Ecological Archives E096195A1
David W. P. Manning, Amy D. Rosemond, John S. Kominoski, Vladislav Gulis, Jonathan P. Benstead, and John C. Maerz. 2015. Detrital stoichiometry as a critical nexus for the effects of streamwater nutrients on leaf litter breakdown rates. Ecology 96:2225–2235. http://dx.doi.org/10.1890/141582.1
Appendix A. Additional path model results, including weight of support for each of the models tested, model performance when specific parameters were removed from path models, selected singleyear model path coefficients, and unstandardized path coefficients for overall models.
Table A1. Support for N, P, or N+P models based on AIC for both overall models tested in this study. Each model is specified based on the parameters being estimated that are different between contrasted models (included are all 6 models tested in this analysis, which evaluated N [as dissolved inorganic nitrogen; DIN], and P [as soluble reactive phosphorus; SRP], litter C:N, and litter C:P as the predictor variables of interest). The number of parameters (K), AIC, the change in AIC (ΔAIC), the weight of support (AIC Wt, Cum. Wt), loglikelihood (LL), χ², and P values are reported for each model. The χ² statistic and corresponding P value indicate overall agreement between modeled and observed covariance, giving the first line of evidence for accepting or rejecting a given model structure. AIC is also indicative of model fit and is weighted based on LL and model parsimony, allowing comparison of multiple acceptable models (Burnham and Anderson 2002).
Model 
K 
χ² 
df 
P 
AIC 
ΔAIC 
AIC Wt 
Cum.Wt 
LL 
C:N, N 
13 
9.3 
5 
0.10 
1600.4 
0.0 
1 
1 
787.2 
C:N, P 
13 
5.1 
5 
0.4 
1625.8 
25.4 
0 
1 
799.9 
C:P, P 
14 
0.7 
5 
0.95 
1833.4 
233.3 
0 
1 
902.7 
C:N, N+P 
14 
11.4 
8 
0.18 
1866.4 
266.4 
0 
1 
919.2 
C:P, N+P 
15 
12.7 
7 
0.08 
2101.2 
498.7 
0 
1 
1034.2 
C:P, N 
14 
44.7 
8 
0 
2130.7 
528.2 
0 
1 
1050.2 
Table A2. Results of removing specific parameters from the full path models to test for the importance of parameters in explaining litter breakdown rates. Parameters were removed by fixing path coefficient estimates to zero. We then assessed modeled and observed covariance structure for each reduced model (using χ² tests), followed by ranking the importance of each parameter based on ΔAIC (full – reduced model) and a χ² difference test (χ²diff test), where P values < 0.05 denote significant reduction in model fit between the reduced and full model. Also reported are the number of parameters in the model (K), the χ²statistic and associated Pvalue for model fit, the degrees of freedom (df), the AIC score, the AIC Wt, cumulative AIC wt, and loglikelihood (LL) of each model.
Model 
K 
χ² 
df 
P 
AIC 
ΔAIC 
AIC Wt 
Cum.Wt 
LL 
χ²diff test 
C:N/N 
13 
9.28 
4 
0.1 
1600 
0 
0.76 
0.76 
787.22 
n.a. 
shredder biomass 
12 
13.98 
5 
0.03 
1603 
3 
0.24 
1 
789.57 
0.03 
discharge 
10 
35.54 
8 
<0.05 
1621 
21 
0 
1 
800.35 
<0.05 
stoichiometry 
11 
47.14 
7 
<0.05 
1634 
34 
0 
1 
806.15 
<0.05 
fungal biomass 
10 
285.32 
8 
<0.05 
1871 
271 
0 
1 
925.24 
<0.05 
C:P/P 
14 
0.71 
0.95 
1833 
0 
0.77 
0.77 
902.7 
n.a. 

shredder biomass 
13 
5.63 
5 
0.34 
1836 
3 
0.22 
1 
905.16 
0.03 
fungal biomass 
11 
21.7 
7 
0.003 
1848 
15 
0 
1 
913.19 
<0.05 
discharge 
12 
20.97 
6 
0.002 
1849 
16 
0 
1 
912.83 
<0.05 
stoichiometry 
12 
50.57 
6 
<0.05 
1879 
46 
0 
1 
927.63 
<0.05 
Table A3. Comparison of path coefficients among PRE, YR1, and YR2 for the links among fungal biomass, shredders, litter stoichiometry, discharge, and litter breakdown rates. Bold text indicates significant path coefficient estimates. Also reported are predicted effects of fungi and C:N/C:P, and C:N/C:P and shredders on litter breakdown rates in PRE, YR1, and YR2. In general, fungi, shredders and discharge became more important for predicting litter breakdown rates in YR1 and YR2 compared to PRE. The absolute magnitude of the effect of fungal biomass on breakdown rates through C:N or C:P or C:N/C:P effects on litter breakdown mediated by shredders tended to increase in YR1 and YR2 compared to PRE.
Model 
PRE 
YR1 
YR2 
C:N/N 

fungi 
0.05 
0.13 
0.11 
shredders 
0.09 
0.16 
0.15 
C:N 
0.69 
0.08 
0.59 
Q 
0.12 
0.59 
0.26 
Compound paths 

Fungi through C:N 
0.09 
0.04 
0.47 
C:N through shredders 
0.03 
0.05 
0.08 
C:P/P 

fungi 
0.09 
0.12 
0.49 
shredders 
0.03 
0.21 
0.29 
C:P 
0.75 
0.01 
0.09 
Q 
0.26 
0.58 
0.28 
Compound paths 

Fungi through C:P 
0.03 
0.00 
0.04 
C:P through shredders 
0.01 
0.01 
0.07 
Table A4. Unstandardized path coefficients (±SE) for the two best supported overall models. Unstandardized path coefficients can be interpreted as the slope of the relationship between the predictor and response variables (in this case, loglog slopes). All pathways are significant with P < 0.05 except for the path between fungi and shredders in the C:P/P model.
C:N/N Path 
Unstandardized coefficient 
±SE 

N 
→ 
fungi 
0.4 
0.08 
fungi 
→ 
C:N 
0.25 
0.03 
fungi 
→ 
litter breakdown 
0.2 
0.08 
C:N 
→ 
shredders 
1.8 
0.52 
C:N 
→ 
litter breakdown 
1.0 
0.19 
shredders 
→ 
litter breakdown 
0.08 
0.03 
discharge 
→ 
litter breakdown 
0.04 
0.01 
discharge 
→ 
shredders 
0.12 
0.03 
C:P/P Path 
Unstandardized coefficient 
±SE 

P 
→ 
fungi 
0.39 
0.05 
P 
→ 
C:P 
0.23 
0.04 
fungi 
→ 
C:P 
0.21 
0.06 
fungi 
→ 
litter breakdown 
0.19 
0.08 
C:P 
→ 
shredders 
1.4 
0.31 
C:P 
→ 
litter breakdown 
0.71 
0.12 
shredders 
→ 
litter breakdown 
0.08 
0.04 
discharge 
→ 
litter breakdown 
0.04 
0.012 
discharge 
→ 
shredders 
0.08 
0.03 