Growth of plants results from two opposing factors: the intrinsic tendency toward unlimited increase (biotic potential) and restraints imposed by environmental resistance and ag/ng. The expansion tendency prevails in the beginning of a tree's life, while growth decline becomes prominent oward the end. The existing growth equations can be transformed (by differentiation, decomposition i to the division components, and taking logarithms) so that the components hat correspond to these two factors are exposed. This transformation reveals two basic forms intrinsic in most of the analyzed equations. Their common feature is that growth expansion is proportional to current tree size. Growth decline of individual trees appears to be more variable and can be rendered with equal accuracy by a variety of expressions. This may reflect that a greater number of factors hinder growth: scarcity of resources, competition, reproduction, diseases, herbivory, disturbances, etc. Consequently, the growth path is inherently imprecise and can be viewed as a wide valley rather than a single line. This analysis laid groundwork for the classification of known equations and made possible the discovery of a promising new equation form. FOR. SCL 39(3):594-616. ADDITIONAL

Analysis of growth equations.

1. Introduction.- 2. Tree Form and Stem Taper.- 3. Tree-stem Volume Equations.- 4. Tree Weight and Biomass Estimation.- 5. Quantifying Tree Crowns.- 6. Growth Functions.- 7. Evaluating Site Quality.- 8. Quantifying Stand Density.- 9. Indices of Individual-tree Competition.- 10. Modeling Forest Stand Development.- 11. Whole-stand Models for Even-aged Stands.- 12. Diameter-distribution Models for Even-aged Stands.- 13. Size-class Models for Even-aged Stands.- 14. Individual-tree Models for Even-aged Stands.- 15. Growth and Yield Models for Uneven-aged Stands.- 16. Modeling Response to Silvicultural Treatments.- 17. Modeling Wood Characteristics.- 18. Model Implementation and Evaluation.-

Modeling Forest Trees and Stands

Proper hypothesis testing is the subject of much debate in ecology. According to studies in cognitive psychology, confirmation bias (a tendency to seek confirming evidence) and theory tenacity (per...

Hypothesis Testing in Ecology: Psychological Aspects and the Importance of Theory Maturation

The present article illustrates the increased interest which is manifested in the microorganisms, Thiobacillus ferrooxidans, involved in the biohydrometallurgical extraction processes. The wide varieties of problems currently studied are very important in order to gain a better understanding about the factors which are governing the growth of microorganisms, and as a consequence, the metal dissolution phenomena. In several mining sites, the microbiological leaching techniques are currently practiced at industrial-scale, especially for recovery of copper and uranium from low-grade materials. However, an accurate assessment of further potential possibilities for the application of microorganisms in leaching metal sulfides requires a more fundamental knowledge about the interactions of the physical and chemical factors with the growth of T. ferrooxidans in pure and mixed cultures including heterotrophic and thermophilic cohabitants. Altogether, the future industrial exploitation of these microbiological leaching techniques are very attractive in many countries of the world.

The role of Thiobacillus ferrooxidans in hydrometallurgical processes

Summary Greenhouse-cultured, container-grown ponderosa pine (Pinus ponderosa var. scopulorum Engelm.), interior Douglas-fir (Pseudotsuga menziesii var. glauca (Beissn.) France), and Engelmann spruce (Picea engelmannii (Parry) Engelm.) were cold acclimated and deacclimated in growth chambers over 19 weeks. Cold hardiness was measured weekly by a whole-plant freeze test and by two quick tissue tests: freeze-induced electrolyte leakage of needles, and differential thermal analysis of buds. The whole-plant freeze test provided results in 7 days, and indicated differences in cold hardiness among stems, buds, and needles. Although the whole-plant freeze test could accurately measure cold hardiness, it was not pmcise, and it required destructive sampling. Results from freeze-induced electrolyte leakage and differential thermal analysis were available in 2 days and 1 hour, respectively. The freeze-induced electrolyte leakage test was a precise, sensitive and objective predictor of changes or differences in tissue cold hardiness. To determine actual cold hardiness, results could be calibrated to the response of the same tissue in the whole-plant freeze test. The speed and objectivity of differentiaJ thermal analysis made this test useful for rapid, general assessment of cold hardiness status, but calibration was difficult, and precision varied.

Comparison of three cold hardiness tests for conifer seedlings

Many functions previously employed in describing growth plhenoimlena can Inow be included in a single new function obtained principally by raising to a power the difference between a weighted elementary functioni and its exponiential raised to another power. Furthermore, new parameters for the simplest two-asymptote, third-degree form of the well-known Pearl-Reed function can be specified so as to locate a point of inflection free from the effects of two additional parameters specifying the manner in which the function approaches its asymptotes. Convenient expressions for derivatives and partial derivatives of all the inew functions and the locationis of points of inflection in terms of the new parameters are given to help interested scientists in preparing short FORTRAN or ALGOL subroutines for use with existiIng computer programs, and in making close initial estimates of parameters so that convergence of iterative solutions will be more likely.

L. R. Grosenbaugh

Papers

Generalization and Reparameterization of Some Sigmoid and Other Nonlinear Functions