Testing and extending metabolic theory: Asymmetric branching and the scaling of resource distribution networks of trees

Background/Question/Methods

The origin of biological allometry has been proposed to be due to the geometry of hierarchical branching networks. The West Brown and Enquist model (WBE) model details specific predictions about how the branching geometry of networks underlies biological allometry. However, the WBE model simplifies biological networks as symmetrically branching—all branches and vessels that are the same number of branchings away from a given stem share identical values for their radii and lengths. However, symmetric branching is often a poor approximation for most trees and plants (vines, cacti, conifers, and plants that are apically dominant or exhibit other diverse architectures) as well as other vascular networks in biology. The branching assumption is central and can be shown to influence all of the predictions of the WBE model. Here, we generalize existing network architecture theory, with a focus on plants, to account for the full spectrum of plant architectures and to incorporate variation in key plant functional traits. To test these ideas we destructively dissected numerous whole-trees that span different architectures and functions (ranging from conifers to angiosperms to ring and diffuse porous) and measure their branching architectures so as to quantify branching asymmetry and whole-tree allometry.

Results/Conclusions

Our analytical derivations provide a quantitative basis for how to incorporate asymmetrical branching into our model of resource distribution networks that accounts for the driving forces of selective environments. By examining various constraints on the branching ratios of length and area (corresponding to the volume filling and area preserving assumptions), as well as constraints on the branching angles, we show how we can more precisely predict whole-plant allometric relationships for resource use and growth. Our analyses across each of the tree species dissected reveals that branching geometry is clearly asymmetrical violating a key assumption of the WBE model. Further, across each tree and species, despite differences in branching architecture there is a remarkable amount of overlap in the degree of branching asymmetry pointing to similarity in the amount of asymmetry that characterizes these networks. Incorporating branching asymmetry into metabolic scaling theory can further improve the predictive ability of the theory. Discussion will also focus on how differing light and competitive environments experienced during ontogeny may select for a certain degree of asymmetrical branching. Further, we point to ways to measure branching traits that can shed light into the various processes that underlie similarity and variation in allometric scaling in biology.