Appendix S6. Results of model selection based on AICc.
We selected the best model with the function dredge (library MuMin Barton 2013) using the
Maximum Likelihood test and Akaike information criterion for model selection corrected for
small sample size (AICc). Models are ranked according to Akaike’s information criterion
(AICc). All models include the block as random factor. All tables show the AICc, the delta
AICc (∆AICc) and the weight of each model.
Table S6A. Results of the linear mixed models testing for the effect of grasshopper traits
(Body Size and Incisive Strength) and survival on the observed LNRR (eqn 4 in the main
text).
Model
Body Size + Incisive Strength + Grasshopper Survival
Incisive Strength + Grasshopper Survival
Body Size + Grasshopper Survival
Incisive Strength
Body Size + Incisive Strength
Grasshopper Survival
Body Size
Null Model
AICc
46.8
47.6
52.9
53.4
54
54.2
55
55.3
Delta AICc
0
0.82
6.12
6.64
7.18
7.42
8.2
8.46
Weight
0.547
0.363
0.026
0.02
0.015
0.013
0.009
0.008
Table S6B. Results of the linear mixed models quantifying grasshopper species feeding niche (standardized herbivory) according to two plant
traits : the leaf dry matter content (LDMC) and the leaf carbon nitrogen ratio (C:N ratio) (eqn 5 in the main text).
(1) C. biguttulus
Model
LDMC + LDMC² + C:N + C:N² + C:N3
LDMC + LDMC² + LDMC3 + C:N + C:N² + C:N3
LDMC + LDMC² + LDMC3 + C:N + C:N²
LDMC + LDMC² + LDMC3 + C:N
LDMC + C:N
LDMC + C:N + C:N² + C:N3
LDMC + LDMC² + C:N
LDMC + C:N + C:N²
LDMC + LDMC² + LDMC3
LDMC + LDMC² + C:N + C:N²
LDMC
C:N
C:N + C:N²
LDMC + LDMC²
C:N + C:N² + C:N3
(2) C. dorsatus
AICc ∆AICc Weight
Model
209.37
0
0.5600 LDMC + C:N + C:N² + C:N3
211.09 1.72
0.2371 LDMC + LDMC² + C:N + C:N²
213.90 4.52
0.0584 LDMC + LDMC² + C:N + C:N² + C:N3
214.27 4.90
0.0484 LDMC + LDMC² + LDMC3
214.85 5.48
0.0362 LDMC + LDMC² + LDMC3 + C:N + C:N²
215.59 6.21
0.0251 LDMC + LDMC² + LDMC3 + C:N
216.76 7.39
0.0139 LDMC + C:N
217.52 8.14
0.0095 LDMC + C:N + C:N²
218.35 8.98
0.0063 LDMC + LDMC² + LDMC3 + C:N + C:N² + C:N3
220.26 10.89 0.0024 LDMC + LDMC²
221.69 12.32 0.0012 C:N + C:N² + C:N3
222.78 13.41 0.0007 LDMC + LDMC² + C:N
223.59 14.22 0.0005 LDMC
224.44 15.06 0.0003 C:N
226.48 17.10 0.0001 C:N + C:N²
AICc ∆AICc Weight
183.52
0
0.46012
185.34 1.81 0.18580
185.75 2.22 0.15134
186.92 3.40 0.08423
188.34 4.82 0.04132
189.57 6.04 0.02242
190.38 6.86 0.01493
190.44 6.92 0.01448
191.13 7.61 0.01025
192.63 9.11 0.00485
193.16 9.64 0.00372
193.46 9.93 0.00320
193.62 10.10 0.00295
198.20 14.68 0.00030
200.87 17.34 0.00008
(3) C. italicus
Model
LDMC + LDMC² + C:N + C:N²
LDMC + LDMC² + LDMC3 + C:N + C:N²
LDMC + LDMC² + C:N + C:N² + C:N3
LDMC + LDMC² + LDMC3 + C:N + C:N² + C:N3
LDMC + LDMC²
LDMC + LDMC² + C:N
LDMC + C:N
LDMC + C:N + C:N²
LDMC
LDMC + LDMC² + LDMC3 + C:N
LDMC + LDMC² + LDMC3
LDMC + C:N + C:N² + C:N3
C:N
C:N + C:N²
C:N + C:N² + C:N3
(5) P. giornae
Model
LDMC + LDMC² + C:N
LDMC + LDMC²
LDMC + C:N
LDMC + LDMC² + C:N + C:N²
LDMC + LDMC² + LDMC3
LDMC + LDMC² + LDMC3 + C:N
LDMC
LDMC + C:N + C:N²
LDMC + LDMC² + C:N + C:N² + C:N3
LDMC + LDMC² + LDMC3 + C:N + C:N²
LDMC + C:N + C:N² + C:N3
LDMC + LDMC² + LDMC3 + C:N + C:N² + C:N3
C:N
C:N + C:N²
C:N + C:N² + C:N3
AICc ∆AICc
189.25
0
193.40 4.15
193.44 4.19
198.19 8.94
200.28 11.04
200.73 11.49
201.93 12.68
202.23 12.99
202.54 13.30
203.51 14.27
203.56 14.32
204.17 14.92
224.30 35.06
226.99 37.74
229.46 40.22
Weight
0.785120568
0.098350467
0.096600826
0.008987074
0.003148063
0.002514911
0.001384567
0.001187306
0.001016980
0.000626809
0.000610692
0.000451711
0.000000019
0.000000005
0.000000001
AICc ∆AICc
171.45
0
171.48 0.03
173.33 1.88
174.12 2.67
174.75 3.30
174.93 3.47
175.66 4.21
176.33 4.88
178.28 6.83
178.29 6.84
178.30 6.85
183.10 11.65
205.18 33.73
208.00 36.55
209.22 37.77
Weight
0.301293166
0.297371965
0.117617021
0.079398840
0.057776595
0.053063206
0.036762701
0.026263595
0.009907913
0.009842736
0.009811781
0.000890461
0.000000014
0.000000003
0.000000002
(4) E. elegantulus
Model
LDMC + LDMC² + LDMC3
LDMC
LDMC + C:N
LDMC + LDMC² + LDMC3 + C:N
LDMC + LDMC² + C:N + C:N²
LDMC + LDMC²
LDMC + LDMC²+ C:N
LDMC + C:N + CN²
LDMC + LDMC² + LDMC3 + C:N + C:N²
LDMC + LDMC² + C:N + C:N² + C:N3
LDMC + C:N + C:N² + C:N3
LDMC + LDMC² + LDMC3 + C:N + C:N² + C:N3
C:N
C:N + C:N² + C:N3
C:N + C:N²
(6) P. parallelus
Model
LDMC + LDMC² + LDMC3 + C:N + C:N² + C:N3
LDMC + C:N +C:N² + C:N3
LDMC + LDMC² + C:N + C:N² + C:N3
LDMC + C:N + C:N²
LDMC + LDMC² + LDMC3 + C:N + C:N²
LDMC + LDMC² + C:N + C:N²
LDMC + C:N
LDMC
LDMC + LDMC² + C:N
LDMC + LDMC²
C:N + C:N²
LDMC + LDMC² + LDMC3 +
LDMC + LDMC² + LDMC3 + C:N
C:N + C:N² + C:N3
C:N
AICc ∆AICc
204.80
0
206.65 1.85
207.03 2.24
207.99 3.19
208.80 4.00
209.35 4.56
209.42 4.62
209.47 4.67
210.19 5.40
212.31 7.51
212.82 8.02
214.79 10.00
234.12 29.33
234.25 29.45
237.00 32.20
Weight
0.40400926
0.16023441
0.13200474
0.08187861
0.05460294
0.04140236
0.04006038
0.03914363
0.02718153
0.00944077
0.00731362
0.00272737
0.00000017
0.00000016
0.00000004
AICc ∆AICc
205.84
0
207.09 1.26
211.15 5.31
214.26 8.42
214.49 8.66
216.88 11.05
217.38 11.54
218.95 13.12
220.56 14.73
221.78 15.95
223.64 17.80
223.77 17.93
224.17 18.34
225.04 19.20
226.18 20.34
Weight
0.60912
0.32500
0.04276
0.00902
0.00803
0.00243
0.00190
0.00086
0.00039
0.00021
0.00008
0.00008
0.00006
0.00004
0.00002
Table S6C. Results of the linear mixed models linking whether grasshopper differences in
trait values reflected their differences in feeding niche (eqn 6 in the main text).
Model
Difference of Incisive Strength
Difference of Body Size + Difference of Incisive Strength
Difference of C:N ratio + Difference of Incisive Strength
Difference of C:N ratio + Difference of Body Size + Difference of Incisive Strength
Null model
Difference of Body Size
Difference of C:N ratio
Difference of C:N ratio + Difference of Body Size
AICc
121
125
125
129
133
135
136
139
∆AICc
0
3.64
3.69
8.04
11.65
14.01
14.83
17.69
Weight
0.745
0.121
0.118
0.013
0.002
0.001
0
0