Self-thinning Rules at Chinese Fir (Cunninghamia lanceolata) Plantations—Based on a Permanent Density Trial in Southern China

Data selection and methods for fitting coefficients were considered to test the self-thinning law. The Chinese fir (Cunninghamia lanceolata) in even-aged pure stands with 26 years of observation data were applied to fit Reineke's (1933) empirically derived stand density rule (N ∝ –¹.⁶⁰⁵, N = numbers of stems, = mean diameter), Yoda's (1963) self-thinning law based on Euclidian geometry (∝ N–³/², = tree volume), and West, Brown and Enquist's (1997, 1999) (WBE) fractal geometry (∝ –⁸/³). OLS, RMA and SFF algorithms provided observed self-thinning exponents with the seven mortality rate intervals (2%–80%, 5%–80%, 10%–80%, 15%–80%, 20%–80%, 25%–80% and 30%–80%), which were tested against the exponents, and expected by the rules considered. Hope for a consistent allometry law that ignores species-specific morphologic allometric and scale differences faded. Exponents α of N ∝ ᵅ, were significantly different from –1.605 and –2, not expected by Euclidian fractal geometry; exponents β of ∝ Nᵝ varied around Yoda's self-thinning slope –3/2, but was significantly different from –4/3; exponent γ of ∝ ᵞ tended to neither 8/3 nor 3.