Modeling forest stand dynamics from optimal balances of carbon and nitrogen.

We formulate a dynamic evolutionary optimization problem to predict the optimal pattern by which carbon (C) and nitrogen (N) are co-allocated to fine-root, leaf, and wood production, with the objective of maximizing height growth rate, year by year, in an even-aged stand. Height growth is maximized with respect to two adaptive traits, leaf N concentration and the ratio of fine-root mass to sapwood cross-sectional area. Constraints on the optimization include pipe-model structure, the C cost of N acquisition, and agreement between the C and N balances. The latter is determined by two models of height growth rate, one derived from the C balance and the other from the N balance; agreement is defined by identical growth rates. Predicted time-courses of maximized height growth rate accord with general observations. Across an N gradient, higher N availability leads to greater N utilization and net primary productivity, larger trees, and greater stocks of leaf and live wood biomass, with declining gains as a result of saturation effects at high N availability. Fine-root biomass is greatest at intermediate N availability. Predicted leaf and fine-root stocks agree with data from coniferous stands across Finland. Optimal C-allocation patterns agree with published observations and model analyses.

Optimal co-allocation of carbon and nitrogen in a forest stand at steady state.

Nitrogen (N) is essential for plant production, but N uptake imposes carbon (C) costs through maintenance respiration and fine-root construction, suggesting that an optimal C:N balance can be found. Previous studies have elaborated this optimum under exponential growth; work on closed canopies has focused on foliage only. Here, the optimal co-allocation of C and N to foliage, fine roots and live wood is examined in a closed forest stand. Optimal co-allocation maximizes net primary productivity (NPP) as constrained by stand-level C and N balances and the pipe model. Photosynthesis and maintenance respiration increase with foliar nitrogen concentration ([N]), and stand-level photosynthesis and N uptake saturate at high foliage and fine-root density. Optimal NPP increases almost linearly from low to moderate N availability, saturating at high N. Where N availability is very low or very high, the system resembles a functional balance with a steady foliage [N]; in between, [N] increases with N availability. Carbon allocation to fine roots decreases, allocation to wood increases, and allocation to foliage remains stable with increasing N availability. The predicted relationships between biomass density and foliage [N] are in reasonable agreement with data from coniferous stands across Finland. All predictions agree with our qualitative understanding of N effects on growth.

Crown ratio influences allometric scaling in trees.

Allometric theories suggest that the size and shape of organisms follow universal rules, with a tendency toward quarter-power scaling. In woody plants, however, structure is influenced by branch death and shedding, which leads to decreasing crown ratios, accumulation of heartwood, and stem and branch tapering. This paper examines the impacts on allometric scaling of these aspects, which so far have been largely ignored in the scaling theory. Tree structure is described in terms of active and disused pipes arranged as an infinite branching network in the crown, and as a tapering bundle of pipes below the crown. Importantly, crown ratio is allowed to vary independently of crown size, the size of the trunk relative to the crown deriving from empirical results that relate crown base diameter to breast height diameter through crown ratio. The model implies a scaling relationship in the crown which reduces to quarter-power scaling under restrictive assumptions but would generally yield a scaling exponent somewhat less than three-quarters. For the whole tree, the model predicts that scaling between woody mass and foliage depends on crown ratio. Measurements on three boreal tree species are consistent with the model predictions.

Bridging process-based and empirical approaches to modeling tree growth.

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.

Nutritional changes in host foliage during and after defoliation, and their relation to the weight of gypsy moth pupae.

Black oak (Quercus velutina Lam.) and gray birch (Betula populifolia Marsh.) trees were defoliated in 0, 1, 2, or 3 successive years. Concentrations of 8 minerals, 4 sugars, and 25 amino acids in the foliage of these trees were measured when gypsy moth, Lymantria dispar (L.), reared on them were in instars I, III, IV, and V. These concentrations were tested for changes among years, and changes due to previous-and current-year defoliations. Most foliar constituents varied in concentration from year to year, though relatively few were affected by current or previous defoliations. In black oak, concentration of total free sugar measured during the fifth instar was reduced by current defoliation and correlated with gypsy moth pupal weight. In gray birch no decrease in sugar concentration due to defoliation was apparent, but pupal weights of gypsy moths reared on these trees were correlated with the ratio of total free sugar to calcium in the foliage measured during the fifth instar. Some implications of these apparent relations for gypsy moth larval growth and population dynamics are discussed.

Bayesian synthesis for quantifying uncertainty in predictions from process models.

The Bayesian synthesis method is reviewed and judged to be useful for determining posterior distributions and interval estimates for inputs and outputs of process-based forest models. The method furnishes posterior distributions of the values of a model's parameters and response variables. The method also provides estimates of correlation among the parameters and output variables. Bayesian synthesis is the only type of uncertainty analysis that affords incorporation of all the information available to the investigator, in addition to the information contained in the model itself.

Initializing a model stand for process-based projection.

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 tessellation 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.