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DATA SUPPLEMENT
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The allometry between secondary sexual traits and
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body size is non-linear among cervids
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Lemaître, J.F*., Vanpé, C., Plard, F. & Gaillard, J.M.
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Université de Lyon, F-69000, Lyon; Université Lyon 1; CNRS, UMR5558, Laboratoire de
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Biométrie et Biologie Evolutive, F-69622, Villeurbanne, France.
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* Corresponding author: jeff.lemaitre@gmail.com; jean-francois.lemaitre@univ-lyon1.fr
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Table S1: Dataset used in the analyses.
Species
Male
Male body antler
mass (Kg)1 length
(cm)2
Male
References
antler
(antler weight)
weight (g)
Alces alces
Moose
482.5
144
11000
Geist & Bayer 19883
Axis axis
Chital
89.5
84.5
2300
Geist & Bayer 1988
Axis porcinus
Hog deer
41
39.9
Blastocerus dichotomus
Marsh deer
130
60
Capreolus capreolus
Roe deer
28
23.35
300
Geist & Bayer 1988
Capreolus pygargus
Eastern roe deer
42
30.45
Cervus albirostris
White-lipped deer
204
115
2950
Leslie 20094
Cervus canadensis
Wapiti
350
133.7
12500
Geist & Bayer 1988
Cervus duvaucelii
Barasingha
236
81.3
7700
Geist & Bayer 1988
Cervus elaphus
Red deer
250
93.6
6300
Geist & Bayer 1988
Cervus eldii
Eld's deer
105
97.15
3400
Geist & Bayer 1988
Cervus nippon
Sika deer
52
48
2520
Geist & Bayer 1988
Cervus timorensis
Timor deer
95.5
67.5
2500
Cranbrook 19915
Cervus unicolor
Sambar
192
104.9
8200
Geist & Bayer 1988
Dama dama
Fallow deer
67
61.5
3500
Geist & Bayer 1988
Elaphodus cephalophus
Tufted deer
18
2.5
Elaphurus davidianus
Père David's deer
214
73.7
7900
Geist & Bayer 1988
Hippocamelus bisulcus
Chilean guemal
95
30
Mazama americana
Red brocket
24.5
11.5
56
Geist & Bayer 1988
Mazama gouazoupira
Gray brocket
18
9.25
Megamuntiacus vuquangensis Giant muntjac
45
22.75
Muntiacus crinifrons
Black muntjak
23
3.55
Muntiacus gongshanensis
Gongshan muntjak 21
7.17
Muntiacus muntjak
Muntjac
19
14.2
Muntiacus putaoensis
Leaf deer
12
3.25
Muntiacus reevesi
Chinese muntjak
13.5
11.4
70
Geist & Bayer 1988
Odocoileus hemionus
Mule deer
112.5
88.5
1650
Geist & Bayer 1988
Odocoileus virginianus
White-tailed deer
154.5
65.6
1500
Geist & Bayer 1988
Ozotoceros bezoarticus
Pampas deer
33.5
21
257
Ungerfeld et al. 20116
Pudu puda
South pudu deer
13
8.5
13
Geist & Bayer 1988
Rangifer tarandus
Reindeer
106.5
91
12000
Geist & Bayer 1988
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All body mass data are extracted from : Plard et al. 2011. Oikos 120: 601-606
All antler length data are extracted from : Plard et al. 2011. Oikos 120: 601-606.
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Geist & Bayer 1988. Journal of Zoology 214: 45-53.
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Leslie 2009. Mammalian Species 42(849): 7-18.
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Cranbook 1991 Mammals of South-east Asia. New York, NY: Oxford University Press.
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Ungerfeld et al. 2011. North Western Journal of Zoology 7(2):208-212.
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Table S2: Analysis of the relationship between antler weight (log-transformed) and body
mass (log-transformed) across 20 cervid species. We compared models based on AICc and
AICcw (see materials and methods section). In the threshold model with 1 slope, antler length
increased linearly (one slope) up to 75.4 kg and remained constant from this body mass while
with the model including 2 slopes, there is 1 slope before and 1 slope after the threshold
value. ΔAICc is the difference of Akaike’s criteria corrected for small sample size between
the candidate model and the best model and k is the number of parameters in the model.
These results are qualitatively similar to the ones obtained with antler length since the
threshold model (1 slope) is very close to the quadratic model (see Table S4). Retained model
is in bold.
k
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3
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Constant
Linear
Quadratic
Threshold (1 slope)
Threshold (2 slopes)
Deviance
82.92
49.20
40.50
42.84
38.14
AICc
87.62
56.70
51.17
53.51
52.42
ΔAICc
36.46
5.53
0.00
2.34
1.25
AICcw
0.00
0.03
0.52
0.16
0.28
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Table S3: Analysis of the relationship between ‘Independent contrasts of antlers length’ and
‘Independent contrasts of body mass’. We compared models based on AICc and AICcw (see
materials and methods section). ΔAICc is the difference of Akaike’s criteria corrected for
small sample size between the candidate model and the best model, and k is the number of
parameters in the model. Retained models are in bold. Here it is important to note that the
number of contrasts in the analyses is relatively low (n = 23) compared to the number of
species (n = 31) in the analyses performed on antler length (see also Figure S2). This might
explain why in this case, the threshold model does not perform better than the linear model.
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Constant
Linear
Quadratic
Threshold (1 slope)
Threshold (2 slopes)
k
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3
4
4
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Deviance
22.68
5.02
4.26
3.68
3.44
AICc
27.28
12.28
14.48
13.90
16.98
ΔAICc
15.00
0.00
2.20
1.62
4.70
AICcw
0.00
0.53
0.18
0.24
0.05
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Table S4: Analysis of the relationship between antler length (log-transformed) and body mass
(log-transformed) across the 31 cervid species. We compared models based on AICc and
AICcw (see materials and methods section). In the threshold model with 1 slope, antler length
increased linearly (one slope) up to 113 kg and remained constant from this body mass while
with the model including 2 slopes, there is 1 slope before and 1 slope after the threshold
value. ΔAICc is the difference of Akaike’s criteria corrected for small sample size between
the candidate model and the best model and k is the number of parameters in the model.
Retained models are in bold.
Constant
Linear
Quadratic
Threshold (1 slope)
Threshold (2 slopes)
k
2
3
4
4
5
Deviance
97.20
46.08
38.54
39.10
38.00
AICc
101.63
52.96
48.09
48.64
50.41
ΔAICc
53.54
4.87
0.00
0.55
2.32
AICcw
0.00
0.04
0.46
0.35
0.14
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Table S5: Analysis of the relationship between antler length (log-transformed) and body mass
(log-transformed) across species with male body mass inferior to 113 Kg (n = 22). We
compared models based on AICc and AICcw (see materials and methods section). In the
threshold model with 1 slope, antler length is fixed constant after the computed threshold
value of male body mass (78 Kg) while with the model including 2 slopes, there is one slope
before and on slope after the threshold value. ΔAICc is the difference of Akaike’s criteria
corrected for small sample size between the candidate model and the best model (in bold) and
k is the number of parameters in the model. Retained model is in bold.
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Constant
Linear
Quadratic
Threshold (1 slope)
Threshold (2 slopes)
k
2
3
4
4
5
Deviance
67.02
32.48
32.44
32.08
32.26
AICc
71.65
39.82
42.79
44.44
44.01
ΔAICc
31.84
0.00
2.98
4.62
4.19
AICcw
0.00
0.69
0.16
0.07
0.08
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Figure S1: Relationship between antler weight and body mass (on a log-log scale) across 20
cervids. The quadratic (full line) and threshold (with one slope, dashed line) models best
described the relationship.
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Figure S2: Relationship between ‘Independent contrasts of antlers length’ and ‘Independent
contrasts of body mass’. The linear (full line) and threshold (with one slope, dashed line)
models best described the relationship.
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