Detailed measurements of the geometry of venation networks are critical for understanding how leaves influence whole plant hydrodynamics and carbon balance. Moreover, knowledge of the geometry and functional topology of leaf networks will enhance the development and testing of theoretical models aimed and understanding the ontogenetic and life history constraints governing leaf evolution. Unfortunately due to the small size and large number of bifurcations comprising most venation systems, almost no exhaustive descriptions of the geometry of entire leaf networks exist.  As a step toward obtaining sufficient data with which to advance theories of leaf network structure, ontogeny, function and evolution, we have developed a series of image segmentation and network extraction algorithms that resolve the geometry of veins, and the areoles they surround, in leaves, and have bundled these algorithms into a graphical user interface: Leaf Extraction and Analysis Framework (www.leafgui.org). The software package allows any user to take images of leaf veins through a series of interactive thresholding and cleaning steps. The resulting binary image of the leaf venation network is then passed to a series of algorithms that quantify the dimensions and connectivity of leaf veins and the areoles they surround.

Results/Conclusions

The software, written in Matlab, has been compiled into a standalone executable file that can run on any platform (Mac, PC, Unix).  The software was used to analyze interspecific scaling patterns from a global dataset of 353 leaves representing 353 species. Our results suggest that the scaling of leaf network morphology is driven by a characteristic length scale likely determined by diffusion limits between veins and stomata. This manifests in several invariant quantities such as mean vein length, mean distance to the nearest vein, whole leaf network density. Moreover, in many respects the scaling of leaf networks is indistinguishable from a null model of an isometric lattice due to the numerical dominance of the highest order veins. However, network scaling differs from the lattice model in important ways, particularly with respect to the frequency distributions of vein lengths and diameters which were consistent with exponential and a power law models respectively. Specifically the ratio of vein branch diameters is remarkably close to that predicted by C.D. Murray over 80 years ago (Murray’s Law). We discuss these results in light of existing theories of plant and leaf network scaling.