Growth analysis of the self-thinning stands of Pinus densiflora Sieb. et Zucc

The competition-density (C-D) effect for self-thinning Pinus densiflora Sieb. et Zucc. stands was analyzed. The relationship between biological time and physical time t followed a hyperbolic curve. The coefficients A_t and B included in the reciprocal equation of the C-D effect in self-thinning stands (i.e. 1/w=A_t+B), where w and , respectively, represent the mean stem volume and the realized stand density, were calculated at each time. With increasing , the coefficient A_t increased abruptly up to a maximum value, and then decreased gradually to a constant level, whereas the coefficient B decreased exponentially. The relationship between the realized stand density and the initial stand density _i was confirmed to follow the equation: 1/=1/_i+, where 1/ represents the asymptotic stand density at a given time. The - relationship was represented by the equation: =p(e–1), where p and are constants. The density in the self-thinning stands tended to converge to the same density level after a sufficient lapse of time, irrespective of the difference in initial stand density. The time-trajectory of the mean stem volume and asymptotic stand density on logarithmic coordinates moved gradually toward the self-thinning line with a slope of approximately –3/2, whereas the time-trajectory of the mean stem volume and full stand density moved initially along the self-thinning line with a slope of approximately –3/2, and then changed to move along the maximum yield line with a slope of –1.0.