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Appendix S1. Parameterization of abundances and landscape effects.

Appendix S2. Parameterization of predation rates.

Appendix S3. Sensitivity analyses.

Table S1. Landscape effects on the abundance of different predator groups used in the model parameterization.

Table S2. Predator attack rates for different predator taxa used in the model.

Table S3. Parameters used in (eqn 9): inline image.

Figure S1. Results of a sensitivity analysis varying aphid fecundity from half to double the value used in the original simulation.

Figure S2. Results of a sensitivity analysis varying predator population sizes by a constant that ranged from 0 to 2, so that all predator species had the same proportional increase or decrease.

Figure S3. Results of a sensitivity analysis varying predator attack rates by a constant that ranged from 0 to 2, so that all predator species had the same proportional increase or decrease.

Figure S4. Results of a sensitivity analysis removing the relation of wolf spiders to proportion of land not covered by annual crops in a 135 m radius.

Figure S5. Results of a sensitivity analysis adding the relation of wolf spiders to proportion of land not covered by annual crops in a 135 m radius also to sheet-web spiders.

Figure S6. Results of a sensitivity analysis adding the relation of wolf spiders to proportion of land not covered by annual crops in a 135 m radius also to large ground beetles.

Figure S7. Results of a sensitivity analysis adding the relation of wolf spiders to proportion of land not covered by annual crops in a 135 m radius also to adult lady beetles.

Figure S8. Results of a sensitivity analysis removing the relation of sheet-web spiders to proportion of land not covered by annual crops in a 1500 m radius.

Figure S9. Results of a sensitivity analysis adding the relation of sheet-web spiders to proportion of land not covered by annual crops in a 1500 m radius also to wolf spiders.

Figure S10. Results of a sensitivity analysis adding the relation of sheet-web spiders to proportion of land not covered by annual crops in a 1500 m radius also to large ground beetles.

Figure S11. Results of a sensitivity analysis adding the relation of sheet-web spiders to proportion of land not covered by annual crops in a 1500 m radius also to adult lady beetles.

Figure S12. Results of a sensitivity analysis removing the relation of large ground beetles to proportion of land not covered by annual crops in a 500 m radius, and to proportion of grassland in a 500 m radius.

Figure S13. Results of a sensitivity analysis adding the relation of large ground beetles to proportion of land not covered by annual crops in a 500 m radius, and to proportion of grassland in a 500 m radius, also to wolf spiders.

Figure S14. Results of a sensitivity analysis adding the relation of large ground beetles to proportion of land not covered by annual crops in a 500 m radius, and to proportion of grassland in a 500 m radius, also to sheet-web spiders.

Figure S15. Results of a sensitivity analysis adding the relation of large ground beetles to proportion of land not covered by annual crops in a 500 m radius, and to proportion of grassland in a 500 m radius, also to adult lady beetles.

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