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Appendix S1. Structure of the numerical model

Figure S1. Optimal tapering coefficient ā as a function of distance from the apex (or total number of ranks N) assuming constant tapering within a tree (i.e., ā is independent of rank number and positive) for four different values of conduit radius. Note that ā is used in this graph, not T.

Figure S2. An example of how the model calculated gross photosynthetic gains, total carbon construction costs and net gains (the difference between the first two) for trees of variable number of ranks (hence distance from the apex).

Figure S3. In this simulated coniferous tree, conduits tapered for a few metres below the tree apex at a constant rate (corresponding to ā=0.20).

Figure S4. An example of the impact of allowing variable maximum tapering rates just below the apex of angiosperm and gymnosperm trees.

Figure S5. Tapering profiles for two phylogenetic groups (angiosperms and gymnosperms) and two ontogenetic classes (large and small plants).

Table S1. List of parameter values employed in the numerical model.

Table S2. Datasets employed in the meta-analysis.

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