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The gulf between process-based and empirical approaches to modeling tree growth may be bridged, in part, by the use of a common model. To this end, we have formulated a process-based model of tree growth that can be fitted and applied in an empirical mode. The growth model is grounded in pipe model theory and an optimal control model of crown development. Together, the pipe model and the optimal control model provide a framework for expressing the components of tree biomass in terms of three standard inventory variables: tree height, crown height and stem cross-sectional area. Growth rates of the inventory variables and the components of biomass are formulated from a carbon balance. Fundamentally, the parameters of the model comprise physiological rates and morphological ratios. In principle, the values of these parameters may be estimated by lower-level process models. Alternatively, the physiological and morphological parameters combine, under reasonable assumptions, into a set of aggregate parameters, whose values can be estimated from inventory data with a statistical fitting procedure.

Summary A stand generation (or initialization) procedure is designed to furnish morphologically plausible model trees for process-based projection. The steps of the initialization are: (i) the generation of the locations of model trees and the tessella tion of tree areas; (ii) the sampling of diameters from a target distribution and assignments of those diameters to model-tree locations; (iii) the calculation of the height of each model tree from its assigned diameter and the distances to its neighbors; (iv) the calculation of the crown length of each model tree from its height and distances to its neighbors; and (v) the recalculation of diameter from height and crown length. Components of dry matter are calculated from the model-tree dimensions and pipe-model theory. Process-based projection with the AMORPHYS model is discussed.

Crown architecture and growth allocation were studied in saplings of eastern white pine (Pinus strobus L.), a species classified as intermediate in shade tolerance. A comparison was made of 15 understory saplings and 15 open-grown saplings that were selected to have comparable heights (mean of 211 cm, range of 180-250 cm). Mean ages of understory and open-grown trees were 25 and 8 years, respectively. Understory trees had a lower degree of apical control, shorter crown length, and more horizontal branch angle, resulting in a broader crown shape than that of open-grown trees. Total leaf area was greater in open-grown saplings than in understory saplings, but the ratio of whole-crown silhouette (projected) leaf area to total leaf area was significantly greater in understory pine (0.154) than in open-grown pine (0.128), indicating that the crown and shoot structure of understory trees exposed a greater percentage of leaf area to direct overhead light. Current-year production of understory white pine was significantly less than that of open-grown white pine, but a higher percentage of current-year production was allocated to foliage in shoots of understory saplings. These modifications in crown structure and allocation between open-grown and understory white pine saplings are similar to those reported for more shade-tolerant fir (Abies) and spruce (Picea) species, but the modifications were generally smaller in white pine. As a result, white pine did not develop the flat-topped "umbrella" crown structure observed in understory fir and spruce, which approaches the idealized monolayer form that maximizes light interception. The overall change to a broader crown shape in understory white pine was qualitatively similar, but much more limited than the changes that occurred in fir and spruce. This may prevent white pine from persisting in understory shade as long as fir and spruce saplings.