Census procedure
For each patch in Site 104, a 1/4 m × 1/4 m pvc frame was placed at three haphazardly chosen locations and all of the enclosed stems were counted (for very small patches, all stems were counted), and the number of stems infested with planthopper eggs was recorded. I then collected a maximum of 10 infested leaves from each patch (only a maximum of 3 leaves were collected from patches <1 m2) and returned them to the laboratory. If no infested leaves were found, the remainder of the patch was searched intensively to ascertain whether the patch was unoccupied by planthoppers and parasitoids. This sampling procedure was designed to minimally impact planthopper and parasitoid densities over time.
Each census was initiated near the end of a planthopper generation (mid July and late August). At this time, leaves possessed a nearly complete record of the sum total of P. crocea eggs laid and hosts parasitized during that generation (Cronin 2003). The inhabitants of a leaf were identified using a stereoscopic dissecting microscope at 12×. Planthopper densities (eggs) and parasitoid densities (parasitized hosts) were reported on a per cordgrass stem basis.
The number of patches included in the census varied over time, ranging from 25 in generation 1, to 105 in generations 2 and 3, to 147 in generations 4 and 5. During the middle of the summer in each year, the size and isolation of each patch was determined. Patch size was determined from digital photographs or from differential GPS measurements. Among these 147 patches, sizes ranged from 0.1 m2 to 126.7 m2, and averaged (± 1 SE) 7.4 ± 1.2 m2.
Patch isolation, which is dependent upon the linear distance to, and size of, neighboring patches (Hanski 1994, Hanski and Kuussaari 1995), was determined only from the nearest patch in each of 4 quadrats (NE, NW, SE, and SW). Here, my index of isolation, I, was computed as:
where Si and Di are the size of (m2) and distance to the nearest patch in the ith quadrat, respectively. Larger values of I indicate greater patch isolation. There is a high correlation between I and a much more inclusive measure of isolation based on all of the cordgrass patches within a 40-m buffer area surrounding the focal patch (R = 0.80, n = 25, P < 0.001; Cronin 2003).
The matrix surrounding a patch was quantified by measuring the proportion of ground cover within a 3 m buffer strip surrounding the patch that consisted of each of the three matrix types (mudflat, brome, native grass). At 0 m, 1 m, 2 m, and 3 m from the patch edge and in 4–16 directions (the number increased with increasing patch size), the percentage of area within a 1/4 m × 1/4 m sampling frame that was occupied by each matrix type was recorded. The proportion of the buffer strip that consisted of each matrix type was computed as the mean of each distance class weighted by its circumference.
Analysis of distributional patterns
The effect of landscape structure (patch size, isolation and proportion of matrix that is mudflat) and planthopper density (mean eggs/stems/patch) on A. columbi density was determined with multiple least-squares regression. Analogously, logistic regression was used to test the effect of these same variables (planthopper incidence substituted for density) on patch occupancy by A. columbi. All continuous variables had right-skewed distributions and were ln-transformed prior to analysis. Because the frequency of occupied patches steadily declined between generations 1 and 5 (see Results), the distribution of densities increased in their deviation from normality over time. For all generations, analyses with and without zeros yielded the same qualitative results, except for generation 5. I therefore conclude that the test is robust for the first four generations despite this violation of the model assumptions, and no least-squares regression was performed for the fifth generation. Tests that are reported below include zero densities (ln[density + 0.1]).
For the analysis of patch occupancy,
the presence/absence of parasitoids in a patch was logit-transformed (ln[p/1
- p]; where p = probability that the patch was occupied) prior
to analysis. The significance level for each independent variable was determined
with a G-test (Hosmer and Lemeshow 2000). I also report McFadden’s 
2),
which is comparable to the coefficient of determination (R2)
reported for the least-squares regression model (Hosmer and Lemeshow 2000).
The least-squares and logistic regression
analyses within the same generation do not represent independent tests and therefore
the critical level of 
for each test was adjusted to account for inflation of the Type I error rate. Using
a Bonferroni correction, the critical level of
was set at 0.025. Interdependence among generations was also likely to occur
as a result of autocorrelations in planthopper and parasitoid abundances within
patches. Because I was interested only in documenting average trends among generations,
and not specific patterns within individual generations, I did not attempt to
correct for any autocorrelation among generations.
Literature Cited
Cronin, J. T. 2003. Patch structure, oviposition behavior, and the distribution of parasitism risk. Ecological Monographs 73:283–300.
Hanski, I. 1994. A practical model of metapopulation dynamics. Journal of Animal Ecology 63:151–162.
Hanski, I., and M. Kuussaari. 1995. Butterfly metapopulation dynamics. Pages 149–171 in N. Cappuccino and P. W. Price, editors. Population dynamics. Academic Press, San Diego, California, USA.
Hanski, I., and I. P. Woiwod. 1993. Spatial synchrony in the dynamics of moth and aphid populations. Journal of Animal Ecology 62:656–668.
Hosmer, D. W., and S. Lemeshow. 2000. Applied logistic regression, Second edition. Wiley and Sons, New York, New York, USA.
Moilanen, A., and M. Nieminen. 2002. Simple connectivity measures in spatial ecology. Ecology 83:1131–1145.