Appendix A. Statistical procedures for the among-patch survey of the distribution of spiders and planthoppers and the spider impact experiment.

*Among-patch distribution
of spiders and planthoppers*

Differences in density among spider
guilds at each planthopper generations were assessed with separate paired *t*-tests
(three spider guild pairings x three planthopper generations = nine separate
tests). To prevent the overall Type I error rate from exceeding the nominal
level of 0.05, we evaluated the significance of each test using a sequential
Bonferroni correction (Sokal and Rohlf 1995). A repeated-measures
ANOVA was used to determine whether spider densities over time were influenced
by features of the landscape (patch size, isolation and matrix composition).
Patch densities at each generation comprised the repeated measure, and a separate
test was performed for each spider guild. Backward stepwise regression was used
to determine whether the density of each spider guild, three landscape variables,
and planthopper density at generation *t* – 1 influenced
planthopper density at generation *t*. Because patch size is known to strongly
affect planthopper densities (Cronin 2003), a patch size × spider
guild interaction term (one for each guild) was included in the model to evaluate
the possibility that these two variables were non-additive in their effects
on planthopper density. A final model was derived that was composed only of
variables that significantly affected planthopper density (*P* 0.05).
For the above statistical tests, all variables except matrix composition were
ln transformed to normalize data distributions and homogenize variances.

Lastly, a logistic regression (Hosmer
and Lemeshow 2000) was used to determine whether the likelihood of a planthopper
extinction was influenced by spider density at *t* – 1 (each
guild as a separate variable; densities ln transformed), planthopper density
at *t* – 1 (ln transformed), three landscape variables (ln
patch size, ln isolation, proportion mudflat), and the interactions between
patch size and density of each spider guild. Because documented cases of extinction
events were relatively scarce in each of the three generations (see *Results*
in text), we based our analysis on the combined data from all three generations.
Here, a patch from a given generation was included in the analysis if planthoppers
were present in the patch the previous generation. Prior to the analysis, the
binomial dependent variable, whether or not the local planthopper population
went extinct at *t*, was logit-transformed (*ln*[*p*/1 – *p*];
where *p* = probability that the patch was extinct at *t*). A backward
stepwise procedure was used to reduce the number of variables in the model to
those that were significant (*P* 0.05).
The significance level for each independent variable was determined with a *G*-test
(Hosmer and Lemeshow 2000).

*Spider impact
experiment*

Because of time constraints, the spider effects experiment was performed in spatial and temporal blocks. Six patches were set up at the same time — one per each treatment combination. We selected patches that were adjacent to one another to minimize spatial differences in precipitation, wind, and temperature. One to two blocks were set up on a single day. Replicates were opened from 24 July until 8 August 2001. For the analysis of the effect of spider and caging (caged, uncaged) treatments on the proportion of planthoppers recaptured within the patch at 48 h, patch size was used as a covariate and release date was used as a random block effect. We used a similar ANCOVA to assess how spider densities at the end of the experiment varied among treatments. In the former analysis, density of each spider guild was ln transformed, and in the latter analysis, the proportion of planthoppers recaptured was arcsine-square root transformed to achieve normality and homogeneity of variances. Pairwise comparisons between treatment levels were evaluated with Tukey's HSD test (Sokal and Rohlf 1995).

Using only the uncaged cordgrass patches from the above experiment, we tested whether the addition of spiders caused an immediate emigratory response by the planthoppers (i.e., was the release and settlement of spiders a disturbance to the planthoppers). Our dependent variable was the proportion of the planthoppers released into a patch that was re-sighted at 30 min, 60 min and 8 h post release. Spiders were released into the patch immediately following the 30-min census. We used a repeated-measures ANOVA to determine whether the proportion re-sighted was dependent on the census period (repeated measure), spider treatment, release date (block effect), and patch size (covariate). The difference in proportion re-sighted between the 30 min and 60 min census period (the contrast of most interest) was evaluated with the same ANOVA design but without the 8 h census period included in the model. Finally, to determine if the spider treatment affected the proportion re-sighted within a single census period, we performed separate univariate ANOVAs (spider treatment, block effect and covariate included), followed by a Tukey's HSD test. A Bonferroni correction (Sokal and Rohlf 1995) was used to control for inflated Type I error associated with multiple ANOVAs on the same data set.

Literature Cited

Cronin, J. T. 2003*a*. Movement
and spatial population structure of a prairie planthopper. Ecology **84**:1179–1188.

Hosmer, D. W., and S. Lemeshow. 2000. Applied logistic regression, Secnd edition. Wiley & Sons, New York, New York, USA.

Sokal, R. R., and F. J. Rohlf. 1995. Biometry, Third edition. W. H. Freeman and Company, New York, New York, USA.