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Appendix S1 Detailed description of the selection of survey fields.

Appendix S2 Detailed description of the selection of explanatory variables.

Appendix S3 The WinBUGS script for specifying the hierarchical linear model that assumes independent coefficients among explanatory variables.

Appendix S4 The R script for running the hierarchical linear model that assumes independent coefficients among explanatory variables.

Appendix S5 Brief description of posterior predictive checking.

Appendix S6 Brief description of the calculation of average predictive comparisons.

Appendix S7 Brief description of the hierarchical linear model with covariance matrices for the coefficients of explanatory variables.

Appendix S8 The WinBUGS script for specifying the hierarchical linear model with the covariance matrices for the coefficients of explanatory variables.

Appendix S9 The R script for running the hierarchical linear model with the covariance matrices for the coefficients of explanatory variables.

Figure S1 Locations of the survey fields.

Figure S2 The range of annual mean temperature, summer precipitation and mean elevation for 100-km2 squares used for predictions (black) and those including the survey fields (red).

Figure S3 DIC values of hierarchical linear models for the abundance of Tetragnatha with the area of forest surrounding the survey fields calculated at different spatial scales, and all the other explanatory variables.

Figure S4 Graphical posterior predictive check to assess the goodness-of-fit of the hierarchical model assuming independent coefficients. Dots show the sums of squares (SSQ) discrepancies (residuals) calculated from the actual vs. replicated data sets for 1000 MCMC samples. The line indicates the 1 : 1 line.

Figure S5 The estimated parameters for the hierarchical linear model with covariance matrices for the coefficients of explanatory variables, fitted to the data on the abundance of Tetragnatha. Points and bars are as defined in Figure 1.

Figure S6 Estimated average predictive comparisons for the abundance of Tetragnatha for each input variable in the hierarchical model assuming independent coefficients. Bars show ± 1 standard-error bounds.

Figure S7 (a) Annual mean temperature (°C), (b) summer (Jun–Aug) precipitation (mm) and (c) mean elevation (m) in the 100-km2 square for predictions.

Figure S8 The predicted benefits of reducing (a) insecticide applications to fields, (b) insecticide applications to nursery boxes and (c) herbicide applications in increasing the abundance of Tetragnatha. The benefits were defined as the inverted site-specific regression coefficients against the number of pesticide applications, predicted for each 100-km2 square.

Figure S9 The uncertainties (coefficients of variation) in the predicted abundance of Tetragnatha under (a) conventional farming (Figure 5a in the main text) and (b) organic farming (Figure 5b). Medians of the estimated posterior distributions are shown.

Table S1 Summary of data used for the analysis. Means and ranges (in parentheses) are shown.

Table S2 The number of replicates for each application level of three pesticide types. There were 85 replicates for organic farming (i.e., without any pesticide applications). The number of pesticide applications was defined as the multiple of the total number of active ingredients in a pesticide and the number of times that pesticide was applied. For example, if an insecticide that includes two active ingredients was applied to a field twice, the number of insecticide applications to the field was recorded as four.

Table S3 Correlation coefficients among explanatory variables used for the hierarchical linear model. Values larger than 0.5 are shown in bold. The number of sampling and the total number of swings (range: 40–540, mean ± SE: 184.2 ± 6.0) in each survey field were not strongly correlated with other explanatory variables (|r| < 0.32).

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