Empirical evaluation of the external branching architecture of diverse trees in light of metabolic scaling theory assumptions

Background/Question/Methods It is widely recognized that plant architecture is a core component underlying the plant phenotype. Indeed, the geometry of plant branching networks plays a major role in the metabolic scaling model proposed by West, Brown, and Enquist (WBE). In the WBE model, self-similar branching networks are fundamental in controlling plant carbon balance and overall metabolism by regulating the scaling of leaf number. Following fractal-like branching, the WBE model assumes the branching ratio (n) is constant across level k. Based on further assumptions, daughter/parent ratios of radii and lengths at level k (β_k and γ_k, respectively) are related to n through constant scaling exponents, where β_k=n^-a and γ_k=n^-b. Since the application of the WBE model is extensive in ecology, an empirical evaluation of these fundamental branching assumptions across a variety of plant species is essential. Here, we assess these assumptions by testing the self-similarity of β_k and γ_k throughout individual plant branching networks and estimating inter-specific variation scaling exponents. To this end, anatomical characteristics of external network architecture (e.g., number of leaves, branch furcations, internode lengths, node radii) were extensively measured in 3 tree species differing in geometric structure and age: Pinus edulis, P. pondersosa, and Ochroma pyramidale. Results/Conclusions Branching ratios, length ratios, and radii ratios were calculated at each level k and compared to WBE model assumptions. In P. edulis, n was not observed to be constant across level k. For example, in a sample of 77 nodes at k=10, the distribution of n was observed to exponentially decrease from n=1 to n=6. In P. ponderosa, β_k and γ_k were also not dependent on k as assumed by WBE theory. This observed variation in n, β_k and γ_k suggests that an asymmetrical branching model might be more appropriate than a symmetrical model for representing external branching architecture of apically-dominant pine trees. Analysis of parent/daughter cross sectional areas in O. pyramidale, however, did support self-similarity. Species differences in patterns observed for β_k , γ_k, and n infer a need for a broader definition of the distribution of values for scaling exponents to fully encompass variation in nature. Hopefully, more general WBE model assumptions related to external network architecture will emerge by accounting for observed inter- and intra-specific variation in branching parameters.