Appendix E. Changes in herbivore abundance and biomass through time in response to temperature and nitrogen addition.
TABLE E1. Results table from a generalized linear mixed effects model (Poisson errors) with the total abundance of larvae as the response. This minimum adequate model was generated by removing nonsignificant parameters from the maximal model (see main text) to provide the best fit (lowest Akaike Information Criterion, AIC score). Each fixed effect was tested here by removing it from the model and testing for a change in unexplained deviance using a likelihood ratio test. Individual coefficients and tests of their significance are shown below. Asterisks indicate level of significance (.≤ 0.1, * ≤ 0.05, ** ≤ 0.01, *** ≤ 0.001). |
|
df |
AIC |
ΔAIC |
Chisq Chi |
P |
|
Fullmodel |
10 |
818.21 |
|
|
|
|
3 way interaction |
10 |
858.90 |
40.69 |
60.681 |
<0.0001 |
*** |
Temperature × nitrogen |
1 |
859.1 |
0.20 |
2.208 |
0.118 |
|
Nitrogen × time |
10 |
896.96 |
38.06 |
58.067 |
<0.0001 |
*** |
Temperature × time |
10 |
903.48 |
44.58 |
64.586 |
<0.0001 |
*** |
Nitrogen |
1 |
914.76 |
11.28 |
21.185 |
0.001 |
*** |
Temperature |
1 |
907.01 |
10.05 |
7.573 |
0.022 |
* |
Time |
10 |
1306.34 |
411.24 |
386.15 |
<0.0001 |
**** |
TABLE E2. Full coefficient table for model of changes in larval abundance through time with Poisson error distribution. |
|
Estimate |
Std.Error |
z value |
Pr(>|z|) |
|
(Intercept) |
-0.5866 |
1.5375 |
-0.382 |
0.702824 |
|
Temperature |
0.3655 |
0.2845 |
1.285 |
0.198943 |
|
Nitrogen |
-0.7540 |
1.3551 |
-0.556 |
0.577941 |
|
time2 |
-2.3766 |
1.3007 |
-1.827 |
0.067668 |
. |
time3 |
-1.1481 |
1.4485 |
-0.793 |
0.428016 |
|
time4 |
-2.7208 |
1.6542 |
-1.645 |
0.100024 |
|
time5 |
2.4634 |
2.7745 |
0.888 |
0.374618 |
|
time6 |
1.2464 |
3.4771 |
0.358 |
0.719999 |
|
time7 |
-3.0267 |
1.8895 |
-1.602 |
0.109195 |
|
time8 |
-5.7385 |
1.5938 |
-3.601 |
0.000318 |
*** |
time9 |
-1.5014 |
1.3955 |
-1.076 |
0.281969 |
|
time10 |
-3.5032 |
1.4435 |
-2.427 |
0.015229 |
* |
time11 |
-2.8313 |
2.7668 |
-1.023 |
0.306154 |
|
temp:nitrogen |
0.1383 |
0.2467 |
0.561 |
0.575070 |
|
temp:time2 |
0.4699 |
0.2341 |
2.007 |
0.044728 |
* |
temp:time3 |
0.1650 |
0.2632 |
0.627 |
0.530655 |
|
temp:time4 |
0.3756 |
0.2968 |
1.265 |
0.205701 |
|
temp:time5 |
-0.8499 |
0.5396 |
-1.575 |
0.115282 |
|
temp:time6 |
-0.7111 |
0.6714 |
-1.059 |
0.289539 |
|
temp:time7 |
0.3625 |
0.3385 |
1.071 |
0.284248 |
|
temp:time8 |
0.9474 |
0.2786 |
3.401 |
0.000672 |
*** |
temp:time9 |
0.2557 |
0.2527 |
1.012 |
0.311667 |
|
temp:time10 |
0.6010 |
0.2574 |
2.335 |
0.019523 |
* |
temp:time11 |
0.1546 |
0.5010 |
0.309 |
0.757606 |
|
Nitrogen:time2 |
5.2323 |
1.8227 |
2.871 |
0.004096 |
** |
Nitrogen:time3 |
3.8904 |
1.9316 |
2.014 |
0.044004 |
* |
Nitrogen:time4 |
5.9396 |
2.4505 |
2.424 |
0.015359 |
* |
Nitrogen:time5 |
-0.1296 |
3.4769 |
-0.037 |
0.970261 |
|
Nitrogen:time6 |
-1.1942 |
4.2108 |
-0.284 |
0.776715 |
|
Nitrogen:time7 |
1.7651 |
2.4506 |
0.720 |
0.471362 |
|
Nitrogen:time8 |
0.9533 |
2.1377 |
0.446 |
0.655643 |
|
Nitrogen:time9 |
4.6734 |
1.9048 |
2.453 |
0.014150 |
* |
Nitrogen:time10 |
3.7820 |
1.8964 |
1.994 |
0.046117 |
* |
Nitrogen:time11 |
-0.6891 |
3.1457 |
-0.219 |
0.826613 |
|
temp:nitrogen:time2 |
-0.9482 |
0.3318 |
-2.858 |
0.004265 |
** |
temp:nitrogen:time3 |
-0.6258 |
0.3530 |
-1.773 |
0.076254 |
. |
temp:nitrogen:time4 |
-1.1555 |
0.4533 |
-2.549 |
0.010802 |
* |
temp:nitrogen:time5 |
0.1595 |
0.6698 |
0.238 |
0.811807 |
|
temp:nitrogen:time6 |
0.3964 |
0.8024 |
0.494 |
0.621338 |
|
temp:nitrogen:time7 |
-0.2214 |
0.4396 |
-0.504 |
0.614484 |
|
temp:nitrogen:time8 |
-0.1139 |
0.3736 |
-0.305 |
0.760451 |
|
temp:nitrogen:time9 |
-0.8084 |
0.3482 |
-2.321 |
0.020262 |
* |
temp:nitrogen:time10 |
-0.5706 |
0.3402 |
-1.678 |
0.093439 |
. |
temp:nitrogen:time11 |
0.4251 |
0.5662 |
0.751 |
0.452764 |
|
TABLE E3. Results of a linear mixed effects model with Gaussian errors and total herbivore biomass through time as the response. This minimum adequate model was generated by removing non-significant parameters from the maximal model (see main text) to provide the best fit (lowest Akaike Information Criterion, AIC score). Each fixed effect was tested by removing it from the model and testing for a change in unexplained deviance using a likelihood ratio test. Individual coefficients and tests of their significance are shown in below. Asterisks indicate level of significance (.≤ 0.1, * ≤ 0.05, ** ≤ 0.01, *** ≤ 0.001). |
|
df |
AIC |
ΔAIC |
Chisq Chi |
P |
|
Best model |
3 |
2233.4 |
|
|
|
|
Temperature |
1 |
2266.3 |
32.9 |
21.485 |
<0.0001 |
*** |
Nitrogen |
1 |
2250.6 |
17.2 |
5.8103 |
0.0547 |
. |
Time |
3 |
2243.7 |
10.3 |
2.8454 |
0.584 |
|
Temperature × time |
3 |
2248.8 |
15.4 |
21.423 |
<0.0001 |
*** |
TABLE E4. Full coefficients table of model for changes in herbivore biomass through time with Gaussian error distribution. |
|
Estimate |
Std.Error |
t value |
pMCMC |
|
(Intercept) |
-16068.08 |
4300.71 |
-3.736 |
0.001 |
** |
Temp |
3594.87 |
802.60 |
4.479 |
0.002 |
** |
nitrogenN |
7794.26 |
5431.11 |
1.435 |
0.188 |
|
time9 |
6049.21 |
5300.90 |
1.141 |
0.302 |
|
time10 |
494.99 |
5300.90 |
0.093 |
0.935 |
|
time11 |
12380.58 |
5300.90 |
2.336 |
0.035 |
* |
temp:nitrogenN |
1742.91 |
1017.14 |
1.714 |
0.118 |
|
temp:time9 |
-1168.03 |
992.75 |
-1.177 |
0.284 |
|
temp:time10 |
79.12 |
992.75 |
0.080 |
0.933 |
|
temp:time11 |
-2508.84 |
992.75 |
-2.527 |
0.022 |
* |
nitrogenN:time9 |
7936.48 |
7496.61 |
1.059 |
0.347 |
|
nitrogenN:time10 |
8633.13 |
7496.61 |
1.152 |
0.300 |
|
nitrogenN:time11 |
9042.91 |
7496.61 |
1.206 |
0.278 |
|
temp:nitrogenN:time9 |
-1568.76 |
1403.96 |
-1.117 |
0.314 |
|
temp:nitrogenN:time10 |
-1856.53 |
1403.96 |
-1.322 |
0.229 |
|
temp:nitrogenN:time11 |
-1650.01 |
1403.96 |
-1.175 |
0.288 |
|