Harry T. Valentine

Tree-growth models: Derivations employing the pipe-model theory

Models of the growth rates of tree basal area and height are derived using the pipe-model theory of tree form. It is assumed that a tree can be totally partitioned into pipes and that each pipe undergoes steady-state growth. The model of basal area growth rate is derived from the growth rate of the aggregate area of the cross sections of all of the pipes comprising the tree. The model of height growth rate is derived considering only those pipes extending to the apex of the crown of the tree. The likelihood of dieback in the crown of a defoliated tree is discussed in light of the resultant model.

sampling methods to estimate foliage and other characteristics of individual trees

The total foliar area or mass of a tree is difficult to measure, as is its bark or cambial area, and various other components of aboveground biomass. A variety of sampling methods is proposed and estimators of these characteristics are presented. Based on probability precepts, all estimators are unbiased. An unbiased estimator of variance for each estimator also is presented. The basis in probability rather than a fitted regression equation provides some important safeguards, and is a useful alternative when fitted re- gression functions are unavailable for a particular species and physiographic condition.

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.

Optimal function explains forest responses to global change

Plant responses to global changes in carbon dioxide (CO2), nitrogen, and water availability are critical to future atmospheric CO2 concentrations, hydrology, and hence climate. Our understanding of those responses is incomplete, however. Multiple-resource manipulation experiments and empirical observations have revealed a diversity of responses, as well as some consistent patterns. But vegetation models—currently dominated by complex numerical simulation models—have yet to achieve a consensus among their predicted responses, let alone offer a coherent explanation of the observed ones. Here we propose an alternative approach based on relatively simple optimization models (OMs). We highlight the results of three recent forest OMs, which together explain a remarkable range of observed forest responses to altered resource availability. We conclude that OMs now offer a simple yet powerful approach to predicting the responses of forests—and, potentially, other plant types—to global change. We recommend ways in which OMs could be developed further in this direction.

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

SummaryBlack 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.

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.

Modeling crown rise in even-aged stands of Sitka spruce or loblolly pine

Abstract A ‘crown-rise’ model that estimates average height to the base of a crown in an even-aged, monospecific stand is derived and fitted to loblolly pine and Sitka spruce data. Estimated standard errors are less than 1 m. The driving variables are average tree height and either tree count per unit area or average inter-tree distance. Two potential uses of the crown-rise model are (1) a component of an empirical or mechanistic forest model, and (2) and alternative to stocking charts for stand density management.

Design unbiased estimation in line intersect sampling using segmented transects

In many applications of line intersect sampling, transects consist of multiple, connected segments in a prescribed configuration. The relationship between the transect configuration and the selection probability of a population element is illustrated and a consistent sampling protocol, applicable to populations composed of arbitrarily shaped elements, is proposed. It is shown that this protocol obviates the arbitrary practice of treating multiple intersections of a single particle as independent probabilistic events and preserves the design-unbiasedness of Kaiser’s (1983, Biometrics39, 965–976) conditional and unconditional estimators, suitably generalized to segmented transect designs. The relative efficiency and utility of segmented transect designs are also discussed from a fixed population perspective.

Line intersect sampling: Ell-shaped transects and multiple intersections

The probability of selecting a population element under line intersect sampling depends on the width of the particle in the direction perpendicular to the transect, as is well known. The consequence of this when using ell-shaped transects rather than straight-line transects are explicated, and modifications that preserve design-unbiasedness of Kaisers (1983) conditional and unconditional estimators are presented. A case against treating multiple intersections as multiple probabilistic events is argued on the basis, also, of preserving design-unbiased estimation.

Multistage point relascope and randomized branch sampling for downed coarse woody debris estimation

New sampling methods have recently been introduced that allow estimation of downed coarse woody debris using an angle gauge, or relascope. The theory behind these methods is based on sampling straight pieces of downed coarse woody debris. When pieces deviate from this ideal situation, auxillary methods must be employed. We describe a two-stage procedure where the relascope is used to select pieces of downed coarse woody debris in the first stage. If the pieces so chosen on the first stage have multiple branches and detailed estimates are required for the entire piece, then a second stage sample is advocated using the randomized branch technique. Both techniques are reviewed and an example is given examining possible surrogate variables for the second stage.