Appendix A. Additional details on the methods and statistical analyses and additional results and figures.

ADDITIONAL METHODS, ANALYSES, AND RESULTS

Estimating aggregation in the fieldLikelihoods and Akaike Information Criteria for log-linear mixed models with negative binomially distributed errors and trap-specific random effects are shown in Table A1.

TABLE A1. Fit statistics for log-linear mixed models with differing constraints on springtail dispersion ( k) across months and plots. Data are from March to August 2001.

Plot Month -2 ln [L] AIC

full full 1166.9 1200.9 full reduced 1177.5 1191.5 reduced full 1169.8 1191.8 reduced reduced 1178.0 1190.0

Brook90 Hyrdrologic Model. –Brook90 predicts soil moisture from local weather, soil and vegetation data by modeling a broad range of hydrologic processes, including evapotranspiration (Federer 1995). We used the soil infiltration settings for this model derived from the Hubbard Brook research site in New Hampshire, but used canopy parameters for evergreen vegetation provided in the model documentation and changed the soil stone content to approximate conditions of our field site.

Moisture effects on movement and aggregation

Individual-based observation of moisture effects on density-independent movement. – Positional fixes (moves) were recorded at 2-s intervals using a video camera and frame capture computer device. The observation arena consisted of a 594 cm^{2}plastic tray with a layer of hardened plaster of Paris. Each individual was used in only one observational trial. The fastest displacing individual reached the boundary region of the observation area after only nine moves. All paths were therefore truncated at the ninth move to reduce the boundary effect and to ensure that each individual in the final data set was represented by an equal number of moves. In our statistical analyses, we assumed that displacement distances for a single individual were temporally autorcorrelated. Thus, we used an autoregressive correlation structure between repeated measurements and assumed heterogeneous variances among observation times.To further explore whether moisture treatment effects on total movement activity could be ruled out as an explanation for displacement differences in observations of density-independent movement, we conducted a post hoc equivalence test for treatment effects on path length (Dixon 1998) using a 20% ratio null hypotheses (H

_{01}: µ_{moist}0.8 · µ_{dry}; H_{02}: µ_{moist}1.2 · µ_{dry}). Path data provided insufficient evidence to reject the hypothesis that the two treatments differed in their effect (H_{01}, df = 33,P= 0.2203; H_{02}, df = 33,P= 0.0448).

Release-recapture experiment. –The enclosures were constructed using 20 cm aluminum sheet flashing. We reduced litter patchiness by overlaying a 2-m layer of sand with sifted (1-cm sieve) white pine litter and then a final layer of coarse pine litter. The eight sticky traps totaled 24 cm of trap length along the 63-cm perimeter of the circular area in the enclosure center.Enclosures receiving the moisture treatment were moistened using a handheld spray bottle, taking care not to moisten the sticky traps. We added

O. hexfasciataindividuals to the enclosures by tapping animals from 10 randomly selected pine cones into a collecting tray and then emptying the tray into a funnel at the center of the enclosure. Mean density in a separate sample of these pine cones was 8.4 +/- 5.1 SD per cone (N= 25), resulting in an estimated average release per enclosure of 84 individuals. Five enclosures of each moisture level were destructively sampled (i.e., all 8 traps were removed) after 1, 2, and 3 days. Captured individuals were then counted under a dissecting microscope.We used Poisson-distributed errors in the statistical analysis because negative binomial distribution did not produce a significantly higher likelihood (LRT:

G= 0.0436, df = 1,P= 0.8346).

Spider effects on behaviorBefore the experiment with spiders, we tested for a relationship between

O. hexfasciatadensity and frass counts. We used 12 half-pint glass jars with a 1-cm layer of plaster of Paris and the distal half of a single decayingP. strobuscone collected from the forest floor. These 12 jars were split into 3 replicate blocks; the four jars in each block were assigned springtail densities of 0, 4, 8, and 12. There was sufficient material for a 13th jar containing 16 individuals, but this density level was not replicated. We removed six scales (bracts) from each cone after one week and counted frass on a ~3 mm wide distinctly colored band that occurs on the inner surface of the distal tips of these scales ("tip region"). We used the sum of these six scales in each jar as the response variable in a regression analysis relating frass counts to springtail density.

Field experimentArthropods were generally unable to climb the clean flashing material from which the enclosures were constructed, but food grade silicon spray was applied to the top edges of the flashing after installation as an extra precaution. During enclosure installation, closeable pitfall traps (25 mm diameter) were installed at the center of each of the four quadrants in each enclosure. This resulted in 144 × 4 = 576 pitfall traps. To ensure that none of the enclosures contained zero

O. hexfasciata, we stocked 20 individuals into each enclosure before beginning the experiment. Other than the initial removal of cones and the application of treatments, the enclosures received no further manipulations or disturbances.

Spatial aggregation. –The objective function used for maximum likelihood estimation ofm,k, andcvof the negative binomial was:

TABLE A2. Likelihood-ratio tests for treatment effects on the coefficient of variation ^{†}forO. hexfasciatacaptures within 144 experimental enclosures arrayed in a Latin square.

Source df Pr >

spider 1 0.00 0.9476 water 2 10.55 0.0051 cone 1 0.34 0.5578 spider × water 2 1.56 0.4575 spider × cone 1 0.01 0.9245 water × cone 2 0.32 0.8523 row 11 15.04 0.1808 column 11 24.74 0.0100

† Cvwas calculated from maximum-likelihood estimation of negative binomial distribution parameters using four traps in each enclosure.

Total trap counts

TABLE A3. Likelihood-ratio tests for treatment effects on total O. hexfasciatacaptures within 144 experimental enclosures arrayed in a Latin square.

Source df Pr >

spider 1 5.86 0.0155 water 2 7.10 0.0287 cone 1 0.00 0.9574 spider × water 2 0.85 0.6553 spider × cone 1 0.71 0.4000 water × cone 2 2.61 0.2707 row 11 13.75 0.2470 column 11 29.72 0.0018

ADDITIONAL FIGURES

FIG. A1. Histograms of monthly O. hexfasciatacounts from two pooled 5 × 5 square pitfall trap arrays opened for two weeks per month from Nov 2000 to Oct 2001. Bin frequencies are represented as circles for clarity. Lines show negative binomial distributions parameterized with a separatemparameter for each month and a singlekparameter across all months. The best model in a repeated-measures analysis places no constraints onmin terms of array and month, whereaskis reduced to a single parameter.

FIG. A2. Net squared displacement of individual O. hexfasciatareleased on dry (n= 18 individuals) and moist (n= 17) plaster surfaces.

FIG. A3. Distribution of the cosine of turning angles from individual releasesof O. hexfasciataon moist (n= 153) and dry (n= 162) plaster surfaces (arena size = 594 cm^{2}). Cosines near 1 indicate obtuse angles (i.e., directional persistence). Cosines near -1 indicate acute turning angles.

FIG. A4. Regression of pellet counts on bracts of P. strobuscones againstO. hexfasciatadensity in jar experiments (Pr >F= 0.0010). Pellet counts are the sum of counts from the tip regionsof six bracts per jar. All density levels except level 16 were replicated three times.

FIG. A5. Plot of litter counts against total enclosure counts(traps+litter+cones), showing spiderandno spidertreatments. One data point is not shown (x= 582,y= 459, treatment =spider added).

Dixon, P. M. 1998. Assessing effect and no effect with equivalence tests. Pages 275–301

inM. C. Newman and C. L. Strojan, editors. Risk assessment: logic and measurement. Ann Arbor Press, Chelsea, Michigan, USA.Federer, C. A. 1995. BROOK90: a simulation model for evapotranspiration, soil water, and streamflow, Version 3.1. Computer freeware and documentation. USDA Forest Service, PO Box 640, Durham, New Hampshire, USA 03824.