Analysis of asymmetries in the African fruit bats Eldolon helvum
and Rousettus egyptlacus (Mammalia: Megachiroptera)
from the islands of the Gulf of Guinea. I. Variance
and size components of bilateral variation
J. JUS TE,
C. L O’ PEZ-GON Z A’ LEZ
& R. E. STRAUSS
*Estacio n Biolo gica De Donaana (CSIC), Sevilla, 41080, Spain
Departamento de Bioquimica y Biologia Molecular IV, Facultad de Veterinaria, Universidad Complutense de Madrid, Madrid 28040, Spain
Department o Biological Sciences, eeaas eech University, uubboc , e 9440431111, US
Keywords:
Abstract
asymmetry;
Eidolon helvum;
fruit bats;
Gulf of Guinea;
Rousettus egyptiacus;
three-dimensional coordinates;
variance components.
A set of cranial characters was examined in the fruit bats Rousettus egyptiacus
and Eidolon helvum to compare trends and relative importance of major
components of bilateral morphometric variation, and their relationship with
character size. Using two-way, sides-by-individuals A N O V A , four components
of variation were estimated for each bilateral variable: individual variation (I),
directional asymmetry (DA), non-directional asymmetry (NDA) and measurement error (E). Both species exhibit similar major trends of variation in
asymmetry across characters, as shown by principal component analysis, using
variance components as variables. Degree of interspecific congruence among
characters was confirmed by a two-way A N O V A with species and variance
components as fixed factors. Congruence of asymmetry patterns between
species suggests that the concept of population asymmetry parameter (PAP)
could be extended to higher hierarchies. PAPs above the species level may
result from common mechanisms or similar developmental constraints acting
on species’ buffering capacities and morphological integration processes.
Introduction
The study of asymmetry is a subject of both theoretical
and empirical interest for the implications it may have in
subjects as varied as ecotoxicology, population genetics
or sexual selection (Zakharov, 1990; Clarke, 1994; Møller
& Thornhill, 1998; although see Simmons et al., 1999).
Asymmetry patterns traditionally have been categorized
into three main groups (Van Valen, 1962; Palmer, 1994).
Fluctuating asymmetry (FA) refers to a pattern of
bilateral variation in a population in which the sample
is normally distributed with a mean of R—L values equal
to zero (Palmer, 1994). Directional asymmetry (DA)
occurs when the mean of asymmetry values differs
significantly from zero, whereas antisymmetry (AA) is a
pattern of bilateral variation in which statistically signifiCorrespondence: Dr Javier Juste, Estacio’ n Biolo’ gica de Don ana (CSIC),
Avda M Luisa s/n, Sevilla 41013, Spain.
Tel.: +34 954 23 23 40; fax: +34 954 62 11 25; e-mail: juste@ebd.csic.es
cant differences exist between sides, but the side that is
larger varies randomly among individuals. Although DA
and AA have been considered to be developmentally
controlled and possibly adaptive, the specific processes
producing these patterns remain a matter of discussion
(Van Valen, 1962; Graham et al., 1993; Palmer et al.,
1994; Rowe et al., 1997). In contrast, FA usually is
considered to represent ‘developmental noise’, the result
of random deviations from ideal symmetry (but see
Emlen et al., 1993; Klingenberg & Nijhout, 1999).
Although seemingly simple, in practice the study of
bilateral variation as a measure of developmental noise
has been laden with methodological concerns. This is due
in part to the diversity of procedures that have been used
to analyse asymmetry data, which sometimes obscured
the meaning of results and made comparisons among
studies nearly impossible. A potentially confounding
factor when comparing asymmetry in terms of variances
is size variation. A number of data transformations has
been used to adjust for size (Palmer & Strobeck, 1986;
Palmer, 1994), under the assumption that scaling does
not reduce or eliminate desired information about
variance patterns. However, arbitrary correction for
presumed size effects may lead to spurious differences
among samples (Palmer, 1994; Rowe et al., 1997).
Another major methodological problem in interpreting
patterns of bilateral variation is that more than one type
of asymmetry may occur simultaneously in a population.
When the focus of a study is to compare levels of
developmental noise, DA and AA are considered to be
nuisance factors that are better eliminated, since they
may obscure the effect of FA (Palmer & Strobeck, 1986,
1992; Palmer et al., 1994). Nonetheless, ‘correction’ or
elimination of characters with significant DA or AA may
be unnecessary and even harmful, for these components
might also reflect developmental instability (McKenzie &
Clarke, 1988; Graham et al., 1993, 1998; Kraak, 1997).
Measurement error is a third concern in asymmetry
studies. Because differences in values of bilateral traits
are usually small, and also because asymmetry analyses
are comparisons of variances, error becomes a key issue
(Palmer & Strobeck, 1986; Palmer, 1994; Merila” &
Bjo” rklund, 1995). Differences in measurement technique
or random measurement errors may lead to spurious,
non-significant results when comparing FA levels
(Jolicoeur, 1963; Palmer & Strobeck, 1986; Palmer, 1994).
To account for these three, typically undesirable,
sources of variation, Palmer & Strobeck (1986, 1992)
proposed to test for significance of DA and error (E), prior
to any FA analysis, by performing a two-way, mixed
model A N O V A with repeated measurements on each side.
This design allows for estimation of significance of these
two factors, with the additional advantage of yielding an
estimate of variance due to FA when AA is not present in
the population. The importance of measurement error
and size adjustment in asymmetry studies has been
thoroughly addressed (Palmer & Strobeck, 1986; Merila”
& Bjo” rklund, 1995; Bjo” rklund & Merila” , 1997) but, to our
knowledge, the relative importance of DA and other
non-directional asymmetries to the total variation among
sides in a character has not been formally evaluated.
Sorting out as many confounding sources of variation as
possible from a sample of bilateral measurements should
provide a better resolution for the FA signal. Furthermore, considering a multivariate set of bilateral measurements in which most extraneous sources of variation
have been partitioned out should allow for a more
accurate description of FA patterns, which in turn will
allow for examination of trends of variation across
populations.
We report the analysis of a multivariate set of bilateral
morphometric characters from two morphologically similar species of African fruit bats (Rousettus egyptiacus and
Eidolon helvum). Using a highly precise system, measurements were taken across the three dimensions and all
areas of the skull, measurements were submitted to sides-
by-individuals two-way A N O V A (Palmer & Strobeck,
1986). Relative magnitudes of components of bilateral
variation of a set of measurements (individual variation,
directional asymmetry, non-directional asymmetry and
measurement error) were assessed and compared, and
their interrelationships evaluated, by analysing them in a
multivariate fashion. We assessed statistical significance of
these components once the size effect is eliminated, and
evaluated the degree of interspecific congruence of asymmetries after other sources of variation are accounted for.
Materials and methods
Morphological measurements
A set 82 homologous cranial landmarks was defined on
bone sutures, foramina and inflection points along the
edges of cranial structures (Fig. 1) on skulls of the two
species of fruit bats (31 E. helvum and 30 R. egyptiacus).
Dental landmarks were set on the bone (at the edge of
the alveoli) to avoid variation due to differential toothwear. To facilitate repeatability, each landmark was
gently marked in pencil on the surface of the bone,
under 20x magnification, before being recorded. Threedimensional coordinates of landmarks were digitized
using a 3-D Reflex Microscope (Reflex Measurement
Ltd, Butleigh, UK). This is a highly precise, non-contact
instrument that uses a small light spot to digitize
coordinates in any position within a magnified field.
The microscope was periodically recalibrated to ensure a
linear scale error of less than 30 4m over 100 mm in the
a-axis (MacLarnon, 1989). Landmarks were collected
under a 20x magnification lens from four different
aspects, and thus the skull was rotated three times to
attain the complete data collection. Four ‘reference
points’ (Fig. 2), visible in two sequential views and
located separated over the skull’s surface, allowed the
shift of the complete set of coordinates from one view to
the next without distorting the shape or scale of the
observations. Amount of error due to the new digitizing
of the four reference landmarks was evaluated after each
shift, and the whole transformation was discarded, and
the digitizing process restarted, if the greatest error of any
of the four reference points was larger than 0.1 mm in
any direction. All landmarks were recorded by a single
individual (J.J.), and were taken without reference to
prior values.
Coordinates were converted to 57 pairs of Euclidian
distances between selected pairs of homologous landmarks on the left and right sides of the skull (Fig. 2). In
addition, five landmarks were taken along the mid-plane
of the skull, and 18 other points (‘pseudo-landmarks’)
were calculated as the mid-points for each of 18 pairs of
left and right homologous landmarks. These 23 landmarks and pseudo-landmarks were used to define the
best-fit (least-squares) midsagittal plane on each skull.
Offset distances from 17 pairs of bilateral landmarks to
Fig. 1 Landmark points selected for the analysis of asymmetry on skull and mandible of the African fruitbats Rousettus egyptiacus and Eidolon
helvum.
the midplane were then calculated and included as
characters in the asymmetry analysis. Including the
latter, a total of 74 pairs of characters (or 74 bilateral
characters) were measured or estimated on each skull
(Fig. 2). All distances were calculated using the microscope’s C3D v1.26 software for a complete data set of 30
individuals of E. helvum and 31 of R. egyptiacus. All skulls
were measured twice, in random sequence, with an
interval of 6 months between the first and second set of
measurements. All specimens were collected in westcentral Africa, and are deposited at the Estacio’ n Biolo’ gica
de Donana (CSIC), Seville, Spain.
Statistical analyses
All measurements were transformed to natural logarithms to linearize any possible allometric relationships
(Bookstein et al., 1985). To investigate the effect of size,
analyses were performed separately on log-transformed
and size-adjusted values. To adjust for the effect of size,
each log-transformed variable was regressed against the
first principal component (PC1) of all the log-transformed variables taken together, and residuals were
calculated. The same set of measurements from additional specimens of E. helvum (224) and R. egyptiacus
(241) from the same geographical area was used solely to
estimate a more robust covariance matrix on which to
base the principal component analysis. Varying degrees
of damage in some specimens resulted in incomplete sets
of measurements; to avoid losing information from these
individuals, missing values were estimated using the
expectation-maximization (EM) method of Little &
Rubin (1987).
Using only the sample measured twice, a two-way,
mixed-model analysis of variance (A N O V A ) was performed separately on each of the 74 bilateral characters,
by species. In this analysis, ‘sides’ is a fixed effect,
whereas ‘individuals’ is a random effect (Leamy, 1984;
Palmer & Strobeck, 1986; Palmer, 1994). Individual
variation of each character is partitioned into directional
asymmetry (DA, the main effect due to ‘sides’), individual variation in size and shape (I, the main effect due to
‘individuals’), non-directional asymmetry (NDA, the
sides-by-individuals interaction, which may include
both fluctuating asymmetry and antisymmetry) and
measurement error (E).
Presence of antisymmetry was tested by species and
character using the Shapiro—Wilk’s test for normality
from the P R O C U N I V A R I A T E of SAS (SAS Institute, 1995).
Additionally, for each character, plots of asymmetry
49
48
47
46
45
44
30
15
4
14
3
27
39
21
36
34
20
26 25 24 23 22
35
18
19
28
33
5
38
31
43
42
69
32
37
33
2
30
44 45 46 47 48
70 727476 78 80 81 67 6664
717375 77
79
82
4
5
7
6
17
10
8
9
34
37
31
12
2
3
29
32
13
1
27
26
25
24
23
22
21
36
20
16
35
38 39
42 19
18
43
41
15
12
14
13
M
40
50
49
11
55
626058 56
68 65 63
61 59 57
54
51
53
52
Fig. 2 Selection of 74 bilateral distances between landmark points across the skulls of Eidolon helvum and Rousettus egyptiacus. Parallel arrows
indicate reference points used in transformation of coordinates (see Material and methods), M = midplane.
values were examined to evaluate visually the presence
of skewness and kurtosis. Sequential Bonferroni adjustment (Rice, 1989) was used to decide on the statistical
significance of multiple univariate comparisons (tablewide = 0.05), by species. Visual inspection of residuals
from these analyses suggests the presence of an additive
error model in the data (Graham et al., 1998; Cowart &
Graham, 1999) for some variables. However, preliminary
simulations (unpublished) suggest that the A N O V A model
used is robust to skewness in the error distributions.
Variance components were estimated using the procedure described by Sokal & Rohlf (1995). The proportions of
the total variance accounted for by each of these components (DA, I, NDA, E) were then estimated as a percentage
of the total variance. Variance proportions were used in
further analyses because they are scaled to sum one,
thereby allowing for comparisons of components across
characters and species. However, because they are not
independent from each other, values were square-rooted
and then arcsine-transformed for further analyses.
To summarize trends of variation in variance components across characters, a PCA was carried out by species
and type of data (log-transformed and size-adjusted)
using characters as observations and variance proportions
as variables. Vector correlations between variance proportions and principal components were used to interpret
the PCA axes. To test for differences in behaviour of
variance proportions across species and between compo-
nents, a two-way, randomized-blocks A N O V A was performed on the same data set. In this test, species and
variance components (I, DA, NDA, E) are fixed factors,
and variables are blocks, and therefore random (Sokal &
Rohlf, 1995). Analyses were carried out using the SAS
system (SAS Institute, 1995) and MATLAB v4.2c.1 (The
MathWorks Inc., 1994) at a significance level of 0.05.
Results
In univariate tests for log-transformed data most of the
variation is accounted for by individual differences (I) in
both species. The I component represents between 2.81
and 99.6% of the total variation in the two samples,
averaging 80.99 and 81.48% for E. helvum and
R. egyptiacus, respectively (Table 1). The directional
asymmetry variance component (DA) accounts for the
smallest proportion of the total variance in both species
(between 0.01 and 35.65%, averaging 1.96% and 2.01%
for E. helvum and R. egyptiacus, respectively). The interaction term (NDA) accounts for 0.16—57.01% of total
variance, with averages of 11.02% and 9.73%; whereas
the error term (E) varies between 0.07 and 40.90% of the
total variation, averaging 6.01% for E. helvum and 6.77%
for R. egyptiacus. For size-adjusted data the range for the I
component also varies between 1.4 and 97.66% but the
average is 68.77% for E. helvum and 72.28% for
R. egyptiacus. DA ranges from 0.0 to 3.15% (averages
J
Table 1 Relative variance components (as proportions of the total variance) from two-way A N O V A s sides-by-individuals (Palmer & Strobeck,
1986) on 74 bilateral characters (right—left distances) of Rousettus egyptiacus and Eidolon helvum. I = individuals, DA = directional asymmetry,
NDA = non-directional asymmetry, E = measurement error. Numbers within parentheses show one of the distances (right side) for each pair
in Fig. 2 that are used to calculate each bilateral character (M = midplane). Asterisks indicate variables significant at a table-wide
= 0.05 after a sequential Bonferroni adjustment of the significance level.
Log-transformed data
Size-adjusted data
Eidolon helvum
Rousettus egyptiacus
Eidolon helvum
Rousettus egyptiacus
Variable
DA
NDA
I
E
DA
NDA
I
E
DA
NDA
I
E
DA
NDA
I
E
1 (2-M)
2 (5-M)
3 (6-M)
4 (10-M)
5 (49-M)
6 (48-M)
7 (47-M)
8 (46-M)
9 (45-M)
10 (44-M)
11 (1—2)
12 (1—5)
13 (2—5)
14 (5—10)
15 (5—9)
16 (9—10)
17 (2—49)
18 (2—48)
19 (2—47)
20 (2—46)
21 (2—45)
22 (2—44)
23 (5—44)
24 (5—45)
25 (5—46)
26 (5—47)
27 (5—48)
28 (5—49)
29 (48—49)
30 (47—48)
31 (46—47)
32 (45—46)
33 (9-M)
34 (11-M)
35 (13-M)
36 (31-M)
37 (33-M)
38 (37-M)
39 (38-M)
40 (10—11)
41 (9—11)
42 (11—13)
43 (9—13)
44 (31—33)
45 (31—37)
46 (31—38)
47 (37—38)
48 (33—37)
49 (13—38)
50 (13—37)
51 (13—33)
5.82
0.71
8.41
1.76
5.20
12.74
2.73
0.16
0.25
0.38
0.24
0.01
0.24
0.03
0.16
0.91
0.11
0.02
0.35
0.06
0.05
0.06
3.96
5.67
11.41
3.12
4.22
3.69
2.95
5.97
1.98
0.46
18.58
0.30
2.05
1.99
0.04
1.86
0.13
0.13
0.07
0.09
1.68
0.24
0.22
0.76
2.24
0.25
1.42
0.77
0.16
16.69
15.60
25.65
6.66
10.84
14.71
12.97
8.78
8.72
10.53
7.07
0.49
1.93
3.19
7.92
1.38
1.92
4.82
2.76
1.54
1.79
1.23
3.40
8.33
10.70
6.17
2.34
1.50
13.15
6.19
4.91
11.95
44.53
7.25
14.79
9.55
29.47
9.34
29.88
3.09
5.81
13.78
12.23
6.79
3.37
20.28
18.49
6.41
39.86
23.81
20.87
71.95
69.34
25.03
79.26
69.38
58.11
76.45
87.25
88.16
86.95
91.84
99.42
97.68
96.03
91.69
96.61
93.71
91.12
96.08
97.85
97.58
98.14
89.87
82.22
74.18
88.91
92.50
93.67
63.10
86.08
89.91
77.31
2.81
88.69
57.43
78.87
64.61
72.61
60.27
96.44
93.86
81.42
85.86
92.29
88.26
73.80
71.58
90.13
50.31
70.17
78.02
5.54
14.35
40.90
12.32
14.59
14.44
7.85
3.81
2.87
2.14
0.85
0.08
0.16
0.75
0.23
1.10
4.26
4.03
0.82
0.56
0.57
0.56
2.76
3.78
3.71
1.80
0.94
1.15
20.80
1.75
3.20
10.28
34.09
3.77
25.73
9.58
5.87
16.19
9.72
0.34
0.26
4.71
0.23
0.68
8.16
5.16
7.70
3.21
8.41
5.25
0.96
0.51
1.59
1.54
2.51
2.19
8.60
4.31
2.31
1.70
1.55
0.45
0.18
0.24
0.21
0.31
1.94
0.38
1.36
2.06
0.58
0.32
0.03
1.55
6.15
10.21
1.07
0.39
5.92
35.65
5.56
0.28
0.18
5.51
0.57
0.69
0.47
2.45
0.39
3.47
0.52
2.69
0.17
4.99
1.42
4.41
0.34
0.05
0.27
0.74
1.11
0.40
16.26
47.34
57.01
13.09
6.66
3.46
2.12
9.16
15.10
20.66
12.00
1.00
1.28
4.13
3.11
1.69
10.23
7.76
5.89
4.89
5.67
4.11
9.28
9.48
8.32
4.42
2.82
2.59
14.90
7.77
11.96
3.07
52.29
18.88
26.13
3.50
20.22
8.09
24.69
16.83
7.63
5.28
8.77
7.23
2.20
10.56
4.22
8.11
7.76
5.52
5.39
63.41
30.45
20.11
62.06
76.82
74.44
77.73
82.34
78.84
72.37
83.36
98.49
97.81
94.97
96.44
95.69
81.58
80.93
86.72
91.23
91.92
94.43
83.50
76.99
73.44
92.24
95.01
86.84
27.82
74.38
82.42
89.98
17.68
71.79
35.54
83.91
69.08
83.33
43.83
81.92
86.63
94.35
86.09
90.60
87.22
83.41
93.93
90.48
84.08
90.08
93.09
19.82
20.62
21.35
22.35
14.32
13.50
15.84
6.19
4.36
5.43
4.19
0.33
0.67
0.69
0.14
0.68
7.80
9.95
5.34
3.31
2.09
1.43
5.67
7.38
8.03
2.27
1.78
4.64
21.64
12.29
5.34
6.77
24.51
8.76
37.64
12.13
8.26
8.19
28.01
0.72
3.04
0.20
0.15
0.75
6.18
5.69
1.80
1.14
7.42
3.29
1.12
0.99
1.51
2.06
0.91
0.60
1.33
0.81
1.10
1.03
1.15
0.35
0.08
0.16
0.00
0.49
0.39
0.34
0.18
0.33
0.18
0.25
0.37
0.69
0.13
0.25
0.62
0.17
0.25
1.99
0.28
0.59
0.13
2.19
0.48
0.07
0.88
1.58
0.88
1.44
0.10
0.63
0.82
0.39
0.35
0.31
0.19
1.22
0.40
0.92
0.25
1.28
34.16
31.15
37.38
18.16
31.52
35.47
32.94
27.71
35.44
31.80
14.09
2.68
6.61
5.47
17.66
4.17
5.61
18.19
9.05
4.42
7.26
5.48
9.23
22.04
24.70
17.16
10.43
7.17
28.33
13.63
9.69
17.32
47.81
11.98
15.15
17.54
43.41
14.74
37.83
7.89
18.60
29.55
32.14
11.25
4.32
34.70
28.91
10.48
45.56
30.08
39.40
53.52
39.08
1.44
47.83
24.55
28.62
46.17
58.97
50.59
60.46
83.96
96.18
91.96
93.09
81.02
89.99
84.68
68.54
87.77
93.35
89.12
90.55
84.72
70.26
68.77
78.43
86.24
86.87
22.59
82.14
83.19
67.33
13.43
80.96
58.76
63.49
46.29
60.15
48.55
90.68
79.09
58.86
66.36
87.13
84.39
56.03
57.53
83.65
43.78
62.56
57.73
11.34
28.27
59.12
33.10
43.33
34.58
20.07
12.21
12.94
6.59
1.60
1.05
1.27
1.44
0.83
5.45
9.37
13.09
2.85
2.05
3.38
3.60
5.37
7.57
6.29
3.79
3.17
5.71
47.09
3.95
6.53
15.22
36.57
6.58
26.02
18.08
8.72
24.23
12.18
1.32
1.68
10.77
1.11
1.27
10.98
9.07
12.34
5.46
9.74
7.12
1.60
0.70
2.25
2.19
0.75
3.08
1.56
2.94
3.15
1.94
0.97
0.41
0.08
0.14
0.25
0.06
0.04
0.63
0.25
0.36
0.22
0.13
0.24
0.62
1.17
0.38
0.12
0.28
0.20
1.58
0.19
0.51
0.20
2.05
1.70
0.68
0.13
0.78
0.09
0.17
0.55
0.09
0.36
1.61
0.54
0.31
0.77
0.20
0.29
0.34
0.35
0.29
23.20
60.12
57.63
18.30
17.80
9.95
4.30
18.65
30.53
41.94
16.89
1.31
1.41
8.81
4.43
3.80
15.09
16.99
17.05
16.40
13.82
7.84
20.46
27.94
10.46
3.59
2.92
3.28
35.48
16.03
22.49
3.04
52.04
44.83
22.26
10.12
23.71
11.01
39.08
22.15
21.26
14.00
17.66
12.40
3.49
20.58
5.32
11.48
12.66
11.06
12.88
48.84
12.96
19.79
51.93
37.74
42.15
48.27
63.77
57.96
46.75
76.13
97.58
97.66
89.38
95.24
94.06
74.23
63.29
69.31
73.93
81.75
89.32
67.79
54.07
81.24
94.76
95.34
92.15
20.77
63.00
68.62
90.56
22.45
31.92
43.45
61.60
66.04
77.37
18.75
75.75
69.93
84.37
79.77
85.62
87.18
68.00
92.35
86.24
75.49
82.61
84.16
27.25
24.67
20.39
29.03
41.38
46.34
44.49
14.43
9.57
10.33
6.57
1.03
0.79
1.56
0.26
2.10
10.05
19.47
13.28
9.46
4.31
2.60
11.13
16.83
7.92
1.53
1.47
4.37
42.16
20.79
8.38
6.20
23.47
21.55
33.61
28.16
9.47
11.53
42.00
1.55
8.72
1.27
0.96
1.43
9.02
10.64
2.13
1.99
11.51
5.97
2.67
Table 1 (Continued)
Log-transformed data
Size-adjusted data
Eidolon helvum
Variable
52 (31—43)
53(38—43)
54 (37—43)
55 (13—43)
56 (13—31)
57 (50—51)
58 (50—52)
59 (51—52)
60 (69—70)
61 (70—71)
62 (72—73)
63 (74—75)
64 (76—77)
65 (78—79)
66 (80—82)
67 (81—82)
68 (69—82)
69 (80—81)
70 (78—80)
71 (76—78)
72 (74—76)
73 (72—74)
74 (70—72)
DA
0.89
1.39
0.17
1.59
3.13
0.01
0.01
0.08
0.08
0.11
0.08
0.14
0.18
0.11
0.94
6.89
0.10
3.65
1.59
0.40
3.44
2.81
0.65
Rousettus egyptiacus
NDA
I
E
31.94
19.58
4.43
45.22
34.89
0.16
0.18
1.53
2.32
2.24
2.87
3.19
4.41
2.08
12.15
15.49
1.56
13.36
2.72
8.50
35.02
2.48
14.36
64.17
72.53
93.33
48.03
58.27
99.53
99.61
94.79
95.91
95.57
96.43
94.16
92.10
95.18
84.38
73.11
98.24
59.69
94.78
84.54
50.10
84.66
69.75
3.01
6.50
2.06
5.16
3.71
0.29
0.20
3.60
1.69
2.08
0.62
2.52
3.31
2.63
2.54
4.51
0.10
23.31
0.91
6.56
11.45
10.04
15.23
DA
0.35
0.25
0.16
0.81
1.87
0.35
0.05
0.24
0.28
0.07
0.13
0.12
0.47
0.43
1.85
2.53
0.14
0.55
5.15
0.06
0.63
0.27
0.18
Eidolon helvum
NDA
I
E
10.59
12.44
6.09
16.44
11.69
1.30
0.52
7.12
4.60
3.64
5.05
9.41
5.34
3.51
6.32
13.19
1.84
0.79
9.66
8.61
6.48
1.68
3.22
85.97
67.97
88.54
78.47
80.87
98.27
99.02
91.74
94.83
95.76
93.86
88.32
93.07
94.71
89.34
81.46
97.92
86.81
81.35
89.07
89.36
91.71
89.29
3.09
19.34
5.22
4.28
5.57
0.07
0.41
0.89
0.30
0.54
0.95
2.16
1.12
1.34
2.49
2.82
0.09
11.86
3.84
2.26
3.54
6.34
7.30
0.62% and 0.61%); NDA from 1.20 to 60.12% (averages
19.65% and 15.82%); and E ranges from 0.26 to 59.12%
(averages 10.96% and 11.28%).
After Bonferroni adjustment, no character was significantly non-normal in either species (see supplementary
material;
www.blackwell-science.com/products/journals/suppmat/JEB/JEB298/JEB298sm.htm).
For
the
log-transform data DA was significant only in 10 characters in E. helvum and 10 in R. egyptiacus (Table 1). Those
that are common to both species (5) are characters
related to the upper dentition of the organisms (Fig. 2).
Adjustment for size eliminates all significance of the DA
component for both species because significance in
the two-way A N O V A model is tested as the ratio of the
variance due to sides over variance due to NDA. The
adjustment eliminates all significance of the DA component by significantly reducing the DA variance. The I
term was significant for 73 variables in E. helvum and 72
in R. egyptiacus. The number of significant variables for
the I term decreases to 70 in E. helvum and 69 in
R. egyptiacus after size-adjustment (Table 1). NDA was
significant for 65 characters in E. helvum and 63 in
R. egyptiacus. Significance remains approximately the
same (64 significant characters in R. egyptiacus) or even
increases (72 significant characters for E. helvum) after
adjustment for size. Variance proportions due to error (E)
remain essentially unchanged after size-adjustment.
Because significance of NDA in the A N O V A is based on
DA
0.91
0.84
0.19
0.39
1.23
0.03
0.07
0.19
0.42
0.21
0.23
0.53
0.73
0.59
0.41
0.35
0.02
1.23
0.32
0.49
1.76
0.23
0.76
Rousettus egyptiacus
NDA
I
E
31.08
25.92
5.87
44.34
43.28
1.48
1.41
3.24
7.43
12.46
14.26
12.38
17.72
12.38
17.41
27.49
8.34
20.03
8.29
16.08
46.79
2.97
16.10
64.67
64.70
91.05
49.93
50.89
96.59
96.72
90.85
85.36
76.55
82.69
79.74
69.50
76.20
78.96
64.91
89.82
44.90
88.53
70.65
35.53
82.84
65.80
3.34
8.55
2.89
5.34
4.61
1.90
1.80
5.73
6.79
10.78
2.83
7.35
12.06
10.83
3.22
7.25
1.82
33.84
2.86
12.77
15.92
13.96
17.35
DA
0.09
1.01
0.34
0.05
1.11
0.07
0.05
0.21
0.44
0.14
0.31
0.41
0.03
0.08
0.30
0.65
0.13
0.14
0.16
0.65
0.27
0.16
0.00
NDA
I
E
13.91
17.96
7.43
26.93
27.38
3.73
1.20
6.02
6.79
3.56
8.78
15.70
7.81
4.40
8.08
25.12
4.27
2.26
28.91
19.07
6.67
1.70
3.56
82.38
54.26
86.16
66.93
61.18
94.25
95.93
92.81
91.22
94.87
88.20
79.18
89.39
93.50
88.21
69.36
94.40
70.64
58.72
75.24
89.38
91.21
87.65
3.63
26.76
6.07
6.10
10.32
1.95
2.82
0.97
1.56
1.43
2.70
4.70
2.77
2.03
3.40
4.88
1.20
26.96
12.21
5.03
3.69
6.93
8.79
the ratio NDA to E, none of which changes after the
adjustment, significance of this term is conserved.
The first principal component of variance proportions
accounts for between 83.5 and 86.6% of the total
variation for both species, for log-transformed and sizeadjusted data. PC1 is highly correlated with the I term
(Fig. 3). After size adjustment, the proportion of variance
explained by PC1 remains about the same, and it is still
highly correlated with I. Thus PC1 is an ‘individuals’ axis,
which nonetheless seems not to be associated with
character size. PC1 has a fairly high and positive
correlation with the DA term in the log-transformed
data of both species. Correlation PC1-DA component is
higher for E. helvum, and slightly smaller for R. egyptiacus.
Both NDA and E are strongly correlated with PC1.
In both species the I term is uncorrelated with PC2.
This component, which accounts for 9.3—13.5% of the
total variation, correlates with the DA component in the
log-transformed data, but correlation approaches zero for
both species after size adjustment. NDA is negatively, and
E positively, correlated with PC2 also in both species.
These relationships change only slightly after size adjustment. PC3 accounts for 6.2% of the total variation or less.
The I variance component is uncorrelated with PC3, DA
has a high correlation with it that is preserved after the
size adjustment, and NDA and E have a small to
considerable correlation, which completely disappears
after the size adjustment.
DA
0
I
-0.5
-1
-1
-0.5
0
0.5
9.3 %
PC2
0.5
NDA
0
I
-0.5
NDA
E
-1
1
-1
-0.5
0
0.5
1 10.1 %
0.5
83.5 %
E
I
0
-0.5
-1
-0.5
0
0.5
1
6.2 %
DA
10.1 %
PC2
0.5
NDA
0
I
-0.5
NDA
-1
1
Correlations with PC2
Correlations with PC1
PC1
DA
PC3
DA
PC2
85.8 %
PC1
4.5 %
1
Correlations with PC3
0.5
E
Correlations with PC2
9.3 %
PC3
Correlations with PC3
1
PC2
Correlations with PC2
Log-transformed data
E
-1
-1
1
Correlations with PC1
-0.5
0
0.5
1
Correlations with PC2
DA
I
-0.5
NDA
-1
-1
-0.5
0
0.5
1
Correlations with PC1
0
PC2
I
NDA
-0.5
E
DA
-1
-1
-0.5
0
0.5
1
Correlations with PC2
Eidolon helvum
0.5
PC1
E
86.6%
DA
0
I
-0.5
NDA
-1
-1
-0.5
0
0.5
1
Correlations with PC1
1 0.7 %
0.5
PC3
13.5 %
PC2
0.5
1 12.5 %
Correlations with PC3
0
85.7 %
PC1
Correlations with PC2
0.5
E
0.4 %
PC3
13.5 %
Correlations with PC3
1
PC2
Correlations with PC2
size-adjusted data
1
0
DA
12.5 %
PC2
E
I
NDA
-0.5
-1
-1
-0.5
0
0.5
1
Correlations with PC2
Rousettus egyptiacus
Fig. 3 Principal component analysis on variance components (as proportions) from a two-way A N O V A size-by-individuals, on the African
fruit bats Eidolon helvum and Rousettus egyptiacus. I = interindividual variation; DA = directional asymmetry component; NDA = nondirectional asymmetry; E = error term. Arrows represent vector correlations of variance proportions with the principal components. Inset
values indicate percentage of variance explained by each principal component.
In general, elimination of variance due to size is
reflected in a reduction of the value of variance proportions due to DA, a reduction in I for some characters but
an increase for others, and a proportional increase in the
error (E) and interaction (NDA) proportions. However, in
absolute terms (variance components, not reported here)
the variance due to DA effectively decreases, as does that
due to individuals. The amount of variance due to error
does not change, and neither does the non-directional
component, which suggests that NDA represents mainly
random variation, and therefore ‘pure’ FA sensu Palmer
(1994), independent of size. Non-significance in normality tests further supports the notion of the NDA component representing random variation between sides,
independent also of measurement error. The randomized-block A N O V A on variance proportions was highly
significant for variance component (F3,511 = 1160,
P < 0.001), but non-significant for all other factors
examined (variables, F73,511 = 0.147, P = 1.00; species,
F1,511 = 0.014, P = 0.907; species-by-variance component, F3,511 = 0.199, P = 0.897).
Discussion
Size adjustment and measurement error
Results of principal components analyses are similar in
both species with respect to the proportion of variance
due to each of the A N O V A components examined (I, DA,
NDA, E). PC1 is an ‘individuals’ axis, PC2 summarizes
variation due to ‘sides’ and NDA (interaction term of the
two-way A N O V A ) relates to both PC1 and PC2, as does the
E term. PC1 seems not to be associated with character
size, but the adjustment reduces the correlation between
PC2 and DA to nearly zero, as expected if DA represents
mostly differences in size between sides. On average, E
accounts for a proportion of the total variance of the
samples similar to that of the NDA component. The E and
NDA terms, however, do not change their relationship to
PC2, after size adjustment, reflecting the lack of relationship between NDA and size. Because E and NDA are
negatively correlated, an increase in E would produce a
proportional decrease in NDA, which may lead to
spurious non-significant FA. Obscuring of the normally
weak signal of FA by a high E is one of the main concerns
in asymmetry studies (Palmer & Strobeck, 1986; Palmer,
1994). On the other hand, because size-adjustment
reduces the amount of error variance from some characters without modifying the NDA component, some
characters become significant for NDA after size correction. The high degree of significance of the NDA
component for these samples may be due to the effect
of measuring with a relatively low error and keeping
variation due to size under control, rather than to the
presence of unusually high levels of asymmetry. This
stresses the importance of estimating precision and
relationship with size in the data before asymmetry
comparisons are attempted. The two-way A N O V A
approach, coupled with a relatively high degree of
precision in measurement, represents a powerful tool
for detection of subtle patterns of variation in bilateral
asymmetries, which otherwise may be easily confounded
by measurement error or size variation (Palmer &
Strobeck, 1986; Palmer, 1994; Merila” & Bjo” rklund,
1995).
Directional asymmetry
Both univariate and multivariate results show that DA
contributes a small proportion of the variance of a
character. This is consistent with
previous results
obtained from house mice (Leamy, 1984) and can be
explained as the result of functional anatomical constraints acting strongly to keep the skull symmetric.
Results of PCA indicate that the DA component (PC3) is
similar for both species. Correlation between E and PC3
becomes virtually zero for both species after adjustment.
This indicates a reduction in non-random variation in the
E component, which is very likely due to systematic error
of the measurer. Significant correlation of DA between
characters and across species suggests the existence of a
general component for DA, even if it is weak (Leamy,
1984). We did not test for between-character correlation
of DAs directly, but PC3 from the size-adjusted PCA
suggests the existence of a DA factor, possibly of genetic
origin, and which nonetheless represents a minimal
fraction (0.5% or less) of the total variation.
Non-directional asymmetry
For the data examined, the variance components due to
NDA behave as if they contained only random variation
(FA sensu Palmer, 1994), given that the NDA component
is not affected by size adjustment in either univariate or
multivariate analyses. As with DA, the multivariate
analyses of NDA indicates that this component has
similar magnitude across characters between species.
Significant correspondence of asymmetries between
populations for a set of characters indicates the presence
of a ‘population asymmetry parameter’ or PAP (Soule’ ,
1967). PAPs usually have been postulated to exist for
intraspecific populations of different genetic composition.
The general idea is that ‘whatever is responsible for
controlling the level of fluctuating symmetry it is, on
average, acting indiscriminantly on all parts o the phenome
(phenotype as a whole) and indirectly on all components o
the gene pool’ (italics as in Soule’ , 1967). Results of PCA
indicate that variance proportions due to NDA behave
similarly in R. egyptiacus and E. helvum. The randomizedblocks A N O V A is consistent with these results, the test was
highly significant for the variance component term, an
expected result given the large differences between the
proportions of variance explained by I, NDA, E and DA in
each of the species. However, no differences were
detected among variables, which indicates that variance
components behave similarly across the skull within
populations. Moreover, no differences were detected
between species, and the interaction between species and
variance components also was non-significant, which
suggests that variance components in both species are
behaving similarly for all characters examined. These
results indicate that a pattern analogous to a PAP, but at
the generic level, exists for these bats. Because similar
patterns have been detected for both DA and NDA, it is
possible that the expression of asymmetry, whatever its
origin, is a characteristic of the structural pattern common to these species. The general morphology of the
skull of these bats is recurrent across the different fruit’ lvarez
bat lineages, and represents a primitive pattern (A
et al., 1999). The evidence available suggests existence of
asymmetry parameters above the species level. This
consistent pattern can result from common mechanisms
or similar developmental constraints acting on the
buffering capacities and morphological integration in
both genera. Equally, it may also be an expression of the
evolutionary stable configuration (sensu Wagner &
Schwenk, 2000) of this particular skull morphology. In
such a framework, Eidolon and Rousettus would show
different character states of the same fundamental
design. Whatever in fact the case may be, generalized
patterns of asymmetry can be detected when a large
number of characters is examined, and when potentially
confounding sources of variation are partitioned out.
When a cleaner signal is obtained, the occurrence of
generalized, skull-wide asymmetry patterns preserved
beyond the species level becomes apparent. The search
for similar patterns on various levels of the taxonomic
hierarchy, as well as in organisms with different structural programmes, would clarify their relevance within
the paradigm of FA as a variation of random origin and
hence a measure of developmental stability.
Acknowledgments
Funding for this research was provided to J.J. by a
postdoctoral grant from the Spanish Ministerio de Educacio’ n y Ciencia, and the Department of Biology at Texas
Tech University (USA). We thank R. Cifelli of the
Oklahoma Museum of Natural History (The University
of Oklahoma) for his encouragement to the project and
for his generosity loaning their Reflex microscope and
C. Iba’ nez, E. Costas and K. Jarrett for their constant
support. R. D. Owen, and the Department of Biological
Sciences, Texas Tech University, supported this project
throughout. The Spanish Committee of the MaB Program
of UNESCO kindly supplied additional funding for the
completion of this study. J. Graham provided insightful
comments, suggestions and criticisms on the data analysis. The final content and interpretation of the analysis
is fully the responsibility of the authors.
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Received 15 January 2001; accepted 28 March 2001