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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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