Appendix D. Additional path-analysis results.
 |
FIG. D1. Results of path analysis using 2006 data. Standardized path coefficients again supported a strong direct path between nonnative grass litter through native shrubs to leafhoppers and spiders. Note that native-shrub tissue was not measured in 2006 so this represents the largest model possible with available data. |
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FIG. D2. Path analysis of the largest model (Model A) of 2007 data including an additional pathway between native-shrub growth and spiders. Shrub growth may predict spider abundance by the additional structure for web building and refugia larger shrubs provide. In these data, leafhoppers and shrub growth were highly correlated (variance inflation factors of 3.6) making it difficult to tease apart the effect of each on shrub spiders. Models with the path of shrub growth to spiders were similar (Table D1 below) to models without it (Table 1 main text), producing very similar AIC values (not shown). However, the simplest model—which lacked this path—fit the data best (Table D1 below, see ∆AIC of model G). Also the path between shrub growth and spiders was nonsignificant (Fig. D2), suggesting leafhoppers may be the major controller on spider abundance in this study. See also Fig. 4 of main text. However, the correlation between these variables also highlights the limits of path analysis (Petraitis et al. 1996, Shipley 2002): clearly separating the effect of increased prey with increased shrub size and increase habitat/structure for spider with increases shrub size would require experimental manipulation |
TABLE D1. Comparisons of the path models (A–F) described in the main text with the addition of a path between shrub growth and spiders to all models, except G.
Model |
Description of model |
c2 |
df |
P |
∆AIC |
A |
Full model: Detrital food web and plant quality linked to grazing food web |
5.44 |
5 |
0.36 |
|
B |
Model A without plant quality linked to shrub arthropods |
5.68 |
6 |
0.46 |
-0.24 |
C |
Model A without detrial web linked to shrub arthropods |
6.67 |
7 |
0.46 |
-1.23 |
D |
Model A without plant quality |
3.14 |
3 |
0.37 |
-7.69 |
E |
Model A without detrital web |
2.47 |
3 |
0.48 |
-7.03 |
F |
Simple bottom-up model, no plant quality or detrital web, but with connection between shrub growth and shrub spiders |
0.06 |
2 |
0.97 |
-12.62 |
G |
Simplest bottom-up model, Model F without connection between shrub growth and shrub spiders |
2.01 |
3 |
0.57 |
-14.57 |
LITERATURE CITED
Petraitis, P. S., A. E. Dunham, and P. H. Niewiarowski. 1996. Inferring multiple causality: The limitations of path analysis. Functional Ecology 10:421–431.
Shipley, B. 2002. Cause and correlation in biology: a user's guide to path analysis, structural equations and causal inference, First paperback edition. Cambridge University Press, Cambridge, UK.