ANALYSIS OF GROWTH EQUATIONS

Growth of plants results from two opposing factors: the intrinsic tendency toward unlimited increase (biotic potential) and restraints imposed by environmental resistance and aging. The expansion tendency prevails in the beginning of a tree's life, while growth decline becomes prominent toward the end. The existing growth equations can be transformed (by differentiation, decomposition into the division components, and taking logarithms) so that the components that 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.