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Appendix S1 Derivations of model predictions.

Appendix S2 Abbreviations, definitions, units, ranges, mean values and references for all parameters used in the model involving venation traits.

Appendix S3 Experimental methods.

Code S1. MATLAB codes to automatically calculate venation traits.

Data S1. Species list and measurements for 25 Tucson species.

Figure S1 Structure of a model leaf including terminal veins.

Figure S2 Vein spacing and leaf thickness.

Figure S3 Empirically measured venation and functional traits.

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