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Electronic Supplementary Materials
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Studying shape in sexual signals: the case of primate sexual
swellings
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Authors: Elise Huchard 1, 2, *, Julio A. Benavides 1, Joanna M. Setchell 3, Marie J.E.
Charpentier 4, 5, Alexandra Alvergne 1, Andrew J. King 2, 6, Leslie. A. Knapp 7, Guy
Cowlishaw 2, Michel Raymond 1.
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Université Montpellier II
CNRS- Institut des Sciences de l’Evolution de Montpellier, Place Eugène Bataillon, CC
065, 34 095 Montpellier cedex 5, France.
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Institute of Zoology, Zoological Society of London, Regent's Park, London NW1 4RY,
UK
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Evolutionary Anthropology Research Group, Durham University, 43 Old Elvet,
Durham, Dh1 3HN, UK.
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Department of Biology, Duke University, P.O. Box 90338, Durham, NC 27708, USA.
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Centre d’Ecologie Fonctionnelle et Evolutive, Unite Mixte de Recherche 5175, Centre
National de la Recherche Scientifique, 1919 Route de Mende, 34293 Montpellier Cedex
5, France
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Department of Biological Anthropology, University College London, Taviton Street,
London WC1H 0BW, UK
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Department of Biological Anthropology, University of Cambridge, Downing Street,
Cambridge CB2 3DZ, UK.
* Corrresponding author.
E-mail: Elise.Huchard@univ-montp2.fr
Tel: 0033 4 67 14 46 32
Fax: 0033 4 67 14 36 22
Content:
Supplementary Methods ................................................................................................... 2
Camera angle for pictures taken for shape analysis ..................................................... 2
Figure S1. ................................................................................................................. 2
Strategy of harmonic selection ..................................................................................... 3
Figure S2. ................................................................................................................. 5
Figure S3. ................................................................................................................. 7
Supplementary Results ..................................................................................................... 8
Analyses using the second and third principal components extracted from Fourier
coefficients as shape estimators .................................................................................... 8
Table S4. ................................................................................................................... 9
Table S5. ................................................................................................................. 10
References ...................................................................................................................... 11
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Supplementary Methods
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Camera angle for pictures taken for shape analysis
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Figure S1. Camera angle for swelling pictures taken for shape analysis. The pictures
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were taken by the same photographer (within a given species) when the animal was
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standing with its four feet on the ground (to limit biases introduced by the swelling
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angle to verticality: angle φ = 90°) and from directly behind the animal (to limit biases
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introduced by the swelling angle to the right or the left: angle θ = 90°). In contrast,
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swelling rotation within the orthogonal plane determined by Y- and Z-axes, which is
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perpendicular to the ground plane and parallel to the camera objective plane, has no
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influence for the shape analysis: each swelling shape is analysed within an orthogonal
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plane determined by the longest axis of ellipse of the first harmonic designated by the y-
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axis (see Methods and Figure 1 for additional details).
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Strategy of harmonic selection
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When working on a set of outlines, the strategy of harmonic selection must be adapted
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to the needs of the analysis (see e.g. Claude (2008) pp 216-219). Lower-order
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harmonics alone can contain sufficient information to allow groups to be distinguished,
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but the cut-off point between the higher and lower order harmonics needs to be
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identified. Different methods have been proposed to select the optimal number of
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harmonics depending on the analysis carried out. Qualitative methods can simply
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consist of visualizing the contour reconstructions (using inverse Fourier transformation)
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that are produced by increasing the number of harmonics used to build these contours,
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and then comparing by eye these reconstructions to the original contour. Alternatively,
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quantitative methods can be used, as described in Kuhl & Giardina (1982), Haines &
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Crampton (2000) or Claude (2008).
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In our case, the number of harmonics that described meaningful swelling shape
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variation was guided by our research questions. First, we visualized the cloud of
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swelling contour scores on the first two principal components extracted from Fourier
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coefficients when using an increasing number of harmonics (from 2 to 20) to describe a
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swelling contour. A subset of these graphs is displayed on Figure S2 for the PCA
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involving both species (see Methods). Second, we analysed the spectrum of harmonic
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Fourier power. The power of the nth harmonic is Powern = (an2 + bn2 + cn2 + dn2) / 2, with
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an, bn, cn and dn the four elliptic Fourier coefficients of the nth harmonic. The power is
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proportional to the harmonic amplitude and can be considered as a measure of shape
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information. As the rank of the harmonic increases, the power decreases and contributes
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progressively less information. The number of harmonics should be selected so that
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their cumulative power gathers 99% of the total cumulative power (Claude 2008). The
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cumulative power of the five first harmonics of the baboon and mandrill Fourier
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coefficients are presented in Figure S2 (panel f.). Third, we calculated the cumulative
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proportion of variance accounted for by the first five principal components extracted
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from swelling shape coefficients when using an increasing number of harmonics (from
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2 to 50) to describe a swelling contour. The resulting graph (displaying calculations
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made from baboon Fourier coefficients) allows us to assess how quickly the proportion
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of the total shape variation captured by the harmonics stabilizes as the number of
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harmonics increases (Figure S3).
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These three approaches consistently indicate that the use of more than four
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harmonics does not bring additional information to this analysis. We therefore used the
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first four harmonics only.
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Figure S2. Graphical plots (a) to (e) showing the cloud of swelling contour scores on the
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first two axes of the PCA (with PC1 on the x-axis and PC2 on the y-axis, following
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Figure 2), performed on baboon and mandrill Fourier coefficients (respectively labelled
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“B” and “M”), when using an increasing number of harmonics to describe a swelling
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contour: (a) contours analysed using two harmonics, (b) contours analysed using three
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harmonics, (c) contours analysed using four harmonics (same plot as Figure 2), (d)
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contours analysed using five harmonics, (e) contours analysed using ten harmonics. (f)
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The cumulative harmonic Fourier power in the baboon and mandrill swelling contours
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analysed with 1 to 5 harmonics.
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Figure S3.
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principal components extracted from the baboon swelling shape Fourier coefficients,
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using an increasing number of harmonics (from 2 to 50) to describe the swelling
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contour.
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The cumulative proportion of variance accounted for by the first five
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Supplementary Results
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Analyses using the second and third principal components extracted from Fourier
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coefficients as shape estimators
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The Fourier coefficients of the mandrill and baboon swelling contours were first
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analysed together in a PCA to see if swelling shape differs between species (or at the
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genus level). The proportion of the total shape variation accounted for by the first,
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second and third principal components (PC) was 58%, 20% and 10%, respectively. The
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first and second principal components of swelling shape both differed between species
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(PC1: see Results; PC2: F1,31 = 8.85, P < 0.01). In contrast, the third principal
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component of swelling shape did not differ among species (PC3: F1,31 = 1.63, P = 0.21).
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The Fourier coefficients of each species were then analysed in separate PCAs. In
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baboons, the first, second and third PC extracted from the Fourier coefficients (15
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females and 27 cycles), accounted for 56%, 14% and 11% of the variance in shape,
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respectively. The cumulative proportion of variance explained by the three first PCs was
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thus 81%. Analyses using the first PC as a shape estimator are reported in the Results;
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analyses using the second and third PC as shape estimators (i.e. fitted as the response
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variable of the GLMMs instead of PC1) are presented in Table S4.
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In mandrills, the first, second and third PC extracted from the Fourier
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coefficients (18 females and 27 cycles), accounted for 60%, 22% and 7% of the
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variance in shape, respectively. The cumulative proportion of variance explained by the
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three first PCs was thus 89%. Analyses using the first PC as a shape estimator are
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reported in the Results; analyses using the second and third PC as shape estimators (i.e.
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fitted as the response variable of the GLMMs instead of PC1) are presented in Table S5.
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Table S4. Results of the GLMMs carried out using the second and third principal
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components (respectively PC2 and PC3) extracted from the baboon Fourier coefficients
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as response variable. GLMMs were performed as described in the main text.
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Response variable
PC2
Statistic value
Group
X21 = 2.72 x 10-8
Random
Female
X21 = 53.24
factors
cycle
X21 = 11.24
Log(Age)
F1,9 = 1.51
Fixed
Dominance rank F1,9 = 0.31
factors
BMI
F1,9 = 0.47
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P
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< 10-3
10-3
0.25
0.59
0.51
PC3
Statistic value
X21 = 1.27
X21 = 54.29
X21 = 96.29
F1,9 = 0.10
F1,9 = 1.17
F1,9 = 3.39 x 10-3
P
0.26
< 10-3
< 10-3
0.76
0.31
0.95
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Table S5. Results of the GLMMs carried out using the second and third principal
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components (respectively PC2 and PC3) extracted from the mandrill Fourier
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coefficients as response variable. GLMMs were performed as described in the main
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text.
Response variable:
PC2
Statistic value
Random Group
X21 = 6.88 x 10-9
factors Female
X21 = 5.24
Log(Age)
F1,6 = 0.07
Fixed
Dominance rank F1,6 = 0.08
factors
BMI
F1,6 = 0.20
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P
1.00
0.02
0.80
0.79
0.67
PC3
Statistic value
X21 = 9.98 x 10-9
X21 = 1.72
F1,6 = 9.08 x 10-4
F1,6 = 1.03
F1,6 = 1.21
P
1.00
0.19
0.98
0.35
0.31
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References
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Haines AJ, Crampton JS (2000) Improvements to the method of Fourier shape analysis
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Claude J (2008) Morphometrics with R. Springer
as applied in morphometric studies. Palaeontology 43:765-783
Kuhl FP, Giardina CR (1982) Elliptic Fourier Features of a Closed Contour. Computer
Graphics and Image Processing 18:236-258