Biological journal oflhe Linnean Sociely (1992), 45: 167-186. With 6 figures
The origins of allometry: size and shape
polymorphism in the common waterstrider,
Gerris remigis Say (Heteroptera, Gerridae)
DAPHNE J. FAIRBAIRN
Department of Biology, Concordia University, 1455 de Maisonneuue Blud., West,
Montreal, Quebec, Canada H3G IM8
Received 2 Jury 1990, accepted f o r publication 20 September I990
Changes in size, whether ontogenetic or phylogenetic, tend to be associated with changes in shape.
This allometry can arise through two different evolutionary mechanisms: (1) selection acting
primarily on overall size may be associated with changes in shape because of physiological and
mechanical constraints or differential responses of different body components; or (2) selection acting
primarily on shape (on the size of specific body components) may be associated with changes in
overall size because of genetic correlations, and thus correlated responses, of other body components.
To assess the relative importance of these two mechanisms, shape polymorphism is examined along
two axes of size dimorphism (sex and wing morphology) in the common waterstrider, Gerris remigis
Say. Eight measurements were made of body and appendage qomponents of 234 adults, from three
independent populations. Univariate and multivariate analyses reveal that both sexes and wing
morphs differ significantly in size and shape. Shape differentiation along the two axes of size
dimorphism is found to be dissimilar, partially independent of size, and strongly correlated with the
ecological specialization of the various morphs. These observations suggest that selection is acting
directly on shape, and thus that allometry in this species primarily reflects shape-mediated changes
in size (mechanism 2), rather than size-mediated changes in shape. The role of developmental
processes in facilitating this shape differentiation is discussed.
KEY WORDS:-Allometry - scaling
dimorphism - Gerris remigis.
-
body size
-
shape
-
wing polymorphism
-
sexual size
CONTENTS
Introduction . . . . . . .
Methods . . . . . . . .
Results..
. . . . . .
Patterns of variation within traits .
Size dimorphism . . . . .
Correlations among traits . . .
Principal components analysis . .
Discussion. . . . . . . .
Acknowledgements
. . . . .
References.
. . . . . . .
Appendix A . . . . . . .
Appendix B . . . . . . .
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INTRODUCTION
Body size is a keystone trait, closely correlated with many morphological,
physiological, ecological and life-history traits (Peters, 1983; Calder, 1984;
0024-4066/92/020167
+ 20 $03.00/0
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1992 The Linnean Society of London
I68
D.J. FAIRBAIRN
Schmidt-Nielsen, 1984; Barbault, 1988; LaBarberra, 1989; Reiss, 1989). When
comparisons are made across taxa, body size alone is a powerful predictor of
associated patterns in these correlated traits, even when the functional
relationship (if any) between body size and the dependent trait is unknown
(Peters, 1983; Calder, 1984; Schmidt-Nielsen, 1984). Changes in body size either
during growth and development or within and among taxa over evolutionary
time are generally accompanied by changes in shape. Such departures from
geometric similarity are termed allometry, and studies of allometry and the
covariation of size, form and function are the basis of the biology of scaling
(Calder, 1984; Schmidt-Nielson, 1984; LaBarberra, 1989).
Allometric relationships are generally interpreted as reflecting changes in
physiological or structural requirements associated with changes in body size
(Calder, 1984; Schmidt-Nielsen, 1984; Reiss, 1989). The elastic similarity model
relating bone diameter and length is one example of such an interpretation
(McMahon, 1973, 1975). These are strictly adaptive models, but allometry may
also arise as a consequence of indirect, correlated responses of individual body
components to selection acting directly on overall body size (Lande, 1979).
Correlated responses to direct selection on body size form the basis of Lande’s
model for the evolution of brain : body size allometry among congeneric
mammals (Lande, 1979)) and of Leutenegger’s model for the evolution of
hyperallometry for sexual size dimorphism in primates (Leutenegger, 1978).
All of these models presume that allometry arises from selection acting
primarily on overall body size. However, changes in shape associated with
changes in size may also reflect differential selection on different body parts
(Lande, 1979; Zeng, 1988; Riska, 1989). Genetic correlations for size among
morphological traits are generally moderate to high and positive (Falconer,
1981: 284-287; Cheverud, 1988; Riska, Prout & Turelli, 1989). Selection for an
increase in the size of a specific body component will therefore produce
correlated changes in the sizes of other components, and thus an increase in
overall size. Because the correlated responses of non-target traits will generally
be less than the response of the target trait, this selection will produce
simultaneous changes in shape (the relative sizes of body components) and
overall size. For example, Lande (1979) proposed that the brain : body size
allometry among higher mammalian taxa is the result of selection acting
primarily on brain size, with correlated responses in body size.
Thus, allometry or scaling to body size may reflect size-mediated changes in
shape, in which selection acts primarily on overall size and changes in shape
reflect either physiological and structural requirements associated directly with
size, or correlated responses of body components. Alternatively, allometry may
reflect shape-mediated changes in size, in which selection acting primarily on
shape (on the size of specific components), produces allometry through
correlated responses in other body components. This paper describes an
attempt to distinguish between these two models of allometry through an
analysis of size and shape polymorphism in the common waterstrider, Gerris
remigis Say.
Waterstriders are semi-aquatic, true bugs (Hemiptera, Heteroptera, Gerridae)
found on the water surface (Andersen, 1982). They are generally elongate, with
long, slender appendages, and females are significantly larger than males in most
species (Andersen, 1982; 184, 3 14; Fairbairn, 1990). Sexual selection on males
SIZE AND SHAPE POLYMORPHISM IN GERRZS REMZGZS
I69
may lead to male-biased dimorphism in the length of the mid-femur (Hayashi,
1985) or width of the front femur (Rubenstein, 1984; Kaitala & Dingle,
unpublished data) in some species, and Arnqvist (1989) reports a n abdominal
peg found only in male Gerris odontogaster. However, conspicuous sexual
dimorphism in shape due to the development of secondary sexual characteristics
is not typical of this family, and sexual dimorphism has therefore been
considered primarily as dimorphism for overall size (body length, Vepsalainen,
1985; Fairbairn, 1988a, 1990).
Dimorphism for migratory ability is relatively common within the Gerridae,
particularly among temperate species (Brinkhurst, 1959; Vepsalainen, 1974;
1978; Calabrese, 1979; Andersen, 1982: 296-308). In many species, fully-winged
(macropterous) morphs, capable of flight during at least some phase of their life
cycle, coexist with short-winged or wingless (apterous) morphs that are
incapable of flight. Within species, macropters are significantly larger than shortwinged and apterous individuals, and sexual size dimorphism is reduced in the
macropterous morph (Nummelin, 1988; Fairbairn, 1990). Although Andersen
(1982: 201) suggests that wing loss or reduction is associated with significant
changes in the shape of the thorax, the dimorphism associated with wing
morphology has been analysed primarily in terms of general size rather than
shape (Nummelin, 1988; Fairbairn, 1990).
Gerris remigis is a large, sexually dimorphic species found on the surfaces of
streams and small rivers throughout temperate North America (Scudder, 1971;
Calbrese, 1977; Polhemus & Chapman, 1979; Fairbairn, 1990). Although
primarily apterous over most of its range, G. remigis populations in Arizona,
California and Oregon contain high proportions of macropterous individuals,
and are classified as wing-dimorphic (Calabrese, 1974a; Polhemus & Chapman,
1979; Fairbairn, unpublished data). These populations thus display two
dimorphisms for total length: sexual dimorphism in which females are longer
than males, and wing-dimorphism in which macropters are longer than
apters. These two axes of size dimorphism in G. remigis provide an excellent
system for testing the two models of the evolution of body-size scaling developed
above. Size-mediated changes in shape should be evident along both axes of size
dimorphism. For example, we might expect the larger morphs to have relatively
longer legs because of the functional requirements of support and locomotion on
the water surface (Andersen, 1982: 212-217, 341, 349). In contrast, changes in
shape and size arising from direct selection on specific body components (shapemediated changes in size) should reflect different selective regimes along the two
axes. For example, reproductive specialization in males and females may lead to
dimorphism in the size and shape of the genitalia and abdomen (due to the
requirements of egg production and storage in females), as well as in sexually
selected traits such as width of the front femur.
Shape differences are also expected along the axis of wing dimorphism. Wing
polymorphisms are common in several insect orders, and loss or reduction of
wings is generally associated with increased fecundity and earlier maturity, thus
giving the non-migrant morph a reproductive advantage (Harrison, 1980; Roff,
1986). Specialization of the non-migrant morph for reproduction can be
extreme, leading to major differences in size and shape between morphs (Roff,
1986). More commonly, differences are less dramatic and involve reduction in
thoracic length or volume and increases in the relative size of the abdomen in
170
D.J. FAIRBAIRN
Figure I . Map of California, U.S.A., showing the locations of the three streams from which
G. rernigis were collected for this study.
non-migrant individuals (Roff, 1986). In the Gerridae, wing reduction has been
shown to be associated with reduced development time, direct reproduction
(reproduction without intervening adult diapause), and increased fecundity
(Zera, 1985; Spence, 1989). Evidence for the latter is available for G. remigis
(Fairbairn, 1986). Thus, although size and shape dimorphism are not extreme
along this axis in the Gerridae (Andersen, 1982: 201; Fairbairn, 1990), adaptive
differences in shape between wing morphs should reflect specialization for flight
in macropters and for reproduction in the non-migrant (apterous) morph.
METHODS
Adult Cerris remigis were collected in the autumn of 1988 from three wingdimorphic populations in California (Fig. 1). These sites were chosen because
they contained dense populations of G. remigis, with high proportions of both
macropterous and apterous individuals, and are sufficiently separated to contain
genetically independent populations (Preziosi, 1990). All three sites are small,
clear, permanent streams. Site 1, Scott Camp Creek, flows into Siskiyou Lake;
Site 2, Cappell Creek, flows into Lake Berryessa; and site 3, Salmon Creek, flows
SIZE AND SHAPE POLYMORPHISM IN GERRZS REMZGZS
171
\
1
0.5 cm
Figure 2. Schematic drawing of a macropterous, female Gerris rcmigis. The right side of the drawing
is shaded to illustrate the appearance of the specimens in silhouette, as projected onto the grid for
measurement. ff, Front femur; pl, pronotal lobe; el, elytra; mf, mid-femur. Eight measurements were
taken as follows: a-f, total length; b-d, thoracic length; d-e, abdominal length; e-f, genital length;
maximum width of the front femur; length of the mid-femur; thoracic width at point c; and
maximum thoracic height. The specimens were turned on their sides and projected in lateral view
for measurement of thoracic height.
into the Kern River. Samples were collected on September 5, September 11 and
November 5, respectively. The phenology of these populations has not been
studied in detail, but all sampled adults were in reproductive diapause.
Reproductive diapause occurs in the late summer and autumn throughout
California (Fairbairn, unpublished data), and at higher latitudes and altitudes
may extend into overwinter diapause as seen in northern and eastern
populations of this species (Matthey, 1974; Calabrese, 1978; Fairbairn, 1985).
All individuals were collected in hand nets and immediately preserved in 70%
ethanol. Total sample sizes were 188, 235 and 108, for sites 1, 2 and 3
respectively. Within each sample, 20 individuals from each class (macropterous
males, macropterous females, apterous males, apterous females) were
subsampled at random for measurement. The sample from site 3 contained only
19 macropterous females and 15 apterous females, and thus all were included in
the measurement sample.
Eight measurements were made on each individual (Fig. 2). Whole bodies
and legs were mounted separately on microscope slides and projected onto a grid
using a photographic enlarger. Linear distances were then determined using a
digitizer attached to a microcomputer. Because the image was projected in
silhouette, lengths of body components were assessed with reference to structures
visible along the edges of the silhouette, measured parallel to the main body axis
(Fig. 2). Thoracic length was assessed as the distance between the suture
separating the head from the prothorax and the suture separating the
I72
D. J. FAIRBAIRN
metathorax from the coxa of the third leg (b-d, Fig. 2). This closely
approximates thoracic length as measured abdominally along the midline (see
Andersen, 1982; 216). Abdominal length was assessed as the distance from the
latter position to the end of the connexival spines (d-e, Fig. 2). Under this
scheme of measurement, genital length refers only to the portion of the genitals
projecting beyond the connexival spines (e-f, Fig. 2). Since the latter typically
extend part way along the first genital segment (Calabrese, 1974b), this
underestimates the true length of the genital segments. However, it does estimate
the extent to which the genitals contribute to total length, and is valid as a
relative measure for comparisons between sexes and wing morphs. Thoracic
width was measured across the mesothorax, just anterior to the bulbous, lateral
enlargements that serve as points of insertion for the coxa of the mid-leg (c,
Fig. 2). Thoracic height was assessed using a lateral projection (the specimen
viewed laterally), and was measured as the maximum distance across the
mesothorax.
The precision (repeatability) of these measurements was assessed by repeated
measures ( N = 5) of three males and three females, and is expressed as 95%
confidence limits based on these repeated measures. Specimens were removed
from the slides and remounted for each replicate. Precision did not differ
between the sexes, and ranged from kO.002 cm for front femoral width to
f0.006 cm for mid-femoral length. Expressed as a percentage of the mean
values, precision varied from k0.2yOfor total length to f3.4% for width of the
front femur. All traits except the latter and thoracic height had percentage errors
for
of less than f 1yo.All measurements were rounded to the nearest cm x
calculations.
Statistical analyses were conducted using SYSTAT (Wilkinson, 1989), and are
described in detail in the results section. Unless otherwise indicated, distributions
of the variables did not deviate significantly from normality, and variances were
found to be homoscedastic among groups.
RESULTS
Patterns of variation within traits
The trait means and standard deviations for each class at each site are
illustrated in Fig. 3. Three-way analyses of variance were used to determine the
influence of site, sex and wing morphology on each trait (Appendix A), and,
where interactions involving site were significant, trends within sites were
examined using two-way ANOVAs (Appendix B) . Femoral measurements were
also analysed using covariance analysis to correct for differences among classes in
overall body size (total length). Significant interactions involving site generally
reflected differences among sites in the degree but not the direction of
dimorphism, indicating similar patterns of variation among classes on all three
sites. Only those trends found to be consistent across sites are discussed below.
The main effects of site and sex are highly significant (P < 0.001) for all eight
traits. The effect of site primarily reflects the larger size of individuals from site 1
(Fig. 3). O n all sites, females have larger bodies (total length, abdominal length,
thoracic length, width and height) than males, while males have larger genitalia,
wider front femora, and longer mid-femora (Figs 3, 4A). (The differences
I.8
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Abdominal length
Total length
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- ++
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+
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: :%
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++
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between sexes in length of the mid-femora are most apparent when corrected for
differences in total length [ANCOVA, site 1: F = 69.80, d.f. 1, 76, P < 0.001;
site 2: F = 21.93, d.f. 1, 76, P < 0.001; Site 3: F = 63.10, d.f. 1, 71, P <
0.00 13 ) .
The main effect of wing morphology is highly significant for seven of the eight
traits. Macropters are significantly larger than apters in total length, abdominal
length, and all three thoracic measurements (P < 0.001, Figs 3, 4B). Thus,
macropters have larger bodies than apters. However, apters have longer external
genitalia than macropters (P < 0.01). Trends for the two femoral measurements
are not consistent among sites and sexes (Figs 3, 4B).
I74
D. J. FAIRBAIRN
The interaction between sex and wing morph is highly significant (P <
0.001) for total and abdominal lengths. For both traits, apters are more sexually
dimorphic than macropters (Fig. 4A), and the size dimorphism between wing
morphs is more pronounced in males than in females (Fig. 4B). These trends
indicate that wing loss (aptery) is associated with a greater reduction in
abdominal and total length in males than in females, as noted by Fairbairn
(1990) for eastern populations of G. remigis.
The major conclusion of these analyses is that sexes and wing morphs differ
significantly with respect to body, genital and appendage dimensions. For body
measurements (total length, abdominal length, thoracic length, width and
height), females are significantly larger than males and macropters are larger
than apters. In contrast, males exceed females in genital and appendage
measurements, and apters have larger genitals than macropters. Although
differences in shape are generally similar along the two axes of size dimorphism
(sex and wing morphology), males and females differ most significantly in
abdominal length, genital length and width of the front femur, while macropters
and apters differ most significantly in abdominal length and thoracic height and
width (Appendix A, Fig. 4A, B). These differences suggest morph-specific
changes in shape associated with size dimorphism.
Size dimorphism
Monte Carlo simulations indicated that size ratios are normally distributed
and unbiased in the absence of true dimorphism, but become negatively skewed
as the underlying dimorphism increases. Raising the ratio to the power 1.5
(Sokal 8z Rohlf, 1981: 425) successfully normalized the size ratios over the ranges
observed in this study, and thus analyses of size ratios using parametric statistics
are based on (size r a t i ~ ) ' . ~ .
The tendency for females to have larger bodies but smaller external genitalia
and femora than males is clearly illustrated by the distribution of size ratios
(Fig. 4A). Two-way analysis of variance reveals significant differences in sexual
size dimorphism among traits (F = 478.7, d.f. 7, 32, P < 0.001) and between
wing morphs (F = 15.28, d.f. 1, 32, P < 0.001). The interaction between trait
and wing morph is also significant (F = 5.91, d.f. 7, 32, P < 0.001), indicating
that wing morphs differ more for some traits than for others. Abdominal length
shows the strongest female bias and also the greatest difference between wing
morphs, with apters much more dimorphic than macropters. Total length and
thoracic height show similar, but less pronounced trends. In contrast, the most
dimorphic trait, genital length, is male-biased and shows a similar degree of
dimorphism in apters and macropters.
A similar analysis was conducted on the size ratio between wing morphs
[(mean size of macropters)/(mean size of apters)] (Fig. 4B). Because the
variances of these ratios were significantly heterogeneous, statistical comparisons
were made using Kruskal-Wallis two-way ANOVA (Zar, 1984: 219-222). As for
sexual size ratios, the ratios of wing morphs vary significantly among traits
(H = 41.25, d.f. 7, P < 0.001): macropters tend to have larger bodies and
shorter genitals than apters (Fig. 4B). Sex does not significantly influence the
size ratio of wing morphs (H = 1.513, d.f. 1, P > 0.10), and the interaction
between sex and trait is also not significant (H = 1.429, d.f. 7, P > 0.98).
SIZE AND SHAPE POLYMORPHISM IN GERRZS REMZGZS
175
A
0.6
1
L
0.4
I
I
I
I
I
I
I
I
I
0.81
I
I
I
I
I
I
I
I
Figure 4. Size ratios for all eight traits. Data presented are means ( * standard deviations)
calculated from estimates at each site. A, Sexual size ratios [(mean female size)/(mean male size)] for
each wing morph. 0 , apters; 0 , macropters; B, Size ratios for wing morphs [(mean size of
,
females.
macropters)/(meansize of apters)] for each sex. 0 , males; .
The patterns of dimorphism illustrated in Fig. 4 are generally similar, with
positive size ratios for body measurements and neutral ( 1 .O) or negative ratios for
leg and genital measurements. Thus, along both axes of size dimorphism (sex
and wing morphology), the larger morph (females and macropters) has a larger
body overall, but smaller genitals. However, the similarity of the two axes is not
complete: abdominal and genital measurements are dimorphic along both axes,
but show stronger sexual dimorphism; width of the front femur shows strong
sexual dimorphism only; and thoracic height is much more strongly dimorphic
between wing morphs than between sexes.
Correlations among traits
Pearson product moment correlations were calculated among all pairs of traits
at each site. The resulting matrices were then compared using pairwise Mantel
tests, based on 1000 randomizations (Manley, 1986: 53-57). These revealed high
levels of correlation among the three matrices ( r = 0.90, 0.84, 0.97, for sites
1 x 2, 1 x 3, and 2 x 3, respectively, P < 0.001), indicating that the patterns of
correlations among traits are very similar at the three sites. Data from the three
sites were therefore combined by adjusting individual measurements according
D.J. FAIRBAIRN
I76
to the deviations of site means from the grand mean for each trait. Pairwise
correlations among all traits were then calculated from these pooled data
(Table 1). The significance of each correlation was determined using
Bonferroni-adjusted probabilities (Wilkinson, 1989: 368) which adjust the
experimentwise error rate to 0.05.
Twenty-four of the 28 Pearson correlations are significant with P < 0.001
(Table 1). Length of the mid-femur is only weakly correlated with other traits,
and is not significantly correlated with abdominal length, or thoracic width and
height. The only other non-significant correlation is between width of the front
femur and thoracic length. Body measurements are positively correlated with
each other, but negatively correlated with genital length and width of the front
femur. The latter two traits are positively correlated with each other and with
length of the mid-femur. These patterns reflect the shape differences among
groups (sexes and wing morphs) : larger-bodied individuals (females and
macropters) tend to have smaller external genitalia and legs.
T o determine patterns of correlation within groups, partial correlations were
calculated between all pairs of traits, with sex and wing morph held constant
(Table 1). Probabilities were adjusted to give a n experimentwise error rate of
0.05. Twenty-one of the 28 pairwise correlations are statistically significant.
Genital length is negatively correlated with abdominal length, but all other
significant correlations are positive. Thus, within groups, the sizes of all
measured body and leg components, tend to covary positively: larger animals are
larger all over. Shape changes within groups appear to be restricted to the
relative size of the abdomen and genitals. All of the non-significant correlations
involved genital length or width of the front femur. Thus, the variance of these
two traits within groups appears to be relatively independent of size variation in
other body traits.
Principal components analysis
Principle components analysis (PCA) provides a useful tool for summarizing
patterns of variability within sets of correlated variables. When PCA is
performed on morphometric data, the first principal component frequently
extracts a general index of size (both isometric and allometric), while subsequent
TABLE
1 . Pairwise correlations among body variables based on combined data for all sites. Above
the diagonal: standard Peanon Product Moment correlation coefficients. Below the diagonal:
partial correlation coefficients, with the effects of sex and wing morphology held constant.
Statistical significance corrected for an experimentwise error rate of 0.05, and only significant
correlations are shown; n = 234, ns = non-significant.
1
TL
1. Total length
2. Abdominal length
3.Thoracic length
4.Thoracic width
5. Thoracic height
6. Genital length
7. Mid-femoral length
8.Front femoral width
0.72
0.85
0.55
0.44
ns
0.64
0.34
2
3
4
AL
ThL
ThW
0.84
0.85
0.53
0.75
0.62
0.72
0.47
0.34
0.39
-0.29
0.33
ns
0.61
0.42
ns
0.59
0.28
5
ThH
6
GL
0.70
0.62
0.61
0.78
-0.60
-0.91
-0.29
-0.43
-0.43
0.39
ns
ns
0.35
0.27
ns
ns
0.24
0.22
7
8
MFL
FFW
0.25
-0.47
-0.80
11s
0.43
ns
ns
ns
0.32
-0.33
-0.30
0.88
0.45
0.46
SIZE AND SHAPE POLYMORPHISM IN GERRIS REMIGIS
177
t
I
I
I
I
- - - -cI
I
I
-I
I
I
I
I
I
I
I
I
-2
0
-I
2
I
PC1
(a),
Figure 5. Mean scores of apterous females (O), macropterous females (a),
apterous males
and
macropterous males (D) on the first two principal components of a general principal components
analysis. Vertical and horizontal bars indicate f 1 SD.
components emphasize variance in shape that is independent of size (Cock, 1966;
Manly, 1986: 61; Somers, 1989; LaBarberra, 1989). The results of PCA
performed on measurements of G. remigis, excluding total length, are shown in
Table 2 and Fig. 5. The first two components explain 82% of the total variance,
and none of the other components account for more than 1/7th of the trace.
Thus, only the results for the first two components are presented.
The first component is highly positively correlated with abdominal length and
all three thoracic measurements, but is highly negatively correlated with genital
TABLE
2. Results of Principal Components Analyses based on size measurements of G. remigis,
excluding total length
~
~~~~~~
~~
General PCA
Trait
Abdominal length
Thoracic length
Thoracic width
Thoracic height
Genital length
Mid-femoral length
Front femoral width
Eigenvalues:
yo Variance explained:
Size-adjusted PCAt
PCI Loadings*
PC2 Loadings*
PCl Loadings*
0.948
0.663
0.792
0.770
-0.849
-0.094
-0.754
-0.158
0.616
0.421
0.360
0.429
0.840
0.564
0.976
0.957
0.955
0.833
-0.979
0.797
-0.814
3.84
55.1
1.92
27.4
5.82
83.1
*Correlations between trait values and PCs.
tPCA based on a doubly-centered matrix of log-transformed measurements (Somers, 1989).
178
D. J. FAIRBAIRN
length and width of the front femur. Large individuals with relatively small front
femora and genitalia score highly on this component. As might be expected from
the previous analyses, females tend to have positive scores on PC1, while males
have negative scores (Fig. 5). Within each sex, macropters tend to have higher
scores than apters. Two-way ANOVA reveals highly significant differences
between sexes (F = 1248.3, d.f. 1, 230, P < 0.001) and wing morphs (F =
485.6, d.f. 1, 230, P < 0.001), as well as a significant interaction between these
variables (F = 8.50, d.f. 1, 230, P < 0.005). The interaction between sex and
wing morph is expressed as greater sexual dimorphism among apters than
among macropters, and greater differences between wing morphs among males
than among females (Fig. 4). These are the same patterns revealed by previous,
univariate analyses.
The second principal component is most strongly correlated with femoral
length and width, and thoracic length. All correlations are positive, with the
exception of the correlation with abdominal length, which is small and negative.
Animals with relatively large thoraxes and thoracic appendages score highly on
this component. Macropterous males have primarily positive scores and apterous
females, at the other extreme, have primarily negative scores (Fig. 5). Within
each sex, macropters tend to have higher scores than apters, while, within each
wing rnorph, males tend to have higher scores than females. The differences
between sexes and wing morphs are highly significant (sex: F = 62.31, d.f. 1,
230, P < 0.001; wing morph: F = 45.53, d.f. 1, 230, P < 0.001), and there is
no significant interaction between these two variables (F = 0.055, d.f. 1, 230,
P = 0.81).
This principal components solution successfully reduces the patterns of
variation in seven morphometric traits to two principal components, and both
sexes and wing morphs are clearly separated along both of these axes (Fig. 5). As
expected, PCI emphasizes variation in general or overall body size, while PC2
emphasizes shape differences, in particular, differences in the size of the thorax
and thoracic appendages relative to the abdomen. However, the variation in
shape defined by the size of body components relative to the genitalia and
appendages is included in PCl (this represents changes in shape that are
correlated with changes in size, allometry). Thus, PC 1 contains information
about both size and shape.
T o separate the allometric shape component from isometric changes in size, I
used a doubly-centred PCA based on log-transformed measurements (Somers,
1989). This method removes isometric size variation from the covariance matrix,
and thus the PCA is based on shape variation alone. This ‘size-adjusted’ PCA
was highly successful, with the first principal component accounting for 83.1% of
the variance. None of the other components accounted for more than 1/7th of
the trace, and so these are excluded from further analysis. PC1 is highly
correlated with all seven traits. The correlations are negative for width of the
front femur and genital length, but positive for all other traits (Table 2). Males,
with their long external genitalia and wide front femora, tend to have negative
scores on this shape component, while females have positive scores (Fig. 6). This
difference between the sexes is highly significant (2-way ANOVA: F = 2 151.3,
d.f. 1, 230, P < 0.001). Within sexes, macropters tend to score higher than
apters (F = 100.7, d.f. 1, 230, P < 0.001). The discrimination between wing
morphs is not as clear as that between sexes, and is due primarily to the
-
SIZE AND SHAPE POLYMORPHISM IN CERRZS REMICIS
-
I
I
-
-1.5
-1.0
I
I
I
I
-0.5
0.5
0
I .o
1.5
179
2.0
PC1
Figure 6. Mean scores ( ~ S D of
) apterous females (O), macropterous females (a),apterous males
(n),and macropterous males (m) on the first principal component of a ‘size-adjusted’ PCA (see
text for explanation).
relatively longer genitals of apters. The effect of wing morphology is independent
of sex (F for interaction = 0.264, d.f 1, 230, P = 0.6).
These principal components analyses indicate that the major differences in
shape between sexes and between wing morphs are similar, and are primarily
due to differences in the size of body components relative to the genitalia and
front femora. The genitalia contribute to morph discrimination along both axes
(sex and wing morph), but width of the front femur contributes primarily to
discrimination between sexes. These differences among morphs are strongly
correlated with overall size, and thus appear in both the general and ‘size
adjusted’ PCAs. They represent allometric changes. The size of the thorax and
legs relative to the abdomen (PC2 from the general PCA) makes a smaller, but
still significant contribution to the shape differences between morphs along both
axes, and this shape change is independent of size.
DISCUSSION
The preceding analyses clearly indicate that both sexes and wing morphs of
G. remigis differ significantly in size and shape. Females tend to have larger
bodies than males, and macropters tend to have larger bodies than apters. These
patterns are reversed for genital and appendage measurements, and the contrast
between these and body measurements provides the major shape differentiation
between sexes and between wing morphs. When the effects of size are statistically
removed, sexes and wing morphs can still be distinguished by the size of the
thorax and thoracic appendages relative to the abdomen, males and macropters
having relatively small abdomens. Several lines of evidence favour the hypothesis
that this differentiation in size and shape between sexes and between wing
morphs is the result of selection acting primarily on shape rather than overall
size:
(I) Shape dtferences are independent of size. The clearest evidence of this comes
from the second principal component of the general PCA. The mean scores on
PC2 differed significantly between sexes and between wing morphs, indicating
significant shape differentiation that is independent of size. Additional evidence
can be gleaned from a closer look at the allometric differentiation between sexes
and between wing morphs. The general observation that females and macropters
have larger bodies but smaller external genitalia and appendages than males and
apters conceals finer scale differentiation within these two major groups of traits.
The largest differences between sexes occur in abdominal length, genital length
and width of the front femur. In contrast, the most pronounced dimorphism
between wing morphs occurs in the height and width of the thorax. Wing
I80
D. J. FAIRBAIRN
morphsshow relatively little dimorphism for width of the front femur, and sexes
show relatively little dimorphism for thoracic measurements. Thus, allometric
shape differentiation along the two axes is dissimilar and cannot be ascribed
primarily to size-mediated changes in shape.
(2) Shape dajGerentiation is consistent with ecological specialization. As predicted,
males and females differ primarily with respect to traits directly associated with
their reproductive roles. I n female gerrids, eggs are produced and stored in the
abdomen, and the number of mature eggs stored is positively correlated with
total length (Fairbairn, 1988a). This correlation is probably due to the strong
positive correlation between total and abdominal length, the functional
relationship being between abdominal size (volume) and number of eggs. Thus,
female fitness, in terms of reproductive success, is correlated with abdominal size.
Wickman & Karlsson (1989) found a similar pattern of sexual dimorphism in
seven butterfly species: abdominal mass made up a significantly larger
proportion of total mass in females than in males. As in G. remigis, this result is
most easily explained by a high correlation between reproductive output and
abdominal. size in females. In contrast, reproductive success in male C. remigis
shows no correlation with body size, but is significantly correlated with width of
the front femur (Rubenstein, 1984; Fairbairn, 1988a). Wide front femora
presumably assist males in grasping females during copulation and during
prolonged periods of pre- and post-copulatory guarding (Wilcox, 1984;
Fairbairn, 1988a; Kaitala & Dingle, unpublished data). Finally, the difference
in genital length between the sexes obviously reflects reproductive function, and
is typical of the Gerromorpha in general (Andersen, 1982: 51-55).
The shape differences between wing morphs are also consistent with their
presumed specialization, macropters being adapted for migration by flight, and
apters for reproduction (Harrison, 1980; Dingle, 1985; Roff, 1986). The dorsal
longitudinal wing muscles are the largest muscles in the gerridean body, and
when fully developed occupy more than 60% of the volume of the mesothorax
(Andersen, 1973). Attachment of these and other flight muscles, as well as t h e
two pairs of wings, is associated with changes in the shape and thickness of the
cuticular structures of the thorax (Matsuda, 1960; Andersen, 1973). Apterous
G. remigis have neither wings nor flight muscles. I t is, therefore, not surprising
that the primary difference between wing morphs occurs in the size and shape of
the thorax. However, the reproductive specialization of the apterous morph is
also evident: apterous morphs of both sexes have larger genitalia than
macropters.
(3) Patterns of growth facililate the independent evolution of shape. The shape
differentiation between sexes and wing morphs may be facilitated by underlying
patterns of growth (Cock, 1966). In the Gerridae, leg segments show
hyperallometric growth through all five nymphal stages (Matsuda, 1960). Thus,
the legs elongate faster than the body. The growth ratio of leg segments to body
length tends to be relatively constant through the first four nymphal stages, but
significant increases or decreases occur in the final instar (Matsuda, 1960, 1961).
These allometric relationships suggest that regulation of appendage growth is
relatively independent of body growth, and can be adjusted late in development
in association with the development of adult morphology. This is consistent with
the observation that the primary shape differentiation among morphs in
G. remigis is due to the relative size of body and appendage components.
SIZE AND SHAPE POLYMORPHISM IN GERRIS REMIGIS
181
Differences in the relative sizes of body components may also be explained by
differences in underlying patterns of growth. Blackith, Davies & Moy (1963)
studied patterns of growth of body components in the seed bug, Dysdercusfasciatus
Sign, and discovered three centres of hyperallometric growth. One centre
develops early in postembryonic life in the mesothorax, and is responsible for
rapid enlargement of the mesothorax throughout all preimaginal stages. Blackith
et al. (1963) note that “the enlargement of the mesothorax is associated with its
specialized role in adult flight”. A second centre of accelerated growth occurs in
the middle abdominal segments during the first and second nymphal stages, and
is responsible for early lengthening of the abdomen. The final centre of
accelerated growth develops at the posterior end of the abdomen during the
fourth instar, and is responsible for the development of sexual dimorphism in
abdominal length and genital length and structure. The existence of relatively
independent centres of growth in the mesothorax, anterior abdomen and
posterior abdomen, would facilitate changes in the growth ratios, and thus final
size ratios, among these three body areas. Differences in the relative sizes of the
thorax and abdomen in macropterous and apterous G. remigis could be produced
by differences in the relative growth rates of the mesothoracic and anterior
abdominal growth centres during the early instars, as rudimentary wing pads are
forming in the macropterous morph (wing pads are visible in the third instar;
Andersen, 1982: 297). Similarly, sexual dimorphism for abdominal length could
be explained by differences in the relative growth of the posterior abdominal
growth centre during the later nymphal stages, associated with differentiation of
the sexes. [In the Gerridae, genital differentiation begins in the fourth instar and
the sexes can be distinguished in the fifth instar (Andersen, 1982: 330)].
Although there is no direct evidence that the patterns of growth of body
components in G. remigis are similar to those described for Dysdercus, patterns of
growth among exopterogote insects are very conservative and similar across a
broad range of taxa (Wigglesworth, 1954; Matsuda, 1960; Blackith et al., 1963;
Sehnal, 1985). Thus, in the absence of contrary evidence, it is not unreasonable
to generalize among species within a single suborder, in this case the
Heteroptera.
( 4 ) Phenotypic correlations among traits suggest patterns of genetic correlation, and thus
of correlated responses, that are consistent with the observed dzferences among morphs in both
shape and overall sire. When based on samples of more than 40 individuals,
patterns of phenotypic correlation among morphometric traits are strongly
correlated with patterns of genetic correlation (Cheverud, 1988). Thus, the
patterns of phenotypic correlation observed in the present study probably reflect
underlying patterns of genetic correlation. These patterns suggest high positive
correlations among body traits (abdominal and thoracic measurements), but
negative or non-significant correlations between these and genital and
appendage traits. Thus, selection favouring an increase in size of a given body
component, such as the abdomen in females or thorax in macropters, can be
expected to produce a correlated increase in other body components, and thus
an increase in overall body size. Such shape-mediated changes in size may
explain the larger overall size of both females and macropters. However, the
negative or non-significant correlations between body traits and appendage and
genital traits suggest that selection on body components would have a negative
influence, or no influence at all on genital and appendage size, and vice versa.
182
D. J. FAIRBAIRN
Thus, the larger morphs (females and macropters) tend to have relatively small
genitals and appendages. Lack of positive genetic correlations between
appendage and body components also may explain why sexual selection for wide
front femora in male G. remigis (Rubenstein, 1984; Kaitala & Dingle,
unpublished data) is not associated with sexual selection for overall size, or with
a male-biased body size ratio (Rubenstein, 1984; Fairbairn, 1988a, 1990).
These four lines of evidence are certainly consistent with the hypothesis that
most of the morphological differentiation among morphs in G. remigis reflects
direct selection for differences in shape. However, we cannot dismiss the
possibility that some of the size differentiation reflects selection acting directly on
overall size. Mating and foraging success are correlated with overall size in
female G. remigis, but not in males (Rubenstein, 1984; Fairbairn, 1988). Thus,
the larger size of females may reflect direct selection for overall size, as well as
selection for relatively larger abdomens. Similarly, body size in insects and other
flying animals tends to be positively correlated with flight capacity (flight
velocity, duration and distance) (Pyke, 1978; Dingle, Blakely & Miller, 1980;
Peters, 1983: 84-99; Calder, 1984: 162-194; Casey, May & Morgan, 1985;
Slansky & Haack, 1986), and thus, the larger size of macropterous G. remigis
may well reflect selection for larger overall body size, as well as increased
thoracic size.
If the size differences among morphs are at least partly the result of direct
selection for overall size, is there any evidence for size-mediated differences in
shape? The one shape change predicted a priori, hyperallometry for appendage
size, was not observed. Although ontogenetic and phylogenetic comparisons
indicate that legs become proportionally longer as body size increases in the
Gerridae (Matsuda, 1960; Andersen, 1982: 2 12-2 17), differences between sexes
and wing morphs in G. remigis show the opposite trend. The only other shape
difference that is consistent along both axes of size dimorphism is the negative
correlation between total length and genital length. This has been interpreted
(above) as reflecting direct selection on genital size, associated with reproductive
specialization. However, the negative correlation between body and genital size
could indicate an underlying functional relationship, perhaps associated with the
mechanics of coupling (Grad & Maly, 1988). Under this hypothesis, smaller
animals must have relatively larger genitals to facilitate coupling. Until this
hypothesis can be tested, the possibility that the observed allometry for genital
length reflects size-mediated changes in shape cannot be discounted.
The primary purpose of this study was to determine if correlated changes in
shape and size (allometry) primarily reflect size-mediated changes in shape, or
shape-mediated changes in size. The preceding comparisons of shape
dimorphism along two axes of size dimorphism in G. remigis are most consistent
with the latter hypothesis. Differences in shape between sexes and between wing
morphs in this species appear to reflect differential selection on different body
parts (including genitalia and appendages) associated with the ecological
specialization of each morph. Size dimorphism along both axes probably results
from a combination of correlated responses to selection acting on specific body
components, and selection acting directly on total size. The relative importance
of these two components cannot be determined at present, but there is little
evidence that selection for overall size, if present, produces size-mediated changes
in shape. The results of this study thus suggest that shape-mediated changes in
SIZE AND SHAPE POLYMORPHISM IN GERRZS REMIGIS
183
size, such as proposed by Lande ( 1979) to account for brain : body size allometry
among mammalian taxa above the species level, may also play a significant role
in producing allometry within species.
ACKNOWLEDGEMENTS
I would like to thank Derek Roff for his unfailing, ever-enthusiastic assistance
in collecting samples for this project. I am also most grateful to Hugh Dingle for
providing facilities, advice and encouragement during my sabbatical year at the
University of California at Davis. D. Roff, R. Preziosi and J. Grant criticized
earlier drafts of this manuscript, and the manuscript has benefited from their
comments. Finally, I would like to express my great appreciation to Sharon
David, who measured all 234 waterstriders for this study. Without her care and
diligence, this study would not have been possible.
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APPENDIX A
Three-way analyses of variance for the effects of sex, wing morphology and site on eight
measurements of body and appendage size in Gerris remigis. For all comparisons, degrees of freedom
are 1 for all effects involving only sex and wings 2 for all effects involving site, and 222 for error.
Sx-sex, W-wing morphology, St-site. *** P < 0.001, ** P < 0.01, * P < 0.05
Main effects
Variable
Total length
Abdominal length
Thoracic length
Thoracic width
Thoracic height
F
P
F
P
F
P
F
P
F
p
F
p
Length of mid-femur F
p
Width of front
F
femur
p
Genital length
Interactions
Sex
Wings
Site
sx*w
233.0
***
120.4
218.9
16.28
2719.7
411.4
***
32.03
***
77.30
***
57.33
***
1.23
0.27
0.27
0.61
2.25
0.13
9.47
10.95
***
87.62
470.6
***
124.9
73.96
102.2
1.02
0.31
7.29
197.0
***
983.95
***
**
0.61
0.54
1.69
0.19
0.59
0.55
1.46
0.23
3.09
222.2
***
***
***
**
***
0.21
0.81
1.05
0.35
46.66
**
***
***
1.56
0.21
1.70
0.19
2.48
0.09
2.20
5.93
***
2 1.25
9.08
**I
***
240.4
***
Sx*w*St
79.02
272.7
***
W*St
***
72.89
3218.4
***
***
***
Sx*St
***
218.42
***
***
11.14
0.18
0.67
0.38
0.54
***
15.55
***
0.11
0.24
0.78
0.45
0.63
3.11
*
2.20
0.11
APPENDIX B
Two-way analyses of variance for the effects of sex and wing morphology
within sites. Degrees of freedom are 1 for sex, wings and sex * wings, 76 for
error on sites 1 and 2, and 70 for error on site 3. *** P < 0.001, **
P < 0.01, * P < 0.05
Main effects
Variable
Site
Sex
Wings
Interaction
Sex * Wings
Total length
I F
P
2 F
P
3 F
P
I F
P
2 F
P
3 F
P
28.78
31.91
***
5.03
***
5 I .54
***
4.33
78.70
40.86
***
6.73
159.5
***
28.70
90.88
***
10.51
106.3
26.52
Abdominal length
***
183.1
***
778.8
***
679.9
***
595.5
***
***
*
*
*
***
**
***
*
I .30
0.28
2.72
0.07
3.39
*
D. J. FAIRBAIRN
I86
APPENDIX B. Conl.
Main effects
Interaction
Sex * Wings
Variable
Site
Sex
Wings
Thoracic length
I F
553.3
***
12.67
P
2 F
***
0.25
0.62
44.18
***
12.55
***
0.00
16.57
27.15
P
3 F
P
Thoracic height
Genital length
I F
P
2 F
P
3 F
P
I F
P
2 F
Length of mid-femur
P
3 F
P
I F
P
2 F
Width of front femur
P
3 F
P
I F
P
2 F
P
3 F
P
I .o
***
33.45
***
42.67
***
17.33
***
1412.2
***
***
118.14
***
229.85
***
151.90
***
1.67
0.20
0.39
0.54
0.31
0.58
7.36
32.76
***
5.75
553.3
***
12.67
994.3
28.44
0.25
0.62
9.64
***
***
34.84
0.92
0.34
0.44
0.51
555.2
***
322.8
***
188.8
***
***
***
0.66
0.42
0.01
0.93
5.89
6.97
*
7.00
**
0.02
0.88
**
*
**
2.23
0.14
1.53
0.22
1.63
0.20
3.70
0.06
1.19
0.28
2.22
0.14