Effects of additive or multiplicative error structures on self-thinning lines for larch plantations in northeast China

Accurately modeling the self-thinning line is crucial for effective forest management, yet the debate continues on whether to use nonlinear regression with additive error on the arithmetic scale or linear regression with multiplicative error on the log-transformed scale. This study examines larch plantations in Northeast China as a case study to evaluate these error structures, incorporating the effects of relative density (RD) and quantile regression (QR) quantiles. Using the optimal error structure, the potential influences of the site index (SI) and the Martonne aridity index (MA) on the self-thinning lines were also analyzed. Results revealed significant differences in slope and intercept estimates between the two error structures, with both estimates positively correlated QR quantiles and RD values. Likelihood analysis identified the multiplicate error structure was superior, underscoring the necessity of logarithmic transformation when modelling the self-thinning lines. The MA index exhibited a significantly greater impact on self-thinning lines compared to SI, increasing the maximum stand density index (SDImax) by approximately 7.37 % under RCP2.6, 7.12 % under RCP4.5, and 9.09 % under RCP8.5. This translates to an additional approximately 25.21–31.08 tCO₂ per hectare sequestrated in living biomass when QMD approaches the reference level (25.4 cm).