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West, Brown and Enquist (1999 a ) modeled vascular plants as a continuously branching hierarchical network of connected links (basic structural units) that ends in a terminal unit, the leaf petiole, at the highest link order (WBE model). We applied the WBE model to study architecture and scaling between links of the water transport system from lateral roots to leafy lateral branches and petioles in  Populus deltoides  Bartr. ex Marsh. trees growing in an agroforestry system (open-grown trees) and in a dense plantation (stand-grown trees). The architecture of  P. deltoides  violates two WBE model assumptions: (1) the radii of links formed in a branching point are unequal; and (2) there is no terminal unit situated at the end of a hierarchical network, rather, petioles are situated at any link order greater than 1. Link cross sections were taken at various link orders and morphological levels in roots and shoots of open-grown trees and shoots of stand-grown trees. Scaling of link radii was area-preserving. From roots to branches, vessel diameters were scaled with link order in accordance with a 1/6-power, as predicted by the WBE model indicating general vessel tapering. However, analysis of the data at the morphological level showed that vessel radius decreased intermittently with morphological level rather than continuously between successive link orders. Estimation of total water conductive area in a link is based on conducting area and petiole radius in the WBE model. The estimation failed in  P. deltoides , probably because petioles are not a terminal unit. Biomass of stand-grown trees scaled with stem basal radius according to the 3/8-power predicted by the WBE model. Thus, the WBE model adequately described vascular allometry and biomass at the whole-tree level in  P. deltoides  despite violation of Assumption 1, but failed in predictions where the leaf petiole was used as a terminal unit.

Applying a universal scaling model to vascular allometry in a single-stemmed, monopodially branching deciduous tree (Attim's model)