Appendix D. Statistical analyses.
Analysis of long-term outcomes
In order to determine the long-term outcomes of the productivity manipulation, I compared species abundances in 1997 (the most recent year preceding the experiment for which I had census and productivity data for all five sites), to those of 2002. I analyzed these data using a three-way ANOVA (Year, Site, Species) with Species as the repeated measure because densities of all three species were measured on a single experimental unit (individual host plant).
Analysis of spatial effects
The second analysis involved a spatial comparison of the experimental and control sites at the end of the experiment. This allowed me to look in more detail at how the species responses at the experimental site differed from the various control sites, and determine whether there were any dispersal effects that attenuated with increasing distance from the site of perturbation. I analyzed these data using a two-way ANOVA (Site and Species) with Species as the repeated measure. I used the average density of each species over July, August and September ("summer density") as the dependent variable in both analyses. This average reflects the typical steady state abundances attained by the parasitoids following their spring emergence.
Analysis of seasonal dynamics
Seasonal dynamics leading to the long-term outcome can reveal the effects of superparasitism vs. a refuge on species' abundances. I compared seasonal changes in species' densities using a three-way ANOVA with Species and Season as repeated measures. The four seasons: spring 2001, summer 2001, spring 2002, and summer 2002 corresponded respectively, to 1, 3, 10, and 13 parasitoid generations since the initiation of the productivity manipulation. Spring density was calculated as the avearge density of each species over April, May, and June. Summer density was calculated as described above.
The expectations for the seasonal dynamics analysis are as follows. If the trade-off and superparasitism operate in the absence of a temporal refuge, one should expect a monotonic decrease in the IGPrey's abundance and a monotonic increase in the host's and IGPredator's abundances at the experimental site compared to the controls, i.e., a significant Species × Site interaction but no Species × Season interaction. If the trade-off and a refuge operate in the absence of superparasitism, changes in species' abundances will no longer be monotonic. Because the IGPredator is inactive during late fall, winter and early spring, its abundance should decline from summer 2001 to spring 2002; because the IGPredator's absence provides the IGPrey with a temporal refuge, the latter's abundance should increase during the same time period. Since both species co-occur during the rest of the year, the IGPredator's abundance should increase from spring 2002 to summer 2002 while the IGPrey's abundance should decrease or stay the same (if the refuge effect is sufficiently strong). These seasonal differences should be greater (or qualitatively different) at the experimental site compared to the controls. Thus, one expects significant SpeciesSeason and Species × Season × Site interactions. I used profile analysis (SAS 2002) to investigate the response patterns of species over changing seasons. Profile analysis addresses hypotheses about Species × Site interactions between two successive seasons. This is achieved by tranforming the repeated measures data (i.e., species abundances in diffrent seasons) to a set of contrasts, which are then analyzed by univariate (ANOVA) or multivariate analyses (MANOVA; von Ende 2001).
The assumptions of ANOVA require that observations be independent and normally distributed, and that error variances be homogeneous (Sokal and Rohlf 1995; Winer et al. 1991). Densities log-transformed so that they conformed to these requirements. These transformations also satisfy the requirement of repeated measures ANOVA that the dependent variable has a multivariate normal distribution (SAS 2003; Winer et al. 1991).
LITERATURE CITED
SAS Institute. 2003. SAS User's Guide, version 9.1. SAS Institute, Cary, North Carolina, USA.
Sokal, R. R., and F. J. Rohlf. 1995. Biometry. W. H. Freeman, New York, New York, USA.
von Ende, C. N. 2001. Repeated-measures analysis: growth and other time dependent measures. In S. M. Scheiner and J. Gurevitch, editors. Design and analysis of ecological experiments. Oxford University Press, Oxford, UK.
Winer, B. J., D. R. Brown, and K. M. Michaels. 1991. Statistical analysis in experimental design. McGraw-Hill, New York, New York, USA.