Serrano et al.
ELECTRONIC SUPPLEMENTARY MATERIAL
Composite indices of fluctuating asymmetry (CFA) combine information on
fluctuating asymmetry (FA) of several traits in a single index. The aim of these
indices is to provide a realistic and powerful indicator of developmental
instability in an organism (Leung et al 2000). Each FA index of a single trait
depends heavily upon statistical inference, consequently a number of conditions
should be evaluated beforehand in order to obtain reliable CFAs.
Thus, we first performed the FA analysis of index FA1 (absolute
differences between right and left side) separately for each trait and on each
sex, following Palmer & Strobeck’s (2003) recommendations. Then, we
estimated the CFA2 index (Leung et al 2000) as the summation of the
standardized absolute FA values (FA values of a given trait divided by the
average absolute FA for that trait). The CFA2 is considered the most robust,
simplest and powerful composite index of fluctuating asymmetry (Leung et al
2000).
We selected two traits, the distance in mm between the Gonion caudale
and Mental foramen (GM, a relatively plastic trait) and the distance between the
Gonion ventrale and the deepest point of the mandible notch (GD, probably a
more conserved trait) (Figure 1) as described by von den Driesch (1976) pages
56-57. We selected these two traits because they describe the two main axes of
mandible growth (Chapman & Chapman 1970) and show low vulnerability to
injury. Each side was measured twice on different days by E.S., using a digital
calliper (accuracy of 0.01 mm).
Fluctuating asymmetry analysis for GM and GD
1º) Inspect data for bad raw measurements or aberrant individuals.
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Results: The box plots on replicate measurements of right (R) and left (L) GM
and GD (check for bad raw measurements) and (R – L) differences of both traits
(check for aberrant individuals) did not reveal outliers.
2º) Test for between-sides differences due to measurement error by a
Mixed -ANOVA of sides (fixed factor) * individuals (random factor).
Result: the analysis of asymmetry variation is justified because the betweensides variation was significantly greater than that expected due to measurement
error in both traits for both GM (sides * individuals, F1, 32 = 585.47, P < 0.001
and F1, 40 = 447.5, P < 0.001, for females and males respectively) and GD (sides
* individuals, F1, 32 = 18.44, P < 0.001 and F1, 40 = 38.35, P < 0.001, for females
and males respectively) and the error variance (mean square due to error as %
of mean square between-sides differences) was a small fraction of the betweensides variance for both GM (2 % for females and 2.6% for males) and GD (3%
for females and 5.4% for males). Thus, differences between replicated
measurements were lower than the absolute differences between right and left
sides in both traits (Table 1).
3º) Check for homogeneity of variances among treatments (periods of
contrasted density)
Result: no significant differences were observed for heterogeneity of variances
for GM (chi-squared = 0.287, df , 32, P = 0.59 for females and chi-squared =
1.52, df 1, 40, P = 0.217 for males) and GD (chi-squared = 0.211, df 1, 32, P =
0.64 for females and chi-squared = 3.2, df 1, 40, P = 0.07 for males)
4º) Check for independence between FA and trait size (linear correlation
test).
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Result: There is independence between |R – L| and trait size [(R+L)/2] in both
GM (r = 0.095, S = 5409.8, = 0.59 for females, and r = -0.11, S = 12813.24, P =
0.46 for males) and GD (r = 0.2, S = 4744.5, P = 0.24 for females, and r = -0.24,
S = 14306.9, P = 0.12 for males). Additionally, from the visual examination of
the graphic representation of both parameters (e.g. for GM, see Figure 3) it
seems clear that there is independence between trait size and differences
between the right and left sides of jaw size.
5º) Check for departures from directional asymmetry.
Result: the R-L of GM (Mixed -ANOVA step 2º, sides = F1, 32 = 0.384, P = 0.54
for females and F1, 40 = 2.84, P = 0.09 for males) and GD (sides = F1, 32 = 2.41,
P = 0.13 for females and F1,
40
= 0.57, P = 0.45 for males) did not exhibit
directional asymmetry.
6º) Because the advantage of combining FA indices from different traits
decreases as the degree of correlation between traits increases, we first
checked for the correlation between FA traits (linear correlation test).
Result: FA (absolute R – L differences) values of GM and GD were uncorrelated
both in females (r = 0.02, F1, 31 = 0.02, P = 0.88) and males (r = 0.06, F1, 40 =
0.15, P = 0.69).
7º) Check for departures from normality of the CFA2
Since the distribution of CFA2 of both females and males showed a light
positive skew, we log-transformed the composite index before checking for
departures from normality.
Result: the log-transformed CFA2 distribution did not exhibit departures from
the normal distribution, either in females (W = 0.94, df 32, P = 0.12, ShapiroWilk test) or males (W = 0.9765, df 40, P = 0.54).
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Chapman, D. I. & Chapman, N. 1970 Development of the teeh and mandibles in
fallow deer. Acta.Theriol. 15, 111-131.
Leung, B., Forbes, M. R., & Houle, D. 2000 Fluctuating asymmetry as a
bioindicator of stress: comparing efficacy of analyses involving multiple
traits. Amer.Nat. 155, 101-105.
Palmer, A. R. & Strobeck, C. 2003 Fluctuating asymmetry analyses revised. In
Developmental Instability: Causes and Consequences (ed. M. Polak), pp.
279-319. New York: Oxford University Press.
von den Driesch, A. 1976 A guide to the measurement of animal bones from
archaeological sites. Peabody.Mus.Bull 1, 1-137.
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Table 1. Descriptive statistics for the absolute differences (in mm) between right
and left GM and GD (Fig 1) and for the differences between replicated
measurements on both traits (|M1º - M2º|). AV = average, SE = standard error,
Min and Max = minimum and maximum values of each trait.
Females
|Right
GM
GD
Males
– Left|
|Right
|M1º - M2º|
– Left|
|M1º - M2º|
Av
1.05
Av
0.15
Av
0.9
Av
0.17
SE
0.024
SE
0.014
SE
0.024
SE
0.02
Min
0.04
Min
0.03
Min
0.3
Min
0.04
Max
2.1
Max
0.4
Max
2.5
Max
0.6
Av
0.62
Av
0.17
Av
0.62
Av
0.18
SE
0.02
SE
0.02
SE
0.015
SE
0.03
Min
0.03
Min
0.02
Min
0.2
Min
0.03
Max
1.5
Max
0.7
Max
1.2
Max
0.65
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Figure caption
Figure 1: Right jaw bone of a yearling Fallow deer (Dama dama) female. The
arrows indicate the distances in mm between the Gonion caudale and the
Mental foramen (GM) and between the Gonion ventrale and the deepest point
of the mandible notch (GD).
Figure 2. Relationship between CFA (log-transformed) of jaws and individual
body condition in juvenile fallow deer.
Figure 3. Relationship between the Gonion caudale - Mental foramen distance
(GM, in mm) and the absolute differences between the right and left GM.
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Figure 1.
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Figure 2
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Figure 3
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