Abstract
Plant vascular networks are central to botanical form, function, and diversity. Here, we develop a theory for plant network scaling that is based on optimal space filling by the vascular system along with trade-offs between hydraulic safety and efficiency. Including these evolutionary drivers leads to predictions for sap flow, the taper of the radii of xylem conduits from trunk to terminal twig, and how the frequency of xylem conduits varies with conduit radius. To test our predictions, we use comprehensive empirical measurements of maple, oak, and pine trees and complementary literature data that we obtained for a wide range of tree species. This robust intra- and interspecific assessment of our botanical network model indicates that the central tendency of observed scaling properties supports our predictions much better than the West, Brown, and Enquist (WBE) or pipe models. Consequently, our model is a more accurate description of vascular architecture than what is given by existing network models and should be used as a baseline to understand and to predict the scaling of individual plants to whole forests. In addition, our model is flexible enough to allow the quantification of species variation around rules for network design. These results suggest that the evolutionary drivers that we propose have been fundamental in determining how physiological processes scale within and across plant species.