Boris Zeide

Tolerance and self-tolerance of trees

Abstract The fact that tolerant species survive better than intolerants in mixed stands does not mean that in pure stands tolerants have less mortality than intolerants. Tolerance is not necessarily associated with self-tolerance which can be defined as the ability of trees to grow and to survive under the stress of intraspecific competition. The relative rate of volume growth with respect to the decrease of the number of trees captures both processes involved in the definition of self-tolerance (growth and mortality) and can be used as its measure. A positive correlation was not found between this measure and tolerance as determined from tolerance tables for southern pines. Therefore, self-tolerance appears to be a quality of stands independent of tolerance.

How to measure stand density

Foresters have produced many measures of stand density. Yet, none of these is entirely satisfactory. A majority of the measures (stand density index, basal area, and leaf area) present number of trees per unit area as a function of one factor: average tree size. This paper identifies the second factor driving self-thinning: the accumulation of gaps between tree crowns inevitable even in dense stands with a sizeable overlap of crowns. A model accounting for both factors allows us to quantify stand density and find a single number characterizing the density of undisturbed stands. The number changes with species, being higher for more shade tolerant ones. It is found that the second factor affects survival of trees but not their growth. This means that there are two kinds of stand density.

Impacts and management implications of ice storms on forests in the southern United States

This review explores the ecological and silvicultural impacts of ice storms on forests in the southern United States. Different environmental factors like weather conditions, topography, vegetation, stand density, and management practices influence the degree of glaze damage a particular forest may experience. Additionally, the frequent contradictions in the relationships between these factors and the resulting damage suggests a complexity that makes each ice storm unique and difficult to predict. We recommend a series of silvicultural responses to ice storms, including density management, planting species selection, postevent evaluation, salvage, stand rehabilitation, and long-term monitoring of forest health. Published by Elsevier B.V.

A relationship between size of trees and their number

Abstract It is known that stem diameter at crown base, Dc, has a closer relationship with crown size than diameter at breast height, D. Because number of trees per unit area, N, depends on crown size, it is likely that average Dc will be a better predictor of tree number than D. It is shown that if the relationship between the logarithms of N and Dc is linear, then a similar relationship between N and D is not. A new size-number relationship is proposed that attempts to reconstruct Dc using readily available variables, D and total tree height.

Fractal geometry in forestry applications

Abstract Fractal geometry can be used to describe length, surface, and volume of natural objects such as trees, rivers, and mountains. Unlike the straight lines of classical geometry, natural lines do not have unique invariable lenghts. They become longer when we use smaller units of measurement which are able to reveal finer details of the line. Although both unit and length change, the parameter governing these changes remains invariant. This parameter, called the fractal dimension, is specific for each line. Fractal dimensions of natural lines are greater than one and the excess indicates the degree of convolution. Not all tree variables are fractals. Stem surface is fractal, but volume is not. Therefore, volume as well as tree height should be calculated using the methods of classical geometry. At the same time, potential applications of fractal geometry are not limited to quantifying natural lines and surfaces. Fractal geometry may produce new methods for estimating stand density, predicting forest succession, and describing the form of trees. It is shown that the fractal dimension of tree crowns is a good indicator of various tree and site features such as species tolerance, crown class, and site quality. Therefore, the crown fractal dimension could be the most meaningful single number for tree description. At the same time, improved video cameras could make this dimension the easiest tree variable to measure.

Natural thinning and environmental change: an ecological process model

Abstract The proposed model of natural thinning is based on ecological processes, which integrate all relevant physiological processes. Within the traditional all-encompassing framework of carbon balance, this study develops a more instrumental framework of the reciprocal relationship between the area occupied by the average tree and the number of trees per unit area. The model includes two other terms reflecting aging of trees and effects of environmental change. Parameters of this model were estimated using data from permanent sample plots established in northern Ontario. The resulting model accurately describes natural thinning of even-aged stands and makes it possible to quantify each of the constituent processes, including the effects of environmental change on forest ecosystems. During the period 1952–1987, this effect has produced 16% increase in number of trees of a given size per unit area.

Quality as a characteristic of ecological models

Abstract Trade-offs between model characteristics (accuracy, generality, robustness, and so on) should not be accepted as inevitable. Good models manage to combine desirable features, and such a combination constitutes the quality of a model. A good model should reflect the overwhelming importance of reproductive effort to living beings. The quality of a model can also be judged by the constancy of its parameters and the absence of patterns in residuals. A novel (or rather long-forgotten) approach to model construction is proposed. It calls for the simultaneous formulation of two idealized extreme models of the same process prior to quantification of the central tendency. Examples and implications of this approach are discussed.

Signal-transfer modeling for regional assessment of forest responses to environmental changes in the southeastern United States

Stochastic transfer of information in a hierarchy of simulators is offered as a conceptual approach for assessing forest responses to changing climate and air quality across 13 southeastern states of the USA. This assessment approach combines geographic information system and Monte Carlo capabilities with several scales of computer modeling for southern pine species and eastern deciduous forests. Outputs, such as forest production, evapotranspiration and carbon pools, may be compared statistically for alternative equilibrium or transient scenarios providing a statistical basis for decision making in regional assessments.

Pattern of height growth for southern pine species

Abstract Along with unique features, the dynamics of a given forest stand have much in common with the known dynamics of previously studied stands. The assumption that two points are necessary and sufficient to determine any growth curve made it possible to condense the accumulated knowledge on height growth to 16 types; further research showed that this number can be reduced to three. This study introduces a harmonizing function permitting the ultimate compression of growth information to one height growth pattern. The harmonizing function complements growth equations; it describes the cross-section of growth curve families, that is, their values at the same age. The constructed growth pattern and the harmonizing function contain all possible site index curves for fast-growing species. Even though the growth pattern requires less information than the Chapman–Richards equation (two versus at least three points), it is more accurate than the equation fitted to three points. Compared with the one-point approach realized in site index curves, the deviation of the pattern from the actual growth is three times smaller. Although it has wider applicability than a particular set of site index curves, the application of the developed pattern requires more information. While the selection of a site index curve from a given set is based on one height–age pair, the growth pattern requires two height–age pairs. The pattern uncovers the information implicit in the two measured heights and is capable of representing stand growth in both stable and variable environments. A step-by-step application of the pattern and the harmonizing function for reconstructing height growth from two points is provided.

The Science of Forestry

ABSTRACT Forestry is a large field with a long history and extensive contents consisting of practical recommendations arrived at by trial and error. In contrast, the science of forestry is a new development relying on reasoning to produce the optimal system of forest management aimed at satisfying human needs and preserving nature at the same time (though not at the same place). The presented overview of this science consists of two parts. The first one develops a theory of tree growth and stand dynamics. The second part applies this theory to optimize forest management and suggest practical recommendations. What unites these two parts is a general method of inquiry. It starts with defining one problem, designs two opposing explanations, and then fuses them into a single solution. Hence, the name: the 1–2–1 method. Unlike material variables of process-based models, the explanations employed by the method are abstractions that outline the boundaries embracing all possible solutions. Each explanation in its turn may be subdivided into two opposites until a solution is reached by bringing the opposites together. The 1–2–1 method accounts for any number of variables by arranging them hierarchically into paired groups. Why exactly two explanations? Because each complex problem has two opposite sides, waiting to be uncovered. We may never know how many factors determine tree growth, yet there is one thing as certain as any mathematical proposition: All these factors are of two kinds—those that facilitate growth and those that restrain it. A factor that does neither is not really a factor. The basic positive process of tree growth is uninhibited cell division. Negative processes include, among others, aging and impediments associated with increasing tree size. When these and several other processes are expressed analytically, we get a meaningful and accurate model of tree growth comprising three pairs of opposites arranged in two levels. The model generalizes empirical equations developed in forestry and exposes biological mechanisms that justify the structure of the equations and explain their success. The resulting growth model describes density-independent growth. The complementary process of competition has inter- and intraspecific components. It is shown that to maximize forest productivity interspecific competition has to be minimized while the intraspecific kind optimized. Uniting the growth model with that describing the effect of intraspecific competition produces the growth-density model that solves many questions of forest management. In particular, the model helps to reconcile two main goals of management: (a) maximizing the financial returns from wood products, and (b) preserving forests with all their biodiversity and invaluable ecosystem services. Still, the thrust of this review is not another growth model or management system. The main point is an attempt to make forestry a science by consistent reasoning from first principles such as discreteness of plant biomass, the inverse relationship between average size and number of trees, and the conflict between the biotic potential and environmental resistance.