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Appendix S1 Correlation coefficients of the environmental variables.

Appendix S2 Relationships between the explanatory capacity of models before and after the extraction of their shared components.

Appendix S3 Patterns of deviances corrected simultaneously by their shared components through functional groups.

Appendix S4 Testing the robustness of the main results.

Appendix S5 Associations between range size and explained deviances. Patterns of range-corrected deviances through taxonomic/functional groups.

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