equal (calculations
performed by the CPC program; Phillips 1998b). Although
this specific procedure does not have a formal justification
in phylogenetic reconstruction theory, it is in fact simply
averaging the eigenstructure of all seven extant species,
which is the proper procedure given no phylogenetic signal.
The D matrix was computed by using the mean trait values
of each species as data points, and by directly estimating the
variances and covariances of the five traits. This assumes no
phylogenetic signal. The constraint hypothesis was tested by
comparing the ancestral GAFmatrix to the D matrix. This
was done by calculating the angle between the corresponding
eigenvectors of the two matrices. We chose to compare ei-
genvectors because these represent the orientation of a matrix
in the multivariate space, and it is the direction of species
divergence that the ancestral GAFmatrix predicts. The ei-
genvectors of these two matrices were obtained by a principal
component analysis on each matrix separately. Only the first
and second principal components were used because, to-
gether, these explain approximately 90% of the whole vari-
ation (see Results section). The angle in radians between two
eigenvectors is calculated as ? ? cos?1[(eigenvectorAF)T
(eigenvectorD)] whereTindicates vector transposition. For
simplicity of interpretation, angles in degrees, not in radian,
are presented in the results section. The correlation between
the two vectors, rv? cos? (Cheverud and Leamy 1985), is
also reported. Testing the null hypothesis that ? ? 0 was not
possible because each matrix is based on only seven data
points, a number too low to allow statistical testing through
resampling methods. Instead, the range of values obtained
by deleting one species at a time (therefore producing a total
of seven angles) was reported.
RESULTS
Overview of the Data
Mean phenotypic trait values (Table 3) varied significantly
across species according to a one-way MANOVA (Wilk’s ?
? 0.01, F30, 32460? 168, P ? 0.001). A series of Tuckey
posthoc tests revealed that this overall difference between
species reflected differences in each of the five traits and
across almost all pairs of species (results not shown). The
largest species (G. firmus) was between 18% and 43% larger
than the smallest one (G. integer or G. veletis), depending on
the trait. The presence of genetic variation was tested in each
species separately using a nested MANOVA with family and
cage-nested-within-family as independent variables. All tests
revealed a very highly significant family effect, and a ma-
jority of tests revealed a significant cage effect (results not
shown). The magnitude of the family effect was always at
least twice as large as the cage effect (results not shown).
Heritabilities ranged from 0.14 to 0.73 and averaged 0.43
across traits and species. Genetic correlations ranged from
0.22 to 0.95 and averaged 0.72. Phenotypic correlations
ranged from 0.37 to 0.94, with an average of 0.74. Appendix
1 lists all among-family heritabilities, genetic correlations,
and genetic (co)variances, and Appendix 2 displays all phe-
notypic correlations and phenotypic (co)variances.
Phylogenetic Signal
We tested for the presence of a phylogenetic signal in the
mean trait values. The phylogenetic signal was estimated
separately for each of the five traits using the methodology
described in Blomberg et al. (2003). The K statistic, which
Page 6
2292
M. BE´GIN AND D. A. ROFF
FIG. 1.
statistic) against the phylogenetic distance between the correspond-
ing species. Values are ln-transformed on both axes. The correlation
between these two variables is not significant according to a Mantel
test (r ? 0.007, P ? 0.34), indicating an absence of phylogenetic
signal in GAFmatrices.
Plot of the pairwise difference between GAFmatrices (T%
FIG. 2.
Each result corresponds to a simultaneous comparison of all the
species under a particular node (e.g., the result for the root node
includes all seven species). Branch lengths are proportional to phy-
logenetic distances (see Table 1 for values). This graph shows that
there is no phylogenetic signal in GAFmatrices.
Flury hierarchy applied to each clade of the phylogeny.
quantifies phylogenetic signal while taking tree structure into
account, ranged from 0.24 to 0.55 (these are relatively low
values for size-related traits; Blomberg et al. 2003), which
indicated substantially less phylogenetic signal than expected
under a Brownian motion model (K ? 1 is the expectation
under this model). Unfortunately, the statistical significance
of the signal could not be tested because of our low sample
size (seven species). However, the low K values suggested
that a tree without structure (i.e., a star phylogeny) would be
more appropriate. This was confirmed, for each trait, by the
estimates of the mean square errors (MSE) of the tip data,
which were always lower for a star phylogeny than for the
original tree (results not shown). This suggested that a star
phylogeny fit the morphological data better than the original
phylogeny (Blomberg et al. 2003). We therefore used a star
phylogeny in all further analyses of trait value evolution.
The phylogenetic signal in GAFmatrices was estimated
with two different approaches. First, we plotted the difference
between pairs of GAFmatrices (estimated using the T% sta-
tistic) against the phylogenetic distances corresponding to
the same pairs of species. We used this procedure because
the proper methodology described by Blomberg et al. (2003)
is so far only developed for univariate data. The current pro-
cedure is however expected to provide very similar results
(T. Garland, Jr., University of California, Riverside, CA,
pers. comm., 2003). We found an absence of correlation be-
tween T% and phylogenetic distances (r ? 0.007, P ? 0.34;
Fig. 1), indicating that closely related species are not more
likely to have a similar GAFmatrix than are distantly related
species. Similarly, an absence of correlation with phyloge-
netic distance was found for P matrices using the T% statistic
(r ? ?0.20, P ? 0.58). This analysis was repeated for cor-
relation matrices, using the matrix correlations between pairs
of species as data points to plot against phylogenetic dis-
tances. The same result of no association was found for both
rAFmatrices (r ? 0.06, P ? 0.50) and rpmatrices (r ? ?0.11,
P ? 0.82). The second approach consisted in using the Flury
method to compare simultaneously all members of a clade
(i.e., all species under a particular node), going hierarchically
from the external nodes to the all-inclusive root node (Step-
pan 1997a). If GAFmatrix variation was phylogenetically
structured, we would expect matrix similarity to increase to-
wards the tips of the phylogeny. No such pattern was detected
(Fig. 2). The observed pattern was strongly influenced by the
two species that were found by the Flury hierarchy to have
a different GAFmatrix: G. integer and G. texensis (see below,
Table 4). For each clade that included one of these two spe-
cies, a result of ‘‘Unrelated structure’’ was found, with the
exception of the root node (Fig. 2). The result for the root
node was perhaps counterintuitive, but probably indicated
that the signal corresponding to the five similar matrices was
strong enough not to be overridden by the noise brought by
the two different matrices (G. integer and G. texensis). How-
ever, little is currently known about the statistical behavior
of the Flury method when many matrices are simultaneously
compared, and caution should be used in the interpretation
of such results. This analysis supported the results of the T%
analysis (see paragraph above), and confirmed the absence
of a phylogenetic signal in GAFmatrix variation. We there-
fore used a star phylogeny to analyze GAFmatrix evolution.
Comparisons of (Co)variance Matrices
To investigate the extent to which GAFmatrices differ
across species, we made all pair-wise comparisons of GAF
matrices using the T method and the Flury hierarchy. The T
method results for GAFmatrix comparisons revealed that two
species (G. integer and G. veletis) were significantly distinct
from the five other species (Table 4). Because multiple tests
were performed, we used binomial probabilities to test the
hypothesis that our results could be obtained by chance alone.
Given that a significant probability is expected by chance in
5% of the cases, the probability of observing six significant
Page 7
2293
FROM MICRO- TO MACROEVOLUTION THROUGH G
TABLE 4.
Results of pairwise comparisons of matrices. Results for the among-family matrices are shown above the diagonal and results for the phenotypic matrices are
presented below the diagonal. Variance-covariance matrices were compared using the T method and the Flury hierarchy, whereas correlation matrices were compared using
the Mantel test. The results of the T method consist of the T% statistic (this statistic increases with an increasing difference between two matrices) followed by the probability
corresponding to the null hypothesis that the two matrices are equal. The Flury hierarchy results consist of the model that best describes the difference between two matrices.
The Mantel test results consist of the correlation between two matrices, followed by the probability corresponding to the null hypothesis of no association between the matrices.
Gryllus
integer
G.
veletis
G.
firmus
G.
pennsyl.
G.
texensis
G.
rubens
Teleogryllus
ocean.
(Co)variance matrices: T method
G. integer
G. veletis G. firmusG. pennsylvanicus
—
57.6***12.0 29.9*
51.9
—
68.5*** 83.2***
99.9* 85.7**
—
24.3*
102.3*
88.2** 18.3
—
84.8 76.129.8 27.5
111.7*
98.6**22.718.4
87.6 72.419.226.2
G. texensis
G. rubens
T. oceanicus
39.8***
9.4
16.7
92.2***55.1*** 72.5***
28.1**14.8
9.7
37.9**31.8* 30.9*
—
42.5*** 23.6*
37.9
—
21.4*
35.8 31.9
—
(Co)variance matrices: Flury hierarchy†
G. integer
G. veletisG. firmus G. pennsylvanicus
—
PCPC1PCPC1
Unrelated
Unrelated
—
PCPC1
Unrelated
Equal
CPC
—
Unrelated
Proportional
Equal Equal
—
UnrelatedUnrelatedUnrelated
Equal
Unrelated
Equal
CPC
Equal
CPCCPC
ProportionalProportional
G. texensis
G. rubens
T. oceanicus
Unrelated
PCPC3 PCPC1
Unrelated
PCPC1
Unrelated
Unrelated
Proportional
Unrelated
UnrelatedUnrelatedUnrelated
—
Unrelated
PCPC3
Unrelated
—
Unrelated
EqualEqual
—
Correlation matrices: Mantel test
G. integer
G. veletisG. firmus G. pennsylvanicus
—
0.66 0.96**0.93**
0.86*
—
0.66 0.83
0.94* 0.77
—
0.94*
0.90* 0.83*0.81
—
0.95* 0.83**0.95 0.91*
0.63 0.76*0.670.64*
0.880.65 0.94* 0.77
G. texensis
G. rubens
T. oceanicus
0.97* 0.96**0.93*
0.66 0.720.52
0.99** 0.97**0.96*
0.96** 0.96* 0.90**
—
0.98*0.98*
0.67*
—
0.95*
0.92* 0.65
—
* P ? 0.05, ** P ? 0.01, *** P ? 0.001.
† Flury hierarchy: Equal, the two matrices share their principal components structure; Proportional, the two matrices share their eigenvectors but their eigenvalues differ by a constant; CPC, the
two matrices share their eigenvectors but not their eigenvalues; PCPC1 or PCPC3, the two matrices only share the first or the first three eigenvectors, respectively; and Unrelated, the two matrices
do not share their principal components structure.
Page 8
2294
M. BE´GIN AND D. A. ROFF
FIG. 3.
Matrix elements are multiplied by 1000 and are based on ln-transformed data. This graph is designed for comparing species with respect
to the overall pattern and therefore bars are not identified (but see Appendices 1 and 2 for values).
Magnitude of (A) GAFmatrix elements and (B) P matrix elements. Each histogram bar represents a variance or a covariance.
probabilities out of 21 tests (Table 4) by chance alone is P
? 0.001. We therefore conclude that the observed pattern of
significance is real. Table 4 shows that G. integer and G.
veletis differed from the other five species by 52% to 112%
(T% statistic), whereas the remaining species differed by no
more than 38% among themselves. These results can be easily
confirmed by the visualization of a simple plot of the matrices
(Fig. 3A), which revealed that the differences between spe-
cies detected by the T method reflected mostly differences
in the overall magnitude of matrix elements, as opposed to
a strong effect related to one or a few traits. A generally
similar result was found concerning the P matrix compari-
sons, with only one species (G. veletis) being consistently
significantly different (Table 4, Fig. 3B).
The pair-wise results of the Flury hierarchy revealed that
two species (G. integer and G. texensis) were significantly
different from the others in the principal component structure
of their GAFmatrix (Table 4); all verdicts of ‘‘Unrelated
structure’’ were associated with either G. integer or G. tex-
ensis. When any other two species were compared, a verdict
of ‘‘CPC,’’ ‘‘Proportionality,’’ or ‘‘Equality’’ was always
reached, indicating a conservation of the eigenvectors of the
GAFmatrix across species. When all seven species were com-
pared simultaneously, the Flury hierarchy yielded a result of
‘‘CPC,’’ which indicated that most of the species shared their
eigenvectors, but not necessarily their eigenvalues. In con-
trast, the analysis of P matrix variation revealed much less
common structure across species (Table 4).
Comparisons of Correlation Matrices
We investigated the differences between species with re-
spect to their among-family correlation matrices (rAF) and
phenotypic correlation matrices (rp) using the Mantel test.
The pair-wise comparisons of rAFmatrices across species
indicated a high level of correlation between these matrices,
with values ranging from 0.63 to 0.95 (Table 4). One species,
G. rubens, had a lower average across-species correlation
(average r ? 0.67) than the others species which ranged from
0.78 to 0.87. Despite their high value, approximately half of
these correlations were not statistically significant according
to the Mantel test (a binomial test showed that the number
of observed significant tests in Table 4 was not expected by
chance alone, P ? 0.001). This apparently counterintuitive
result can be explained by the fact that these high correlations
between matrices were produced mainly by one trait (OVIP).
This trait had a high leverage on the correlation between any
two rAFmatrices because it was consistently represented by
Page 9
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FROM MICRO- TO MACROEVOLUTION THROUGH G
TABLE 5.
and genetic covariances (below the diagonal). The lower part shows the across-extant-species variances, correlations (above the diagonal),
and covariances (below the diagonal). The ancestral GAFmatrix was reconstructed by maximum likelihood as the best pooled matrix
given the constraint that the GAFmatrices of all seven extant species are equal. The D matrix was estimated using the mean trait values
of the seven species as data points. Variances and covariances were multiplied by 1000 and are based on ln-transformed data.
The upper part of the table shows the ancestral among-family genetic variances, genetic correlations (above the diagonal),
Variance FEMURHEADPTHL PTHWOVIP
Ancestral GAFmatrix
FEMUR
HEAD
PTHL
PTHW
OVIP
D matrix
FEMUR
HEAD
PTHL
PTHW
OVIP
1.14
1.28
1.57
1.38
2.13
—
1.00
1.03
1.07
0.98
0.82
—
1.14
1.17
1.05
0.77
0.81
—
1.22
1.03
0.85
0.88
0.83
—
1.01
0.63
0.64
0.56
0.59
—
12.00
2.59
6.48
2.54
11.68
—
4.10
8.20
5.19
9.24
0.74
—
3.54
2.24
3.56
0.93
0.86
—
3.74
5.92
0.94
0.87
0.92
—
4.19
0.78
0.65
0.68
0.77
—
lower genetic correlations than the other four traits within
each species (Appendix 1). The results of the Mantel test
therefore suggested that species are similar in that they all
have low genetic correlations associated with the trait OVIP,
whereas less similarity between species existed with regard
to the genetic correlations of the other traits. This showed
that the results of the Mantel test are rightfully dependent on
the structure of the matrices being compared, and that high
correlations between species are not necessarily significant
if produced by only one trait. The analysis of phenotypic
correlation matrix variation indicated that the matrices of all
but one species (G. veletis) were significantly highly corre-
lated with each other (Table 4). The peculiarity of G. veletis
was that the trait OVIP was not consistently associated with
lower genetic correlation values in this species (Appendix
2).
Matrix Evolution versus Trait Evolution
To test whether GAFmatrices have evolved as a correlated
response to trait evolution, we plotted the differencesbetween
pairs of matrices (using the T% statistic) against a composite
index of morphological differences between the same pairs
of species (euclidean distances:
?
i?1
5
??
?x ¯
? x ¯ ?,
12
i1
i2
where x ¯i1and x ¯i2are the mean values of trait i for the two
species). Because there was no phylogenetic signal in the
trait values or in the GAFmatrices (see above), we did not
use a phylogenetic correction. We found no statistically sig-
nificant association between GAFmatrix distance and eu-
clidean distance (r ? 0.37, P ? 0.14). Similarly, an absence
of correlation with euclidean distance was found for P ma-
trices using the T% statistic (r ? ?0.33, P ? 0.82). This
analysis was repeated for rAFand rpmatrices, using the ma-
trix correlations between pairs of species as data points to
plot against euclidean distances. The same result of no as-
sociation was found for both rAF(r ? 0.31, P ? 0.17) and
rpmatrices (r ? 0.04, P ? 0.60).
Is P a Good Surrogate for G?
We investigated the extent to which patterns observed at
the level of phenotypic variation mirrored patterns observed
at the level of among-family genetic variation. The elements
of GAFwere moderately to highly correlated to the elements
of P within a species (range of the correlation coefficients:
0.54 to 0.96), a pattern also observed when comparing the
elements of the rAFmatrices to the elements of the rpmatrices
within a species (range: 0.71 to 0.98). Note that the statistical
testing of these correlations is not strictly valid because of
the part/whole relation between G and P, and therefore we
report no probability. By contrast, the correspondence be-
tween P matrix comparisons and GAFmatrix comparisons
across all species is highly dependent on the method em-
ployed. The results of the T method at the P and GAFlevels
only differed concerning G. integer (Table 4). Indeed, the
correlation coefficient for T% values between P and GAF
analyses was 0.86 if G. integer was removed from the anal-
ysis, but only 0.28 if it was kept in. The results of the GAF
matrix analysis using the Flury hierarchy differed completely
from the results of the P matrix analysis (Table 4). The results
of the Mantel test were more ambiguous. On the one hand,
the rAFand rpanalyses both indicated a generally high level
of correlation between species (the lowest correlation was
0.52, Table 4), but on the other hand, the results of the rAF
matrix comparisons were weakly correlated to the results of
the rpmatrices comparisons (r ? 0.21). Overall, these results
suggested that analyses of P and GAFmatrices may differ in
important ways depending on the method used and the species
studied.
Testing the Constraint Hypothesis
We reconstructed the ancestral GAFmatrix corresponding
to the seven extant species, and also estimated the D matrix
(Table 5). To investigate whether species divergence has pro-
ceeded along the multivariate direction that is the less ge-
netically constrained (i.e., more genetically variable), we es-
timated the angle ? (and the corresponding vector correlation
rv) between the first, and then second, eigenvector of these
Page 10
2296
M. BE´GIN AND D. A. ROFF
two matrices. The first vector explained approximately 80%
of the total variation in both matrices and was characterized
by trait loadings ranging from 0.40 to 0.49 in the ancestral
GAFmatrix and from 0.24 to 0.61 in the D matrix (eigen-
structure was similar for correlation matrices). The angle be-
tween the two first eigenvectors was 19.7 degrees (rv? 0.94),
and ranged from 10.9 to 27.8 degrees. The second eigenvector
explained approximately 10% of the variation in both ma-
trices, and was highly negatively correlated with OVIP and
weakly positively correlated with the four other traits. The
angle between the second eigenvector of the two matrices
was 14.0 degrees (rv? 0.97), and ranged from 11.8 to 39.4
degrees. We repeated this procedure using the rAFmatrices
(Table 5) and found an extremely close correspondence be-
tween the first eigenvectors, with an angle of 2.4 degrees (rv
? 0.999), and a range from 1.6 to 7.2 degrees. Much less
accuracy characterized the second eigenvectors, with anangle
of 26.1 degrees (rv? 0.90), and a range from 18.9 to 56.0
degrees. Overall, because no vector correlation was lower
than 0.90, and because the eigenvector loadings were at least
qualitatively similar in the two matrices, these results sug-
gested that the across-species trait divergence is oriented fair-
ly similarly to the among-family genetic variation of the an-
cestral species. However, this conclusion is more reliable in
the case of the first eigenvector, for which the range of angles
was narrower.
It is not possible to illustrate the above analysis in one
graph because of its five-dimensional nature, and therefore
we showed all bivariate combinations of traits separately
(Fig. 4). Note that the angles between eigenvectors presented
in the above paragraph corresponded to the whole dataset,
not to any of the pairs of traits shown in Figure 4. The
coordinates of the ellipses (two-dimensional representations
of matrices) drawn in Figure 4 were obtained using a program
written by Patrick Phillips (University of Oregon, Eugene,
OR). Each ellipse was centered on the reconstructed ancestral
mean trait values (estimated as the average values across
extant species) and was oriented in space as a function of its
eigenvector loadings. Ellipse size corresponded to one stan-
dard deviation. This figure allowed a visual confirmation of
the finding (see paragraph above) of a relatively similar ori-
entation of the ancestral GAFmatrix (solid ellipse) and D
matrix (dotted ellipse, Fig. 4).
DISCUSSION
G Matrix Variation across Species
The first part of this study described the pattern of GAF
matrix variation across seven species of field crickets. Our
results suggested that the GAFmatrix corresponding to mor-
phological traits was generally conserved across species.
Most species expressed a similar amount of among-family
genetic variation (Fig. 3A), had the same covariance matrix
structure (T method and Flury hierarchy), and had a similar
among-family correlation pattern with respect to the ovipos-
itor length (Mantel test). Despite this overall similarity, some
variation was apparent. The matrix corresponding to G. in-
teger differed significantly from the others according to the
T method and Flury hierarchy, and G. veletis, G. texensis,
and G. rubens were all found to differ significantly from the
other species by one of the three statistical approaches. How-
ever, it is important to note that G. integer had the largest
standard errors relative to the size of the (co)variance esti-
mates, and therefore that the finding that this matrix differed
from the others may be exaggerated because of poor matrix
estimation. Our conclusion is therefore that, although the GAF
matrix is not static and does differ across some species, its
average rate of evolution is low. A number of studies have
also shown that, contrary to theoretical expectations (Turelli
1988; Reeve 2000), G matrices often remain relatively con-
stant across populations or species in nature (reviewed in
Roff 2000; Steppan et al. 2002), even in cases where strong
natural selection is known to occur on the studied traits (Bak-
er and Wilkinson 2003). The G matrix is thought to be shaped
by the interaction between the mutational covariance matrix
(U, representing the univariate and pleiotropic effects of mu-
tations) and the matrix of quadratic selection (? matrix, in-
cluding stabilizing and correlational selection parameters),
although the relative importance of these two terms in nature
is not known (Lande 1980; Arnold 1992; Jones et al. 2003).
A recent simulation study (Jones et al. 2003) showed that G
matrix stability is strongly enhanced by pleiotropic mutations
and strong correlational selection, which implies that a G
matrix made of highly correlated traits is likely to be constant
through time, as we found here. No information is available
on these mutation and selection parameters in field crickets,
and therefore it is not currently possible to further understand
the general stability of G in this group of organism. More
research is required on G matrix evolution but, more im-
portantly, information on the U and ? matrices are needed
to better understand patterns of G matrix variation.
The next objective of this study was to identify predictors
of GAFmatrix variation. We first tested the hypothesis that
GAFmatrix evolution is a correlated response to trait value
evolution, which predicts that two species that are morpho-
logically different also differ with respect to their GAFma-
trices. Our results showed that there was no significant as-
sociation between these two variables in field crickets, a pat-
tern observed in other G (Podolsky et al. 1997) and P matrix
studies (Steppan 1997b; Marroig and Cheverud 2001; Baker
and Wilkinson 2003). Second, we tested whether GAFmatrix
evolution can be predicted using phylogenetic information.
Our findings indicated an absence of phylogenetic signal in
GAFmatrix variation, contrary to a previous conjecture based
on only three of the current seven species of crickets (Be ´gin
and Roff 2003). Particularly revealing in the current study
is the fact that the GAFmatrix of the Australian cricket T.
oceanicus was not different from most other matrices, despite
the fact that this species was distantly related to all six other
species. However, Blomberg et al. (2003) reported that using
a small number of species will often hamper the capacity to
detect phylogenetic signal in a trait, and that a signal is fre-
quently found when more species are included. This suggests
that, unless the signal is strong, the detection of a phylo-
genetic signal for matrices can only be achieved using a larger
numbers of species, a possibility that is only feasible with P
matrices. Such studies have so far reported an absence of
phylogenetic structure (Cheverud 1989; Badyaev and Hill
2000; Marroig and Cheverud 2001; Baker and Wilkinson
2003) or have only detected a weak signal (Goodin and John-
Page 11
2297
FROM MICRO- TO MACROEVOLUTION THROUGH G
FIG. 4.
on the ancestral mean trait values (diamond), and correspond to 1 SD. Both axes correspond to ln-transformed trait values in milimeters.
In each plot, the trait on the x-axis is given above the trait on the y-axis. Mean trait values of the seven extant species (black dots) are
plotted to provide an idea of species divergence. Each plot represents a bivariate plane which is part of the whole five-dimensional
dataset. This graph shows the general similarity in orientation of the two matrices.
Plots allowing the comparison of the ancestral GAFmatrix (solid ellipse) and D matrix (dotted ellipse). Both ellipses are centered
son 1992; Steppan 1997a, b; Ackermann and Cheverud 2000;
Ackermann 2002). Coupled with the current findings, this
may indicate that G matrix evolution is typically not strongly
associated with phylogenetic distances.
An alternative framework for predicting G matrix evolu-
tion is to test for the association between that matrix and
some variable that can be linked to selection or genetic drift
in the wild. A few studies have found such associations.
Latitudinal gradients have been shown to be correlated with
the additive genetic variance of photoperiodic response and
developmental time in the pitcher-plant mosquito Wyeomyia
smithii (Hard et al. 1993; Bradshaw et al. 1997), with the
Page 12
2298
M. BE´GIN AND D. A. ROFF
additive genetic variation of two morphological traits in two
crickets of the genus Allonemobius (Roff and Mousseau
1999), and with the additive genetic variance of wing char-
acters in the fruit fly Drosophila melanogaster (van’t Land
et al. 1999). Changes in a G matrix corresponding to a suite
of morphological traits in the amphipod Gammarus minus
have been shown to be consistent with the hypothesis of an
adaptation to caves (Fong 1989; reanalyzed in Jernigan et al.
1994; Roff 2002a). Blows and Higgie (2003) have concluded
through an experimental sympatry experiment using two Dro-
sophila species that natural selection has produced changes
in a G matrix composed of cuticular hydrocarbons. In New
World monkeys, P matrix studies have shown that matrix
variation for cranial morphology was weakly correlated with
diet (Marroig and Cheverud 2001), and the variation of a P
matrix corresponding to hydrocarbon composition was cor-
related with geographical distribution in the mangrove Avi-
cennia germinans (Dodd et al. 2000). The effect of genetic
drift on G has been recently demonstrated through an in-
breeding experiment on the wing morphology of Drosophila
melanogaster (Phillips et al. 2001). This study showed that
the effect of drift on one particular population was not pre-
dictable, but if averaged over large numbers of populations,
the effect of genetic drift on the G matrix was consistent
with classical population genetic theory. These studies show
that G matrices do vary and that their pattern of evolution
can be predicted to some extent. We need more such studies
to gain understanding of the causes of G matrix variation in
the wild.
The current study does not allow for the investigation of
the role of selection or drift in producing G matrix variation
across cricket species. Our only available data indicated that
GAFmatrix variation was not predictable from known selec-
tive regimes in three of the current cricket species (Be ´gin
and Roff 2003). However, the ‘‘plasticity’’ of GAFhas been
explored in some of these crickets and can be related to the
differences across species. A preliminary study had suggested
that rearing environment had an effect on the GAFmatrix,
and that this effect could be greater than the difference be-
tween two closely related species reared in the same envi-
ronment (Be ´gin and Roff 2001). To further investigate the
environmental sensitivity of GAFmatrices, Be ´gin et al. (2004)
have reared G. firmus under three temperatures, and compared
GAFmatrices across temperatures and wing morphologies.
The across-treatment differences in GAFmatrix ranged from
25% to 145% (T% statistic), and five out of six matrices
shared all their eigenvectors (Flury hierarchy). These results
are very similar to the ones obtained here, where the range
of T% values was from 18% to 112%, with five of seven
species sharing their eigenvectors. It therefore appears that
environmentally induced GAFmatrix variation is on the same
order of magnitude as the GAFmatrix variation observed
across species. Because the species used in the current anal-
ysis are presumably adapted to different climates, it is likely
that the common garden conditions produced a slightly dif-
ferent effect on the morphological development of each crick-
et species. This suggests that genotype by environment in-
teraction may be responsible for a part of the GAFmatrix
differences between field cricket species, and that less dif-
ference than currently reported may exist between species
with respect to GAF. This strengthens the conclusion that the
GAFmatrix corresponding to cricket morphological traits has
not changed substantially across evolutionary time scales.
Recommendations on Matrix Comparisons
Estimating G matrices is a very time- and work-intensive
task that severely limits investigators in the number of dif-
ferent groups that can be sampled. Finding that the P matrix,
which is much easier to estimate, is a relatively good sur-
rogate for the G matrix would be of great interest. We have
shown that estimates of phenotypic (co)variances were mod-
erately to highly correlated to among-family (co)variances
within each cricket species (i.e., P vs. GAF), a pattern also
observed with respect to correlations (i.e., rpvs. rAF). Given
that there is no strong theoretical reason to expect P and G
to be always proportional to each other (Willis et al. 1991),
similarity between these two levels of variation has been
observed surprisingly often (Cheverud 1988; Reusch and
Blanckenhorn 1998; Waitt and Levin 1998). A slightly dif-
ferent issue is whether matrix comparison methods generally
produce the same answer when comparing P matrices across
groups than when comparing G matrices across the same
groups. Our results suggested that the answer depends strong-
ly on the statistical approach used. The T method provided
a relatively good correspondence between the results of P
and GAFanalyses, but diverged widely in the case of one
species (G. integer). The Mantel test detected a pattern of
high correlation between species for both rpand rAFmatrix
analyses, but the details of the pair-wise comparisons of spe-
cies differed completely across the two types of matrices.
Finally, the results of the Flury hierarchy differed completely
between P and GAFanalyses, in large part because of an
apparent oversensitivity of this method to sample size (Phil-
lips and Arnold 1999; Steppan 1997a; Ackermann and Chev-
erud 2000; Marroig and Cheverud 2001). Overall, these re-
sults suggest that P is generally proportional to GAFwithin
each species, but the statistical relationship between P and
GAFseems to sometimes differ across species. We therefore
suggest that an estimate of P can be used as a surrogate for
GAFwithin one studied species, but the results of a P matrix
comparison across species should not systematically be used
as a surrogate for the results of the GAFmatrix comparison
between these species, particularly when using the Flury hi-
erarchy.
Many studies have simultaneously analyzed correlation
and (co)variance matrices and found that the former are gen-
erally more conserved across groups than the latter (Lofsvold
1986; Kohn and Atchley 1988; Steppan 1997a; Ackermann
and Cheverud 2000; Marroig and Cheverud 2001; Baker and
Wilkinson 2003). This phenomenon is caused by the presence
of variances in the (co)variance matrix. In addition to that
extra level of information which increases the probability of
finding differences across groups, the presence of different
scales within a (co)variance matrix often increases the dif-
ficulty of adequately appraising the difference between two
or more matrices (Houle et al. 2002). The current study found
that details differed across these two types of analyses, as
they also did across different methods of G matrix analysis.
This reveals that matrices can vary in many different ways
Page 13
2299
FROM MICRO- TO MACROEVOLUTION THROUGH G
and suggests that multiple matrix comparison methods should
always be used simultaneously. This is especially important
because little is known about these methods and because no
current method is fully satisfactory (Steppan et al. 2002).
The G Matrix as an Evolutionary Constraint
The last part of this study tested the constraint hypothesis
of quantitative genetics on field crickets. This hypothesis
predicts that the phenotypic divergence of extant species has
occurred in directions determined by the ancestral G matrix.
We found that, although not completely constrained by the
GAFmatrix, cricket species divergence mostly occurred in
the main multivariate direction of the ancestral GAFmatrix,
especially so when rAFmatrices were used in the analysis.
This result has also been shown in other P or G matrix studies
(Sokal and Riska 1981; Bond and Midgley 1988; Armbruster
1991; Bjo ¨rklund and Merila ¨ 1993; Andersson 1996; Mitchell-
Olds 1996; Schluter 1996; Badyaev and Foresman 2000; Ack-
ermann and Cheverud 2002; Baker and Wilkinson 2003;
Blows and Higgie 2003; Hansen et al. 2003a, b; Marroig et
al. 2004). In addition, Roff and Fairbairn (1999) have used
quantitative genetic information obtained from a population
of the cricket G. firmus to provide a quantitatively accurate
prediction of physiological trait values in a distinct natural
population, thus confirming the capacity of the constraint
hypothesis to predict evolutionary change. Overall, these
studies suggest that quantitative genetics can be relatively
successful at predicting macroevolutionary patterns from mi-
croevolutionary processes.
The most important limitation of tests of the constraint
hypothesis is that this type of analysis is only correlative and
cannot be used to prove a cause-effect relationship unless
information on past adaptive landscapes and past genetic drift
(or, more likely, surrogates for them) is available. In fact,
the results of the current study can be explained by a few
alternative models. First, the observed similarity in orien-
tation between the ancestral GAFmatrix and the D matrix
may indeed reflect the effect of strong genetic constraints
regardless of the adaptive landscape. Although theoretical
studies have shown that the G matrix is irrelevant to long
term evolution when a single stable adaptive peak is assumed
(Lande 1979; Via and Lande 1985; Zeng 1988), the opposite
is true in the context of a complex or fluctuating adaptive
landscape (Lande 1979; Bu ¨rger 1986; Price et al. 1993). Two
alternative models also predict a proportionality between G
and D: genetic drift in the absence of selection, and neutral
traits correlated with a trait under selection (Lande 1979;
Riska 1989). Finally, it is possible that the G matrix is readily
shaped by natural selection and does not constitute a long-
term genetic constraint. In this case, the alignment of the G
and D matrices is expected because the orientation of each
matrix is directly determined by the adaptive landscape (Ar-
nold et al. 2001). Very little information, theoretical or em-
pirical, is currently available for distinguishing between these
alternative explanations. Thus far, only one study has for-
mally compared the orientation of the G matrix to the ori-
entation of the matrix of quadratic selection (Blows et al.
2004) to test whether the G matrix and species divergence
are both shaped by selection. No correspondence was found
between the orientation of selection and G, but selection was
mostly directional. It thus remains to be shown whether
‘‘dome-shaped’’ selection surfaces are typically oriented in
the same direction as G matrices. Despite the extreme dif-
ficulty of identifying causal relationships, several investi-
gators use a simple drift/selection dichotomy in the inter-
pretation of their results, where a strong correlation between
the G and D matrices is interpreted as the effect of drift,
whereas a weak correlation is explained by the effect of se-
lection overriding genetic constraints (e.g, Lofsvold 1988;
Ackermann 2002; Marroig and Cheverud 2004). This is very
appealing, but most likely does not provide a reliable un-
derstanding of past evolutionary events.
In the event that the G matrix is indeed a long-term con-
straint to evolution, the next step is to try to understand what
factor(s) have provided the evolutionary momentum that,
coupled with constraints, resulted in the evolution of field
crickets. Our results showed that the first eigenvector of the
D matrix explained close to 80% of the total variation and
was characterized by approximately equal and positive load-
ings for all five traits. This type of vector is typically inter-
preted as mainly representing the effect of size (Jolicoeur
and Mosimann 1960). Body size is often thought to be adap-
tive (Peters 1983; Calder 1984; Schmidt-Nielson 1984; Roff
2002b) and differences in body size across cricket species
could therefore be the result of selection reflecting different
optimal value in the respective environments of the seven
cricket species studied here. However, this is unlikely to be
the sole explanation because cricket species differ much more
conspicuously at the level of their diapause strategy and call-
ing song (Alexander 1962; 1968; Masaki and Walker 1987;
Huang et al. 2000), which suggests that evolutionary changes
in cricket body size has been caused by a correlated response
to selection on these traits. Furthermore, field crickets typi-
cally live in ephemeral environments (Alexander 1968), and
thus founder effects could be influential in randomly altering
body size. It is a very common finding in many organisms
that the first eigenvector of morphological G matrices is a
size vector (reviewed in Bjo ¨rklund 1996). This suggests that,
as a general rule when the constraint hypothesis is valid,
closely related species can be expected to differ mainly in
size as opposed to shape (Bjo ¨rklund 1991, 1996). In the cur-
rent study, variation in shape was much less important than
variation in size because the second eigenvector of the D
matrix explained only approximately 10% of the variation.
This vector was characterized by a strongly negative loading
on ovipositor length (OVIP) and weakly positive loadings on
the other traits. The ovipositor length is an ecologically im-
portant trait because the depth at which eggs are laid in the
soil is associated with fitness (Masaki 1986, but see Re ´ale
and Roff 2002 for behavioral factors influencing depth). This
peculiar relationship between the ovipositor length and body
size has also been observed across populations of the striped
ground cricket Allonemobius socius, in which body size de-
creases with latitude (Mousseau and Roff 1989) whereas ovi-
positor length proportionally increases (Mousseau and Roff
1995). This latitudinal gradient strongly suggests that selec-
tion may have had an important role in shaping this aspect
of cricket morphology. Overall, field cricket species differ
Page 14
2300
M. BE´GIN AND D. A. ROFF
mainly in size, but also in a specific aspect of shape related
to ovipositor length.
The Comparative Method
The current analysis uses the tools of the comparative
method to estimate across-species covariations and to recon-
struct ancestral values. Because the objective of a phyloge-
netic correction is to remove the non-independence of data
points caused by the resemblance of related species (Felsen-
stein 1985; Harvey and Pagel 1991), this pattern of resem-
blance (i.e., phylogenetic signal) must be quantified, and
proper branch lengths chosen (Blomberg et al. 2003). Our
results indicated that neither trait values nor GAFmatrices
expressed a strong phylogenetic signal, and that a star phy-
logeny better fit the tip data (note that this result does not
invalidate the current cricket phylogeny, it merely states that
morphological trait evolution and GAFmatrix evolution did
not seem to be correlated with mitochondrial gene evolution).
This effectively simplified the analysis because using a star
phylogeny is equivalent to not correcting for phylogeny. The
finding of a signal would have added some additional steps
to the analysis. Some other set of branch lengths would have
been chosen (Blomberg et al. 2003), across-species covari-
ations estimation would have been implemented using In-
dependent Contrasts (Felsenstein 1985; Garland et al. 1992;
Garland and Ives 2000), and the ancestral GAFmatrix would
have been reconstructed using a methodology similar to that
developed by Steppan (1997b). Every study testing the con-
straint hypothesis or other related models should make use
of the tools of the comparative methods.
An inherent problem related to the current analysis is that
ancestral reconstruction is risky and typically associated with
very large standard errors (Schluter et al. 1997). Fortunately,
the current data set is relatively suitable for ancestral recon-
struction because we showed that GAFmatrices were gen-
erally similar across cricket species, and Schluter et al. (1997)
demonstrated that estimation accuracy increases withincreas-
ing rarity of change. It should however be kept in mind that
what we call the ancestral GAFmatrix is in fact the average
of the seven species matrices, which will approximate the
ancestral matrix only if matrix evolution proceededaccording
to the assumptions of the reconstruction method.
Conclusion
Overall, the current results are compatible with the hy-
pothesis that the G matrix has been influential in shaping
extant species morphological divergence in field crickets. Be-
cause G matrices corresponding to morphological traits have
also been found to be similar across species in a variety of
organisms (reviewed in Roff 2000; Steppan et al. 2002), and
because the constraint hypothesis has been supported in sev-
eral plant and animal studies (see references above), it there-
fore appears that quantitative genetic variation is generally
important during morphological evolution, and can be used
to model macroevolutionary patterns.
ACKNOWLEDGMENTS
We thank D. Houle and two anonymous reviewers for their
comments on this manuscript. This work could not have been
done without the invaluable laboratory assistance of R. Nil-
son, E´. Geoffroy, B. Mautz, R. Roff, and A. Mejia. Special
thanks go to K. Emerson, V. Debat, M. Foellmer, and A.
Bertin for stimulating discussions and important input on
statistics and programming. T. Garland, Jr. and E. Rezende
provided advice for the use of the comparative method. We
would like to thank A. Simons for providing the G. penn-
sylvanicus dataset, L. Higgins for collecting G. texensis, M.
Zuk for providing a stock of T. oceanicus, and A. Hedrick
for collecting G. integer. We acknowledge McGill University
for the opportunity to sample at the Gault estate. This work
was supported by Natural Sciences and Engineering Research
Council of Canada (NSERC) and Fonds Que ´be ´cois de la Re-
cherche sur la Nature et les Technologies (NATEQ) schol-
arships to MB and by a NSERC operating grant and startup
funds from the University of California-Riverside to DAR.
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