Appendix C. Additional details on statistical analyses used.
Abundances were analyzed with generalized linear models (GLM) using Poisson distributions with logarithmic link functions. Departure from the Poisson distribution usually occurs by overdispersion (variance > mean), which can be corrected by scaling, i.e., by modifying the scaling parameter of the GLM. Since abundance follows a discrete (counts) rather than a continuous distribution, this procedure will ensure higher statistical power than trying to transform the data to approximate a normal distribution. Overdispersion was corrected by including the statement DSCALE in the GENMOD procedure of SAS (Allison 1999, Agresti 2002). When Poisson GLM could not be applied because the matrix could not be inverted for calculating maximum-likelihood estimates, and neither could the data be transformed in order to satisfy ANOVA assumptions, we used the nonparametric Mann-Whitney U-test. This was necessary for analyzing ant densities for field experiment 1, in which some species had no individuals in the non-baited treatment.
For path analysis we used the program AMOS 5.0 (Arbuckle and Wothke 1999, Arbuckle 2003). Some variables did not meet the assumption of normality; therefore, we transformed them by cox-box trasformations (Sokal and Rohlf 1995) using the procedure TRANSREG in SAS (SAS institute 1990). To distinguish whether an effect was more likely direct (e.g., predation) or indirect (e.g., trophic cascade), we used the principle of parsimony, comparing Akaike’s Information Criterion corrected for small sample size (AICc) between models that had either the direct or the indirect path. The model with the lowest AICc is the most parsimonious (Burnham and Anderson 2002). For path analyses of field experiment 1, we use a categorical exogenous variable defined by the two treatments (1 – control; 2 - treatment). In path analyses of field experiment 2, using treatment (mesh size) as the exogenous variable did not produce statistically significant models, but using variation in densities of Camponotus yielded highly significant effects on the collembolan Tomocerus. Of the three measurements of Camponotus responses to baiting (density in the litter, average numbers at the bait per day, or percentage of days present at the bait), the variable that had the highest predictive power with respect to densities of the other taxa was the percentage of days present. Therefore we used the percentage of days that Camponotus was present at the bait as the exogenous (fully independent) variable in all path analyses that involved this ant. We also used this measure of activity for other ant taxa when they were included in the hypothesis being evaluated.
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