THEORETICAL GROWTH EQUATIONS AND THEIR APPLICATIONS IN FORESTRY

The objective of the present work is twofold, i.e., one of straightening out the cluttering jam of growth equations in search of the most potential one for the growth of trees especially in stem radius, and of applying the theory of growth equation to other important issues of mensuration and forestry to reorganize them into a more rationally-related and interwoven system. In pursuit of the first objective, numerous growth equations were reviewd in Chapter Ⅱ and classified into four categories, i.e., the empiricals, the quasi-theoreticals, the particular theoreticals and the general theoreticals. In doing so discussion was made as to the superiorities of the theoretical equations over the empirical ones, and of the particular theoreticals over the general ones. However, it was also found that as of today there is no particular theoretical equation expressing the growth of individual trees, and thus it was concluded that the available best for describing the growth of individual trees was the general theoretical equation. In Chapter III, the characteristics of the three general theoretical equations thus chosen, i.e., the Mitscherlich, the logistic and the Gompertz were discussed from an a priori theoretical point of view. In further pursuit of the most prospective growth equations for trees, the three general theoreticals were applied to the radial stem growth of 84 white spruce trees in Chapter III. It turned out that although all the equations did not work in application as satisfactorily as expected from the theory, the Mitscherlich revealed the least theoretical discrepancy, while the logistic did the most. The best graphical agreement with the observed growth was attained by the Gompertz, followed by the Mitscherlich, then by the logistic. The easiest to fit was the Mitscherlich, followed by the logistic, then by the Gompertz. A similar analysis as in Chapter Ⅲ was conducted with 349 individual growth records of jack pine in Chapter Ⅳ. All the equations worked better with jack pine than with white spruce in every criterion employed. The most remarkable improvement was achieved by the Mitscherlich. It revealed the least theoretical discrepancy, while the logistic did the most as with white spruce. The best graphical agreement with the observed growth was achieved by the Mitscherlich followed by the Gompertz, then by the logistic. The easiest to fit was the Mitscherlich followed by the Gompertz, then by the logistic. As an overall conclusion of Chapters Ⅲ and Ⅳ, at the present state of knowledge the best growth equation to describe the growth of trees in stem radius would be the Mitscherlich. \n The last two chapters of the present work is devoted to the second objective, i.e., the application of the theory of the growth equation to the other important subjects of mensuration, i.e., the stem taper curve and the height-diameter curve. In Chapter V assuming that the growth of individual trees in stem diameter and height follows the Mitscherlich equation, a theoretical stem taper curve was derived mathematically. Subsequently it was compared with 50 observed stem taper curves and its theoretical compatibility was discussed. The proposed stem taper curves and its theoretical compatibility was discussed. The proposed stem taper curve was also compared with other existing empirical stem taper curves in terms of the goodness of fit to 50 observed taper curves. It turned out that the ten equations compared were separated into five groups significantly differing from each other, of which the proposed equation fell into the second best group. \n In Chapter Ⅵ again assuming that the growth of individual trees in stem diameter and height follows the Mitscherlich equation, a height-diameter curve for all-aged stands was derived. Then based on a similar but slightly different assumption, another height-diameter curve for even-aged stand was derived. Both equations are identical in their mathematical appearance but are different in wha