Supplementary Material s27

Supplementary Material

Path Model Results

We developed one plausible path model for each response variable based on our a priori hypotheses and the results of model selection, with measures of ecosystem size included as the independent variables in all models (Figure S1). Drainage area exhibited a direct negative relationship with trophic position of tetragnathid spiders (Figure S1b). Channel width also had a weak direct negative effect on spider trophic position (Figure S1b). Flood magnitude emerged as a strong indirect pathway for reliance on aquatically- derived nutritional subsidies and trophic position of tetragnathid spiders (Figure S1a, b). In both models, flood magnitude had a positive effect with greater standardized regression weights than either measure of ecosystem size implicating it as a mediator of ecosystem size for determining trophic dynamics of invertebrate consumers. Neither NDVI nor fire was indicated as supported predictors.

Non-linear Patterns

The distribution of both trophic response variables and fire pointed to possible non-linear patterns relative to drainage area. For example, at the confluence of Illilouette Creek and the main stem of the Merced River, drainage area increased 166% (from 33.1 to 52.2 km2). However, at this same location, the catchment burned greater than two times since 1930 increased from 0.7 to 10.0%, the catchment burned one decade prior to sampling increased from 1.2 to 5.8%, and the catchment burned with moderate-to-high severity increased from 0.8 to 4.6%; therefore, the catchment affected by fire increased by 500-1400% (Figure S2). We found significant non-linear relationships between spider trophic responses and individual fire characteristics (Figure S3). Supported breakpoints occurred at upstream-to-downstream discontinuities in the percentage of the catchment affected by fire. The degree to which tetragnathids relied on aquatically-derived nutritional subsidies increased at a single breakpoint for all fire variables (10.91 ± 0.32% [SE] of the catchment burned twice or more since 1930, 5.73 ± 0.41% of the catchment burned in the decade prior to sampling, and 5.35 ± 0.50% of the catchment burned with moderate or high severity since 1984). We detected two breakpoints in the linear relationship between fire characteristics and trophic position of tetragnathid spiders (0.06 ± 0.20% [SE] and 11.03 ± 0.12% of the catchment burned twice or more since 1930, 1.31 ± 0.90% and 9.44 ± 0.20% of the catchment burned in the decade prior to sampling, and 0.94 ± 0.73% and 7.03 ± 0.11% of the catchment burned with moderate or high severity since 1984). In general we observed a positive relationship between fire effects and trophic responses. However, the non-linear relationship between trophic position and fire characteristics was negative between the first and second breakpoints. Flood (a) magnitude R2 = 0.78

0.62 1.07

-0.41 Reliance on aquatically- Channel width derived nutritional subsidies

(b) R2 = 0.60 -0.34 Drainage area 1.21 Flood 1.18 0.78 Magnitude Trophic position -0.32 Channel width -0.18

Figure S1. Constructed path diagrams for each response variable: (a) reliance on aquatically-derived nutritional subsidies by tetragnathid spiders (χ2 = 0.01, p = 0.994, CFI = 1.00, TFI = 1.09, RMSE = 0.00) and (b) trophic position of tetragnathid spiders (χ2 = 0.02, p = 1.000, CFI = 1.00, TFI = 1.05, RMSE = 0.00). Models were based on predicted relationships and further informed by model-selection analysis and ecological plausibility. Each pathway is labeled with a standardized partial-regression coefficient indicating the strength of the relationship. One-headed arrows indicate an assumed causal link and two-headed arrows indicate a correlation with no causality implied. The total variation explained by the model is indicated by R2 values. 5 1200

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Trophic position Reliance on aquatically-derived nutritional subsidies Fire Flood magnitude

Figure S2. Trophic position and reliance on aquatically-derived nutritional subsidies (expressed as a proportion, 0.0-1.0) of tetragnathid spiders along a gradient of drainage area. Fire and flow magnitude are shown to illustrate non-linear environmental variability that may influence trophic responses. “Fire axis” represents frequency, severity, and timing. More positive values indicate a greater percentage of the catchment burned by frequent, severe, or recent fire. 0.9 0.9 0.9 s

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0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 % burned twice or more % burned in 10 years prior % burned with moderate since 1930 to sampling or high severity since 1984 Figure S3. Comparison of linear and piecewise linear relationships of independent variables with trophic responses of tetragnathid spiders: (a) Percent of catchment burned twice or more since 1930 by reliance on aquatically-derived nutritional subsidies (linear: t = 31.06, p < 0.001, R2 = 0.46, AICc = -66.4; piecewise: t = 37.59, p < 0.001, R2 = 0.80, AICc = -98.86); (b) Percentage of the catchment burned in the ten years prior to sampling by aquatically-derived nutritional subsidies (linear: t = 24.60, p < 0.001, R2 = 0.60, AICc = -74.66; piecewise: t = 41.38, p < 0.001, R2 = 0.87, AICc = -109.84); (c) Percentage of the catchment burned with moderate or high severity since 1984 by aquatically-derived nutritional subsidies (linear: t = 25.81, p < 0.001, R2 = 0.60, AICc = -77.74; piecewise: t = 36.09, p < 0.001, R2 = 0.81, AICc = -100.28); (d) Percentage of the catchment burned twice or more since 1930 by trophic position (linear: t = 30.72, p < 0.001, R2 = 0.34, AICc = 31.74; piecewise: t = 40.32, p < 0.001, R2 = 0.81, AICc = -5.81); (e) Percentage of the catchment burned in the ten years prior to sampling by trophic position (linear: t = 32.46, p < 0.001, R2 = 0.48, AICc = 22.79; piecewise: t = 36.89, p < 0.001, R2 = 0.78, AICc = 0.54); and (f) Percentage of the catchment burned with moderate or high severity since 1984 by trophic position (linear: t = 33.53, p < 0.001, R2 = 0.48, AICc = 23.17; piecewise: t = 35.35, p < 0.001, R2 = 0.77, AICc = 2.71).