Growth analysis of the competition–density effect in non-self-thinning Populus deltoides and Populus × euramericana plantations

The competition–density (C–D) effect for non-self-thinning Populus deltoides and Populus × euramericana plantations from 3 to 9 years was analyzed using the reciprocal equation of the C–D effect. The C–D effect was well described by the reciprocal equation, and with the progress of time the C–D curve, on logarithmic coordinates, of the P. × euramericana plantations shifted upward faster than that of the P. deltoides plantations. With increasing physical time t, the biological time τ, i.e. the integral from zero to t of the coefficient of growth λ(t) in the general logistic curve with respect to t, increased rapidly during early growth stages and the increases in τ gradually became slow during later growth stages. This trend was more evident in the P. deltoides plantations than in the P. × euramericana plantations. The coefficients A and B included in the reciprocal equation were calculated at each growth stage. With increasing τ, the coefficient A, the reciprocal of which means the asymptote of yield (=wρ) at a given growth stage, increased abruptly to a maximum value and then tended to decrease gradually to a constant level. On the other hand, the coefficient B, the reciprocal of which means the asymptote of mean stem volume at a given growth stage, decreased exponentially and tended to be close to zero with increasing τ. The λ(t) decreased with increasing stand age, whereas the final yield Y(t) defined as W(t) ρ, where W(t) is the asymptote of w in the general logistic growth curve, increased gradually with increasing stand age. The differences in coefficients A, B, and λ(t) between the two species were reported.