SELF-THINNING LINE AND B-POINT LINE OF THE YIELD-DENSITY DIAGRAM IN A YOUNG BIRCH STAND

A young birch (Betula ermanii) stand was monitored every year for 10 years from 1982 to 1991 for tree diameter, height, and volume, in Hokkaido, northern Japan. Total tree volume of the stand (Y0) increased with a corresponding decrease in tree number (N0), giving a self-thinning line on a double logarithmic scale expressed as Y0 = HN0-c. The reciprocal equation, 1/Y = B/N+A, was applied to the relationship between cumulative volume (Y) and cumulative number (N) from the largest tree in the stand each year. B-points (N(B), Y(B); N(B) = B/A, Y(B) = 1/2A) of each Y-N curve also plotted on a double logarithmic scale gave a line parallel with the self-thinning line. Kendall's rank correlations of individual tree orders between successive two year periods usually lay above 0.936, indicating that the reversion of tree order rarely occurred. Increments in tree diameter during the 2 years immediately before the trees' death were usually very small, while increments for living trees were usually positive. Using the Y-N curves and the B-point curve, and the two conditions (1) that a tree's order does not change with time and (2) that mortality occurs in the smallest trees whose growth rate becomes zero, a relation between tree volume and number in a stand was derived as a line parallel to the B-point line and was demonstrated to be equivalent to the self-thinning line.