Scaling and structure of dicotyledonous leaf venation networks.

There have been numerous attempts to derive general models for the structure and function of resource delivery networks in biology. Such theories typically predict the quantitative structure of vascular networks across scales. For example, fractal branching models of plant structure predict that the network dimensions within plant stems or leaves should be scale-free. However, very few empirical examples of such networks are available with which to evaluate such hypotheses. Here, we apply recently developed leaf network extraction software to a global leaf dataset. We find that leaf networks are neither entirely scale-free nor governed entirely by a characteristic scale. Indeed, we find many network properties, such as vein length distributions, which are governed by characteristic scales, and other network properties, notably vein diameter distributions, which are typified by power-law behaviour. Our findings suggest that theories of network structure will remain incomplete until they address the multiple constraints on network architecture.