Relationship between Maximum Stem Volume and Density during a Course of Self-thinning in a Cryptomeria japonica Plantation

Abstract

Cryptomeria japonica plantation was monitored every year during 15 years from 1983 to 1997 for stem diameter and volume. The reciprocal equation, 1/Y = A + B/N, was applied to the relationship between cumulative volume Y and cumulative number N from the largest tree in the stand each year. The parameters A and B, which means respectively the reciprocal of an asymptotic value of total stand stem volume and the reciprocal of the maximum stem volume, are related by a power function. The power functional relationship between A and B derived a linear relationship of B-points ( <TEX>$N_{B}$</TEX>, <TEX>$V_{B}$</TEX>; <TEX>$N_{B}$</TEX> = B/A, <TEX>$Y_{B}$</TEX> = 1/2A) of each Y-N curve on log-log coordinates. The gradient of B-point line was so steep that the Y-N curve moved parallel upward year by year. The time trajectory of mean stem volume (W) and density (<TEX>$\rho$</TEX>) provided evidence in favor of the 3/2 power law of self-thinning, because the gradient of W - <TEX>$\rho$</TEX> trajectory on log-log coordinates approximated to -3/2 at the final stage of stand development. On the basis of the results of Y-N curves and W - <TEX>$\rho$</TEX> trajectory, the time trajectory of maximum stem volume <TEX>$W_{max obs}$</TEX> and <TEX>$\rho$</TEX> was derived theoretically. The gradient of <TEX>$W_{max obs}$</TEX> - <TEX>$\rho$</TEX> trajectory on log-log coordinates is calculated to be -0.6105 at the final stage. The gradient of <TEX>$W_{max obs}$</TEX> - <TEX>$\rho$</TEX> trajectory was steeper than that of W - <TEX>$\rho$</TEX> trajectory at the early stage, while the former is gentler than the latter at the later stage.stage.e.age.e.