GENETIC VARIATION AND COVARIATION IN
FLORAL ALLOCATION OF TWO SPECIES OF
SCHIEDEA WITH CONTRASTING LEVELS OF
Diane R. Campbell,1,2,3Stephen G. Weller,1,4Ann K. Sakai,1,5Theresa M. Culley,3,6Phuc N. Dang,1
and Amy K. Dunbar-Wallis1
1Department of Ecology and Evolutionary Biology, University of California, Irvine, California 92697
3Department of Biological Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0006
Received June 15, 2010
Accepted September 30, 2010
The evolution of sexual dimorphism depends in part on the additive genetic variance–covariance matrices within females, within
males, and across the sexes. We investigated quantitative genetics of floral biomass allocation in females and hermaphrodites
of gynodioecious Schiedea adamantis (Caryophyllaceae). The G-matrices within females (Gf), within hermaphrodites (Gm), and
between sexes (B) were compared to those for the closely related S. salicaria, which exhibits a lower frequency of females and
less-pronounced sexual dimorphism. Additive genetic variation was detected in all measured traits in S. adamantis, with narrow-
sense heritability from 0.34–1.0. Female allocation and floral size traits covaried more tightly than did those traits with allocation to
stamens. Between-sex genetic correlations were all <1, indicating sex-specific expression of genes. Common principal-components
analysis detected differences between Gfand Gm, suggesting potential for further independent evolution of the sexes. The two
species of Schiedea differed in Gmand especially so in Gf, with S. adamantis showing greater genetic variation in capsule mass
and tighter genetic covariation between female allocation traits and flower size in females. Despite greater sexual dimorphism in
S. adamantis, genetic correlations between the two sexes (standardized elements of B) were similar to correlations between sexes
in S. salicaria.
KEY WORDS: G matrix, genetic correlation, gynodioecy, Schiedea adamantis, Schiedea salicaria, wind pollination.
Many organisms have dimorphic breeding systems in which there
are two or more morphs of different sexual expression. These
breeding systems include dioecy (complete separation of males
and females), along with a variety of other systems such as gyn-
odioecy (females and hermaphrodites coexist in populations) and
more rarely (Lloyd 1974; Weeks et al. 2006) androdioecy (males
and hermaphrodites). Sexual dimorphism between males and fe-
males is a familiar phenomenonin animals, and it is also common
in flowering plants, not only for primary reproductive traits but
also for a broad range of secondary characters (Delph et al. 1996;
Shykoff et al. 2003). In theory, sexual dimorphism is predicted to
evolve according to the nature of sex-specific selection favoring
different trait combinations, but the process also depends on the
C ?2010 The Author(s). Evolution C ?2010 The Society for the Study of Evolution.
Evolution 65-3: 757–770
DIANE R. CAMPBELL ET AL.
in a G-matrix (Lande 1980). In randomly mating populations,
evolutionary responses in sexually dimorphic traits will depend
on the levels of additive genetic variance and covariance within
males and females (Gmand Gfmatrices) and the levels of genetic
covariance between the sexes (hereafter B matrix; Lande 1980;
Reeve and Fairbairn 2001), with additional genetic parameters
also of importance in inbreeding species (Kelly 1999). Gmand
Gfcan differ for a variety of reasons, including differential ex-
pression of genes in different sexes, and linkage of those genes
to genes controlling sex. In species with chromosomal sex de-
termination, the homogametic sex is expected to show twice the
level of genetic variance for sex-linked traits, in the absence of
dosage compensation (Lynch and Walsh 1998). Sex-specific pat-
of sexual dimorphism (Rhen 2000; Fairbairn and Roff 2006).
The expected evolutionary response to selection depends as
well on the magnitude of between-sex genetic covariances (el-
ements of B) and their standardized measures of genetic corre-
lations. Departure from perfect between-sex correlation (r = 1)
for homologous traits indicates some sex-specific gene expres-
sion that contributes to independent evolutionary trajectories for
the different sexes (Via and Lande 1985). Between-sex genetic
correlations are theoretically expected to be lower for traits show-
ing greater sexual dimorphism, provided the dimorphism reflects
sex-specific effects of alleles (Fairbairn and Roff 2006). In sum,
similarities of quantitative genetic architecture between the sexes
tend to impede the evolution of sexual dimorphism, whereas dif-
ferences between Gmand Gfalong with low values for between
sex correlations can accelerate it (Poissant et al. 2010).
Despite this theoretical development, relatively few studies
have measured sex differences in genetic variance and covari-
ance of reproductive traits in flowering plants, and especially few
have included between-sex correlations. A review by Ashman
and Majetic (2006) uncovered between-sex correlations for mul-
tiple traits in only three plant species, with conflicting results.
Silene latifolia and Fragaria virginiana followed the predicted
pattern of an inverse relationship between sexual dimorphism and
siphilitica did not. In all three cases, as well as in the few later
correlations were generally detectably smaller than 1, suggesting
some genetic variation in sex-specific expression.
Although the above studies compared G-matrices between
sexes, similar comparisons across related species differing in sex-
ual dimorphism would provide further insight into the evolution
of those traits. The simplest application of models of phenotypic
evolution assumes that the G-matrix is constant, but comparisons
across species have often found evolutionary changes (review in
Steppan et al. 2002). Selection, drift, and mutation can all play
roles in such changes (Turelli 1988). For example, correlated
selection for particular trait combinations not predictable from
effects of individual traits on fitness can promote the evolution of
generic species have been compared (e.g., Davis 2001; Fishman
et al. 2002; Weller et al. 2007). The between-sex matrix is par-
ticularly rarely characterized. A review by Barker et al. (2010)
uncovered just two cases in plants and three in animals where it
was possible to test whether the elements of B are smaller than
the elements of the within-sex matrices, as expected theoretically
vious studies of plant reproductive characters that have compared
all three Gm, Gf, and B matrices across closely related species.
Gynodioecious species are especially appropriate for such
a comparison, as gynodioecy is frequently an intermediate stage
in the evolutionary transition from hermaphroditism to dioecy
(Charlesworth and Charlesworth 1978). Although cytoplasmic
male sterility genes frequently act in concert with nuclear restor-
ers in gynodioecious species, nuclear control of male sterility is
also possible (Weller and Sakai 1991; Eckhart 1992). In those
cases where control of male sterility is through nuclear genes, fe-
substantial inbreeding depression. If progeny of females increase
in frequency because of their higher relative fitness compared
to progeny of hermaphrodites, hermaphrodites are predicted to
invest more in male function, and eventually lose female func-
tion altogether. Models for sex allocation assume that there is
heritable variation for biomass allocation, and that resources no
longer used for female function can be shunted into male function
(Charlesworth and Charlesworth 1981; Charnov 1982), generat-
ing, all else equal, a negative genetic correlation between alloca-
allocation is central to models for the evolution of breeding sys-
tems, G-matrices for such allocation traits have received little
attention (Sakai et al. 2008).
In this study, we compare G-matrices for biomass allo-
cation between females and hermaphrodites of gynodioecious
Schiedea adamantis (Caryophyllaceae) and between that species
far fewer females in populations. Schiedea adamantis is part of a
lineage of 34 species restricted to the Hawaiian Islands (Wagner
et al. 2005). Within this lineage, S. adamantis and most other
sexually dimorphic species, including S. salicaria, are placed in
one poorly resolved clade of 12 species (Nepokroeff et al. 2005).
In populations of S. salicaria, which represents an early stage in
the evolution of gynodioecy, females occur at a frequency of 12–
13%. Outcrossing rates and inbreeding expression in this species
indicate that it is under selection for increased sexual dimorphism
(Sakai et al. 1989; Weller and Sakai 2005). In a previous study
of S. salicaria, we found moderate narrow-sense heritabilities for
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COMPARISON OF G MATRICES BETWEEN SEXES AND SPECIES
biomass allocation traits, indicating potential for an evolutionary
response to selection for increased allocation to male function in
hermaphroditic individuals (Sakai et al. 2008). In S. adamantis,
females occurred in a frequency of 39% before drought elimi-
nated most members of its only known population. Unlike S. sali-
caria, females of S. adamantis produce considerably more seed
than hermaphrodites, suggesting that even in the absence of the
strong inbreeding depression characteristic of S. adamantis, fe-
males would be favored and increase in frequency (Sakai et al.
In this study, we first quantified the levels of sexual dimor-
phism in floral biomass allocation traits in S. adamantis and
compared them to published data for S. salicaria (Sakai et al.
2008). Next, we asked two questions about heritabilities and the
G-matrices for allocation traits in S. adamantis. (1) How do the
overall levels of heritability and the patterns of genetic variation
and covariation compare between females and hermaphrodites?
(2) Are female allocation traits more closely integrated with each
other, as reflected in tighter genetic correlations, than with male
allocation traits or flower size? Finally, we asked two questions
related to comparisons of our new data on S. adamantis with the
previous study of S. salicaria. (3) Are genetic correlations be-
tween female allocation traits within sexes higher in S. adamantis
than in S. salicaria, as predicted if selection for greater integra-
ogous traits lower in S. adamantis and for specific traits that show
greater sexual dimorphism?
Materials and Methods
Schiedea adamantis St. John is a perennial, woody shrub known
from a single population in dry shrubland on the north slope of
Diamond Head Crater (Oahu, Hawaii) at approximately 125 m
(Wagner et al. 2005). This species presumably had a broader
distribution in the past, based on introgression of genes from
S. adamantis into populations of coastal S. globosa on the wind-
ward side of Oahu (L. Wallace, pers. comm.). The reduction in
range of S. adamantis probably results from grazing by nonnative
ungulates, from introduced rats, and from invasive plant species.
The sole remaining population is gynodioecious, and contained
possibly related to drought, reduced the population size from 244
flowering individuals in 1993 (U.S. Fish and Wildlife Service
adamantis, like other sexually dimorphic species of Schiedea, is
wind pollinated (Weller et al. 1998, 2007). Schiedea salicaria is
similar in general form to S. adamantis, but with only 12–13%
females and is endemic to steep, windswept ridges of the West
Maui Mountains of Hawaii (Wagner et al. 2005).
Both species of Schiedea have mixed-mating systems, with
outcrossing rates of near 1 in females and 0.3 to 0.6 in
hermaphrodite zygotes of S. adamantis and S. salicaria, respec-
tively (Sakai et al. 1997; Weller and Sakai 2005). In partially
selfing populations, responses to selection can depart from those
predicted by additive genetic variances and covariances, depend-
ing on the strength of directional dominance. Models suggest that
such effects are expected to be similar between the two species
of Schiedea, assuming dominance variation is similar (Kelly and
Williamson 2000), because they have similar levels of inbreed-
ing depression (0.6–0.8 in S. adamantis and S. salicaria, respec-
tively) as well as outcrossing rates. Effects of inbreeding may be
low in any case because a fixation index near zero in flowering
adults suggests that inbred individuals do not survive to flower in
S. adamantis (Sakai et al. 1997) or S. salicaria (A. K. Sakai and
S. G. Weller, unpubl. data), likely minimizing direct selection on
reproductive traits in the inbred cohort.
We used a modified partial diallel breeding design to measure
G-matrices and associated measures of heritabilities and genetic
correlations (Fig. 1). Parent plants used for the crossing program
were grown in the University of California, Irvine greenhouse
from seeds that were themselves obtained by a previous genera-
lation. The original seeds were collected in 1988, 1990,1996, and
1997, prior to the drought causing the decline in this population.
from each of 30 families was mated to three females in a partial
1. Crossing design. One heterozygous hermaphrodite
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DIANE R. CAMPBELL ET AL.
Male sterility in Schiedea is under the control of a single nuclear
gene (Weller and Sakai 1991). Hermaphroditic plants are ho-
are homozygous recessive (hh). To ensure that the progeny of
S. adamantis would include both hermaphrodites and females, 30
heterozygous hermaphrodites (genotype Hh) from unrelated fam-
ilies were each crossed to three unrelated females (genotype hh),
subject to the constraint that each female was also crossed with
three hermaphrodites from different families. A total of 90 full
sibships resulted from this crossing program. Using this design,
we estimated additive genetic variances by examining the com-
ponent of variation among the 30 paternal half-sibship families
(Kearsey 1965; Meagher 1992). This crossing program followed
the same breeding design that we used for S. salicaria (except
that the earlier study used 35 families instead of 30; Sakai et al.
2008), allowing comparisons between the species. Both studies
ing; except in rare cases, the hermaphrodite parent and the female
from seed from independent crosses between plants from differ-
ent maternal families. The extra generation of outcrossing had
the advantage of eliminating any maternal effects due to variable
environments in the field. For both species, progeny were raised
in the greenhouse using similar growth conditions. We could not
conduct these studies in the field because of the extremely steep
terrain where these plants grow and the potential negative im-
pacts on the sole population of the federally listed endangered
Seeds from the 90 full sibships were planted in fall 2001, and
progeny were transplanted to 8 cm2pots in 2002 before biomass
measures were made. Liquid fertilizer (Grow More; 20-20-20
NPK plus micronutrients) was applied weekly (350–400 PPM)
and plants were watered as needed until plants reached flowering.
The inflorescence of Schiedea is a determinate, compound dicha-
sium, and flowering is initiated when the most distal flower on
the main axis opens. The distal flowers on the lateral branches,
referred to as terminal flowers in this article, open next, followed
by the axillary, or lateral flowers. Because terminal and lateral
flowers differ substantially in size and morphology (Weller et al.
2006, 2007), we measured allocation in both types of flowers.
Floral allocation traits were measured in 2002 for a total of
933 individuals (approximately five plants per sex for each of the
90 full sibships). Models of sex allocation are usually based on
partitioning of a single resource, and we chose biomass as the
measure of common currency. Whereas biomass may or may not
1986; Ashman 1994), the sheer number of measurements to be
made (total of 448 female plants × 6 traits × 4 flowers + 485
rencies. The six traits for females were: carpel biomass (female
allocation trait at flowering), capsule biomass (female allocation
sepals), each measured for both terminal and lateral flowers. As
as this species has no petals. On hermaphrodites, we measured
these six traits plus stamen biomass (male allocation trait) on ter-
were too small to collect and weigh. Each measure was replicated
on four flowers per plant, but because flowers of S. adamantis are
protandrous, and stamens and carpels mature at different times,
hermaphroditic flowers of different ages were collected for mea-
surements of stamens and carpels. Stamens were collected on
the first day of anthesis, before anthers dehisced. Flowers of both
later to standardize potential age-related differences for remain-
ing measures of biomass. To provide a consistent background
level of pollination for the assessment of biomass allocation to
capsules, two inflorescences of each of three female and three
hermaphroditic individuals of each full sibship were completely
evidence for pollen limitation under field conditions (Sakai et al.
For each trait, biomass was weighed to the nearest 0.001 mg
dried at 67◦C. Full-sibship means were calculated based on plant
means, and the mean for each of the 30 paternal sibships was
calculated as the average of the three full sibships with the same
hermaphrodite used as a paternal parent.
We used both univariate and multivariate methods to compare the
by paternal sibship. For the univariate method, we used paired t
tests, and then adjusted significance levels for multiple compar-
isons using the sequential Bonferroni test. Sexual dimorphism of
each trait was quantified by: SD = [(mean for larger sex/mean
for smaller sex) −1] (Poissant et al. 2010). For the multivari-
ate method, we ran multivariate analysis of variance (MANOVA)
with the factor sex and a blocking factor of paternal sibship, fol-
lowed by a canonical discriminant analysis to identify the traits
contributing most to the difference between sexes.
QUESTIONS 1 AND 2: COMPARISON OF G MATRICES
WITHIN S. ADAMANTIS
Additive genetic variance and covariances, narrow-sense heri-
tability, and genetic correlations were estimated by examining the
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COMPARISON OF G MATRICES BETWEEN SEXES AND SPECIES
ues were estimated separately for the hermaphroditic and female
progeny using Proc Mixed in SAS version 9.1 (SAS Institute,
Cary, NC 2002–2003). The model included effects of paternal
parent and maternal parents, both specified as random factors
because the original parental plants were a random subset of
genotypes in the natural population, and a residual error term. We
did not include an interaction between the paternal and mater-
nal parent because the large number of missing cells in a partial
diallel would complicate its interpretation (Weller et al. 2006).
We obtained standard errors for the heritability estimates using
Proc Iml in SAS, following code given by Holland et al. (2003).
Their code implements the delta method for finding approximate
standard errors for heritabilities based on variance components.
Significance of the paternal effect was tested using a log
likelihood ratio test to compare the full model with a reduced
model containing only the maternal parent effect and residual
error (Littell et al. 1996). A significant effect of the paternal half-
sibship implies significant additive genetic variance (Lynch and
Walsh 1998). Additive genetic variance (VA) was estimated for
each trait in females and in hermaphrodites by multiplying the
paternal variance component by four, as the parents were outbred
(Falconer and MacKay 1996). Narrow-sense heritabilities were
divided by the total variance. Significance levels for heritability
estimates were inspected without adjusting for multiple tests (see
justification in (Moran 2003; Verhoeven et al. 2005) and also
using the sequential Bonferroni method (Sokal and Rohlf 1995).
for females (Gf), for hermaphrodites (Gm), and for between-
sex trait combinations (B), using best linear unbiased predictors
(BLUPs) of sire breeding values obtained from our Proc Mixed
analysis (SAS Inc. 2002–2003; Conner et al. 2003). Pearson cor-
relation coefficients between BLUPs and their confidence limits
based on Fisher’s z transform were calculated for each sex using
Proc Corr in SAS.
We used two methods to ask whether, and how, the G-
components analysis (CPCA) and element by element compar-
isons. CPCA analysis (Phillips 1998; Phillips and Arnold 1999)
allowed us to compare the overall structures of the G-matrices.
The CPCA method takes a multivariate approach to analyze the
eigenstructure of matrices, and has been widely used for com-
parison of G-matrices (Houle et al. 2002; Steppan et al. 2002;
whether the matrices are equal, proportional (indicating similar
structures of genetic covariation but with one sex having propor-
without variation differing by the same constant for each vector),
share some but not all eigenvectors, or are unrelated. We adopted
the jump-up approach for significance testing. In this method, a
model of one shared principal component is first tested against
unrelated structure, and if this test is nonsignificant, a model of
two shared components is tested against unrelated structure, and
so on up to equality of the matrices or until a significant deviation
is encountered. Preliminary analyses with the step-up method (in
which each model is tested against the next lower model in the
hierarchy) generally gave similar results. Vectors were manually
reordered to give the most conservative result, as otherwise rejec-
tion of the null hypothesis that the leading eigenvectors are equal
prevents progression up the hierarchy (Houle et al. 2002). For the
CPCA analyses, we used only the six traits that were measurable
in both sexes.
To identify individual traits that contribute highly to differ-
ences between the matrices, we also compared the G-matrices
element by element, by examining heritabilities and genetic cor-
relations. Heritabilities are equivalent to diagonal elements of
the G-matrix divided by phenotypic variance, and genetic corre-
lations are standardized versions of off-diagonal elements. Heri-
tributions of the parameters. To compare the genetic correlations
(based on BLUP values) for particular trait pairs, we employed
Fisher’s z transform to test for a significant difference.
QUESTIONS 3 AND 4: COMPARISONS OF
G MATRICES BETWEEN SPECIES
We also used both CPCA and element by element comparisons to
compare the G-matrices based on BLUPs between S. adamantis
and S. salicaria (Sakai et al. 2008). Separate comparisons were
both species, we calculated genetic correlations (based on BLUP
values) between traits measured in females and traits measured in
hermaphrodites (standardized elements of B). We used Fisher’s
z transformation to test for a significant deviation from the null
hypothesis of zero, indicating no genetic correlation, and the null
hypothesis of one, indicating a perfect genetic correlation. The
between-sex genetic correlations for homologous traits in the two
sexes were plotted against the level of sexual dimorphism to test
for the theoretically predicted negative relationship.
SEXUAL DIMORPHISM OF BIOMASS TRAITS
IN S. ADAMANTIS
All female allocation traits (terminal and lateral carpels and cap-
sules) had higher biomass in females than in hermaphrodites
(Fig. 2). In contrast, sepal biomass, a measure of flower size,
was greater in hermaphrodites than females for both terminal
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DIANE R. CAMPBELL ET AL.
Figure 2. Sexual dimorphism in resource allocation in Schiedea adamantis. H = hermaphrodite; F = female. Terminal and lateral refers
to flowers at the tips of the dichasial cymes versus those in subtending positions. SD = sexual dimorphism index. P values refer to
comparisons between the sexes using paired t-tests. All differences remained significant after application of a sequential Bonferroni test.
and lateral flowers (Fig. 2C). The least sexual dimorphism
was seen in terminal sepal mass (SD = 0.09) and the great-
est in lateral carpel mass (SD = 0.53). A multivariate ap-
proach also detected significant differences between females and
hermaphrodites (MANOVA, Wilk’s λ = 0.0256; F6,24= 152.16;
itively correlated with terminal and lateral carpel biomass (corre-
lation coefficients = 0.85 and 0.83, respectively), and negatively
correlated with terminal and lateral sepal biomass (correlations
coefficients = −0.42 and −0.32, respectively), indicating that
females differ from hermaphrodites primarily in having larger
carpels and smaller flowers.
QUESTIONS 1 AND 2: COMPARISON OF G-MATRICES
WITHIN S. ADAMANTIS
Heritable variation was detected in all traits measured in females,
sense heritability ranged from 0.44 for lateral carpel mass to a
sule mass (Fig. 3A). Five of six traits measured in both sexes had
estimates of heritability lower in hermaphrodites than in females,
had heritabilities significantly exceeding zero in hermaphrodites
and terminal sepal mass did so after Bonferroni correction. In
hermaphrodites, terminal and lateral stamen mass both had heri-
tability estimates of0.34withSE =0.15(P =0.0004and0.0011,
both significant after Bonferroni correction).
The Gmand Gfmatrices shared all common principal com-
ponents according to the CPCA analysis, but were not propor-
tional (Table 1). So, the eigenvector structures of the matrices
were similar, but the relative amounts of variation captured by
different eigenvectors differed between the sexes. Fitting a com-
mon principal components model, the first eigenvector had a high
loading on terminal capsule mass, followed closely by lateral
capsule mass, and thus largely reflected size of these female
structures. It has an associated eigenvalue that is much higher
for females than hermaphrodites (0.289 vs. 0.0464), indicating
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COMPARISON OF G MATRICES BETWEEN SEXES AND SPECIES
Figure 3. Comparisons of heritabilities and genetic correlations
between the sexes in Schiedea adamantis. The solid line indicates
a 1:1 relationship. (A) Heritability in females (±SE) plotted against
heritability of the same trait in hermaphrodites (±SE). T = termi-
nal; L = lateral. (B) Genetic correlation in females (±95% CI) plot-
ted against genetic correlation between the same pair of traits in
hermaphrodites (±95% CI).∗Genetic correlation between termi-
nal and lateral capsule biomass differs significantly between the
sexes (P < 0.05).
much greater genetic variance in this axis in the female sex. The
second common eigenvector indicates that families either allo-
cate substantially to lateral capsule biomass, or alternatively to
terminal capsule biomass and sepal biomass. The eigenvalues for
females and hermaphrodites associated with the second common
eigenvector were more similar in magnitude (0.0108 and 0.006),
eral, the CPCA results pointed to overall higher genetic variances
and covariances in the females than the hermaphrodites.
Element by element comparison of genetic correlations also
suggests a tighter pattern of trait integration in the females. Es-
timates appeared higher for females for 14 of 15 cases (Table 2,
Fig. 3B). However, for only one of these cases, terminal and lat-
Table 1. Tests of similarity of G-matrices using common principal
components analysis of Schiedea adamantis and S. salicaria. Prob-
ability values are reported for the jump-up method. Entries in bold
indicate the highest step in the hierarchy of null hypotheses that
cannot be rejected and so represent the accepted model. Vectors
were manually reordered to give the most conservative result.
eral capsule biomass, did the genetic correlation in females sig-
nificantly exceed the genetic correlation in hermaphrodites (r =
0.93 vs. 0.74, P < 0.0096). All biomass traits that could be mea-
sured in both sexes had significant positive genetic correlations
genetic correlations departed significantly from perfect correla-
tion, judging from nonoverlap of the 95% CI with a value of one
In the hermaphrodites, genetic correlations between stamen
biomass and other traits were generally smaller (gray symbols in
Fig. 4B) than those between traits reflecting female allocation or
flower size (black symbols). Whereas all genetic correlations for
traits measurable in both sexes differed significantly from zero
(prior to Bonferroni correction), only six of the 13 genetic corre-
lations for trait pairs involving stamen biomass did so (Table 2B).
Lateral stamen biomass correlated positively with terminal and
lateral capsule mass (r = 0.46 and 0.44), although neither corre-
lation retained statistical significance following Bonferroni cor-
rection (Table 2B). All genetic correlations involving stamen
biomass were significantly less than one. Terminal and lateral
sepal biomass, measures of flower size, were mostly genetically
and lateral stamen biomass with terminal sepals, andr = 0.18and
0.52 for terminal and lateral stamen biomass with lateral sepals,
with only the last of these four correlations significant). However,
sepal mass correlated significantly with carpel biomass traits (r =
0.37–0.79, P < 0.05). Genetic correlations in hermaphrodites av-
eraged r = 0.52 (SE = 0.06) for cases involving two female
allocation traits and r = 0.54 (SE = 0.05) for correlations be-
tween a female allocation trait and flower size, compared to only
r = 0.35 (SE = 0.05) for correlations between a female allocation
trait and stamen biomass.
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DIANE R. CAMPBELL ET AL.
Table 2. Within-sex genetic variance–covariance matrices (diagonal and above diagonal) and genetic correlations (below diagonal) in
Schiedea adamantis. All traits were measured in mg. Reported values for the elements of Gf(diagonal and above) have been multiplied
by 1000 for ease in reading. Genetic correlations that differed significantly from zero are shown in bold.
TcarpelTcapsule Tsepal LcarpelLcapsule Lsepal
Tcarpel TcapsuleTsepal LcarpelLcapsuleLsepal Tstamen Lstamen
∗Also significant after table-wide sequential Bonferroni correction.
QUESTION 3: COMPARISON OF G-MATRICES
For females, Gf of S. adamantis and S. salicaria shared three
of five principal components according to the jump-up approach
(Table 1). The three common eigenvectors accounted for 96%
of the total variance for S. adamantis and 94% for S. salicaria,
and so captured most of the structure. Using a common princi-
pal components model, the first common eigenvector had similar
loadings for terminal and lateral capsule mass (0.718 and 0.686),
and a larger associated eigenvalue for females of S. adamantis
than S. salicaria (0.288 vs. 0.117) indicating greater genetic vari-
ance along this axis in S. adamantis. This result is consistent with
the finding of exceptionally high heritabilities for these traits in
females of S. adamantis (circles in Fig. 3A). The second eigen-
negative value for terminal capsule mass, reflecting allocation to
one or the other function. The second eigenvalues for females
of S. salicaria and S. adamantis (0.0174 vs. 0.0102) indicated
similar levels of genetic variation along this axis.
Examining each genetic correlation element by element, the
estimate in females was higher in every case in S. adamantis than
of these differences were statistically significant at the 0.05 level,
based on Fisher’s z transformation, a number significantly larger
than expected by chance according to the binomial distribution.
0.65 vs. 0.17, P = 0.0219). Similar contrasts were seen for the
correlations between terminal carpel and lateral capsule (r = 0.56
vs. 0.05, P = 0.02742), terminal capsule and lateral capsule (r =
0.93 vs. 0.74, P = 0.0073), terminal capsule and terminal sepal
(r = 0.64 vs. 0.15, P = 0.02235), and lateral capsule and terminal
sepal (r = 0.59 and 0.20, P = 0.0307).
For hermaphrodites, Gm of S. adamantis and S. salicaria
shared four of five principal components (Table 1). This shared
the greatest eigenvalue, as a model with just that shared principal
component (without manual reordering of the vectors) is rejected
at the P < 0.0001 level. Inspecting the dominant eigenvectors
for matrices for each species separately indicates a shift in ori-
entation from heavy weighting of lateral compared to terminal
capsules in S. salicaria (loadings = 0.91 and 0.42) to more em-
phasis on terminal capsules in S. adamantis (loadings = 0.62
and 0.73). If a model of common principal components is fit, the
first eigenvector has a particularly high loading on lateral cap-
sule mass (0.88) and to a lesser extent on terminal capsule mass
sex, the associated eigenvalue is higher for S. salicaria (0.264)
764EVOLUTION MARCH 2011
COMPARISON OF G MATRICES BETWEEN SEXES AND SPECIES
adamantis and S. salicaria. Error bars are ±95% confidence inter-
vals. The solid line indicates equal correlations in the two species.
The dotted lines indicate the null hypotheses of zero genetic cor-
relation. (A) Correlations for traits measured in females (standard-
ized versions of the covariances in Gf). Open diamonds indicate
the five trait pairs where the standardized element differs sig-
nificantly (∗P < 0.05) between the species. Others shown with a
filled circle. (B) Correlations for traits measured in hermaphrodites
(standardized versions of the covariances in Gm). Black circles: ge-
netic correlations for the traits also measured in females. Gray
circles: genetic correlations where one or both traits were stamen
biomass.∗The one trait pair (terminal stamen mass and lateral
capsule mass) that differed significantly between the species is
shown by a diamond.
4. Comparisons of genetic correlations between S.
than for S. adamantis (0.039). Consistent with this result, genetic
variation in lateral capsule mass of hermaphrodites was higher
in S. salicaria (coefficient of genetic variance (CVa= 20.23 and
h2= 0.69, Sakai et al. 2008) than S. adamantis (CVa= 18.56 and
h2= 0.42). Furthermore, terminal and lateral capsule mass (the
black circle farthest below the line of equality in Fig. 4B) formed
one of two pairs of traits in this analysis for which the genetic
correlation appeared to have an estimate higher in S. salicaria
than S. adamantis. However, comparing genetic correlations in
hermaphrodites element by element, the only case with a signif-
icant difference between the species was the correlation between
terminal stamen and lateral capsule mass (r = 0.47 vs. −0.17 in
S. adamantis and S. salicaria, P < 0.00963), and with 15 compar-
isons such a result is not significant after Bonferroni correction.
Together, these analyses indicate more genetic variation in lat-
eral capsule mass of hermaphrodites of S. salicaria compared to
S. adamantis hermaphrodites.
QUESTION 4: BETWEEN-SEX CORRELATIONS
Many of the traits that were measurable in both sexes had
moderate-to-strong genetic correlations across the sexes in
S. adamantis, with 24 of 36 cases significantly greater than zero
at the P < 0.05 level prior to Bonferroni correction (for these
traits r = 0.37–0.66, Table 3). In contrast, stamen biomass was
generally uncoupled from those traits, with all but one genetic
correlation indistinguishable from zero (Table 3). Elements of
B tended to be lower in value than the analogous entries in the
within-sex matrices Gfand Gm(mean ± SE = 0.0062 ± 0.0014
vs. 0.0167 ± 0.0056, t test, P = 0.0928). For homologous traits,
the strength of the between-sex genetic correlation did not show
a negative relationship with sexual dimorphism (Fig. 5), as had
been predicted. Schiedea adamantis differed from S. salicaria
in showing stronger sexual dimorphism in the female allocation
traits, especially terminal and lateral carpel biomass. It showed
less sexual dimorphism in flower size, as measured by terminal
in both of these species (Fig. 2 and Sakai et al. 2008). For both
were significantly less than one (Fig. 6), as was also the case for
correlations (Fig. 4), between-sex genetic correlations clustered
near the line of equality between S. adamantis and S. salicaria
(Fig. 6). We detected no differences between the species in any
of the between-sex genetic correlations (all P > 0.05).
Female and hermaphroditic flowers of S. adamantis showed
striking sexual dimorphism in biomass allocation traits, as ex-
pected in a gynodioecious species where females are well rep-
resented (Delph 1996). Both terminal and lateral flowers of fe-
males had significantly greater allocation to carpel and capsule
biomass than hermaphroditic flowers. Flower size, as measured
EVOLUTION MARCH 2011
DIANE R. CAMPBELL ET AL.
Table 3. Between-sex G matrix (B) and associated genetic correlations in Schiedea adamantis.
TcarpelTcapsule Tsepal LcarpelLcapsuleLsepal Tstamen Lstamen
(A) Matrix B. Values are multiplied by 1000.
(B) Genetic correlations between floral traits of female and hermaphrodites in Schiedea adamantis.
Values significant at P<0.05 are in bold.∗Also significant after table wide Bonferroni correction.
hermaphrodites. This pattern could result either from the vestigial
perianth size and presence of stamens, or a sex-specific selective
advantage to larger perianth only in male flowers (Delph 1996).
We observed a significant positive genetic correlation between
allocation to stamens and flower size in hermaphrodites only in
the case of lateral flowers (r = 0.52 and P < 0.05, compared to
Figure 5. Between-sex geneticcorrelations forhomologoustraits
plotted are estimates ±95% CI. Two values are given for each type
of trait, corresponding to terminal and lateral flowers.
r = 0.13 and P > 0.05 for terminal flowers). This restriction of
the correlation to lateral flowers supports a functional hypothesis
(such as a sex-specific selective advantage), rather than a more
general developmental hypothesis.
The extent of dimorphism in the female traits of carpel and
capsule biomass was much greater in S. adamantis, with its 39%
females, than in S. salicaria, with 12–13% females (Sakai et al.
the evolution of dioecy, comparison between the species suggests
Figure 6. Comparison of between-sex genetic correlations for
S. adamantis with those for S. salicaria. Values plotted are esti-
mates ±95% CI. Black diamonds: homologous traits. Black circles:
nonhomologous traits measured in both sexes. Gray circles: corre-
lations involving stamen biomass.
766 EVOLUTION MARCH 2011
COMPARISON OF G MATRICES BETWEEN SEXES AND SPECIES
that as the frequency of females increases over evolutionary time,
increased allocation to male function, relative to female func-
tion, occurs in the hermaphroditic sex. Hermaphroditic flowers
of S. adamantis invested more in male function, in the form of
stamen biomass, than they did in carpel biomass (Fig. 2). In con-
in carpel biomass (Sakai et al. 2008). In S. salicaria, only the lat-
eral flowers exhibit sexual dimorphism in carpel mass, indicating
that selection for sexual dimorphism initially affects lateral flow-
ers more strongly than terminal flowers. Terminal flowers open
first in the inflorescence, have greater biomass in general, and
for hermaphrodites, probably have greater capacity to allocate
resources to both female and male function than lateral flow-
ers. As selection continues for sexual dimorphism in S. adaman-
tis, terminal flowers of hermaphrodites may retain some female
function long after lateral flowers have lost the capacity for seed
QUESTIONS 1 AND 2: COMPARISON OF G-MATRICES
WITHIN S. ADAMANTIS
We detected moderate-to-high narrow-sense heritabilities for all
reproductive allocation traits in S. adamantis (range = 0.34 for
stamen biomass to 1 for capsule mass). These high heritabilities
suggest considerable potential for the continued evolution of sex-
ual dimorphism, despite the relictual nature of the species and
reduced genetic variability as measured by allozyme diversity
(Weller et al. 1996). Schiedea adamantis probably had a wider
distribution until colonization of the Hawaiian Islands by hu-
mans, as evidenced by introgression of its genes into S. globosa
(L. Wallace, pers. comm., 2009). Until the recent crash in popu-
lation size of S. adamantis, hundreds of individuals occurred in
quantitative genetic variation measured in this study.
Our study addressed two questions comparing genetic vari-
ation between the sexes of S. adamantis. First, we compared the
G-matrices for females and hermaphrodites. We found differ-
ences in structure between Gfand Gmthat went beyond a simple
proportional relationship. Overall, CPCA pointed to a greater
amount of genetic variation in capsule mass of females com-
pared to hermaphrodites. Females also showed generally tighter
genetic covariation between capsule mass, carpel mass, and sepal
mass, compared to hermaphrodites. Element by element com-
parisons pointed to terminal and lateral capsule mass in partic-
ular as more closely genetically correlated in females than in
hermaphrodites. One hypothesis for the sex-related differences
is that female allocation traits are linked to the sex-determining
locus. Because females are homozygous for the sex locus and all
hermaphrodites in this study were heterozygous, females could
(Rhen 2000). A second hypothesis is sex-specific selection. For
example, larger carpels and capsules might be favored in females
but not hermaphrodites, as such investment may take away from
success as male parents. In addition, selection for these reproduc-
tive traits may differ between the sexes, because hermaphrodites
include some inbred individuals. A third, nonmutually exclusive,
hypothesis is correlated selection for suites of specific traits. For
example, larger sepals could be favored to protect larger capsules
(Delph 1996) or to provide more carbon for developing seeds, as
the sepals are photosynthetic in Schiedea. Such selection could
lead to strengthening of the genetic correlation between these
traits. This last hypothesis is consistent with the increase in the
relative size of sepals in females compared to hermaphrodites,
so that the two sexes are relatively equal (low SD for sepal size,
Fig. 5), unlike in S. salicaria where sepal mass of hermaphrodites
greatly exceeds that of females, generating stronger sexual
Other studies in both animals and plants have also found dif-
ferences between Gmand Gf. In a review by Arnold et al. (2008),
all 12 comparisons using CPCA rejected hypotheses of equal or
proportional matrices of the sexes. Our finding that the two G-
portional) is similar to the situation for female and hermaphrodite
individuals of wild strawberry (Ashman 2003). Sexes of S. lati-
folia (Caryophyllaceae) showed even greater dimorphism in G-
matrices, with the difference in this case driven by divergence in
covariation between leaf traits (Steven et al. 2007). Interestingly,
the patterns we saw here for reproductive allocation traits did not
match the sex differences in G-matrices for inflorescence traits in
these same two species in that hermaphrodites were the sex with
more genetic variation for lateral flower number (Weller et al.
Our second question was whether female allocation traits
would be more closely integrated with each other than with male
allocation traits or flower size. In the hermaphrodites, female
allocation traits were indeed more closely genetically correlated
with each other (average r = 0.52) than they were with stamen
mass (as a measure of flower size) correlated just as strongly with
carpel and capsule biomass (average r = 0.59) as those traits did
with each other. So, our prediction was only partly upheld. The
could in principle be the result of correlated selection for these
QUESTION 3: COMPARISONS OF G-MATRICES
We also asked how genetic correlations within sexes compared
between S. adamantis and S. salicaria. Despite the close phy-
logenetic relationship, common principal components analysis
EVOLUTION MARCH 2011
DIANE R. CAMPBELL ET AL.
detected differences between species in both within-sex genetic
matrices, Gf and Gm which contained female allocation and
flower size traits. The differences appeared particularly pro-
nounced for females, in that all 15 trait pairs in females had
higher estimates for genetic correlations in S. adamantis, with
five of these cases statistically significant. This pattern is con-
sistent with the hypothesis that along with greater sexual dimor-
phism in S. adamantis, selection for greater integration of those
traits in females has led to the evolution of higher genetic co-
variances. The highly correlated genetic structure within females
may reflect the absence of resource demands for male alloca-
tion, and also a shift in resources away from sepal mass, a proxy
for flower size, to female function. That the changes in genetic
correlation are most pronounced in females also suggests that se-
lection on females may be even stronger than selection to allocate
more resources to male function in hermaphrodites. Relative to
hermaphrodites, females of S. adamantis produce 2.3 times as
many seeds, a difference largely resulting from reduced seed pro-
duction of hermaphrodites of S. adamantis (Sakai et al. 1997). In
contrast, females and hermaphrodites of S. salicaria have equiv-
alent seed production (Weller and Sakai 2005).
previously reported differences in genetic variances and covari-
ances for inflorescence traits (Weller et al. 2007), indicate that
pronounced evolution of G-matrices is possible in plants over
modest stretches of evolutionary time, as these species presum-
ably diverged since the origin of the island of Oahu 3.8 million
years ago (Sakai et al. 1995; Soltis et al. 1996). Many other
across species comparisons have also found differences between
G-matrices (Steppan et al. 2002), but this is by no means the rule
(Arnold et al. 2008). Although we did not measure dominance
variance in these studies, any difference between species in this
genetic parameter could also contribute to different evolution-
ary trajectories in these two partially selfing species (Kelly and
QUESTION 4: BETWEEN-SEX GENETIC
correlations of homologous traits were lower in the more sexually
dimorphic S. adamantis compared to in S. salicaria, and lower
for specific traits that show greater sexual dimorphism. Although
the within-sex G-matrices and their associated genetic correla-
tions differed between the species, we found no evidence that any
between-sex genetic correlations differed. Instead the between-
sex genetic correlations clustered around the line of equality be-
tween species (Fig. 6). Elements of B were lower on average
than those of the within-sex G-matrices, as expected theoreti-
cally whenever correlations between the sexes are less than unity
(Barker et al. 2010). We saw no evidence that the between-sex
genetic correlations specifically for homologous traits decreased
with greater sexual dimorphism in the trait.
IMPLICATIONS FOR EVOLUTION OF BREEDING
SYSTEMS IN SCHIEDEA
evolution of gynodioecious Schiedea salicaria and S. adamantis
were in genetic variances and covariances of female allocation
and sepal size within the females. In both species (see also Sakai
et al. 2008), there was ample genetic variation for responses to
natural selection favoring the continued evolution of sexual di-
morphism, and presumably the evolution of dioecy. Assuming
that S. salicaria, with 12–13% females, represents an early stage
in the evolution of sexual dimorphism, the presence of high lev-
els of inbreeding depression, combined with moderate selfing,
should favor increasing representation of females in populations
(Weller and Sakai 2005). Schiedea adamantis, which is likely to
represent a later stage in the evolution of sexual dimorphism, also
had abundant heritable variation for allocation patterns, despite
the greater specialization of hermaphrodites in male function,
and females for female function. In both species, all between-sex
genetic correlations were less than one, and the within-sex G ma-
trices differed between sexes, both properties indicating some
sex-specific gene expression that would promote the evolution of
sexual dimorphism. However, in S. adamantis, these properties
that tend to accelerate evolution of dimorphism must be weighed
against a possible (although not significant after Bonferroni cor-
rection) positive genetic correlation of stamen mass and capsule
mass in hermaphrodites that would tend to slow evolution of
greater maleness in that sex. Taken together, these two species
provide insights into the evolutionary processes associated with
the evolution of sexual dimorphism in Schiedea, a lineage where
10 of the 32 extant species have evolved sexual dimorphism. Un-
fortunately, studies of this nature, which depend on comparisons
among species and sufficient sampling within species for quanti-
tative genetic analyses, are likely to become increasingly difficult
in the future with continuing losses of biodiversity.
We are grateful to A. Andres, L. Chau, T. Dang, L. Duong, J. Kutaka, C.
measurements. We also thank Y. Alliman, R. Basile, Y. Theau, and W.
Yang for care of plants, C. Corn and the State of Hawaii for the permit to
on the manuscript. This research was supported by the National Science
Foundation (DEB 9815878) with NSF REU support for PD.
768EVOLUTION MARCH 2011
COMPARISON OF G MATRICES BETWEEN SEXES AND SPECIES
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Associate Editor: J. Kelly
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