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Official Journal of the Japan Wood Research Society

Table 2 Developed models for stem diameter in relation to cambial age and obtained AIC values in each model

From: Relationship between the xylem maturation process based on radial variations in wood properties and radial growth increments of stems in a fast-growing tree species, Liriodendron tulipifera

Model

Equation

Random effects

AIC

a-1

\(\mathrm{D}_{ij}=\left({a}_{0}+{Tree}_{0j}\right)\mathrm{exp}\left(-{e}^{{a}_{1}-{a}_{2}\mathrm{CA}_{ij}}\right)+{e}_{ij}\)

Asymptotic value

236.15

a-2

\(\mathrm{D}_{ij}={a}_{0}\mathrm{exp}\left(-{e}^{{a}_{1}+{Tree}_{1j}-{a}_{2}\mathrm{CA}_{ij}}\right)+{e}_{ij}\)

Start position of the curve

 − 

a-3

\(\mathrm{D}_{ij}={a}_{0}\mathrm{exp}\left(-{e}^{{a}_{1}-\left({a}_{2}+{Tree}_{2j}\right)\mathrm{CA}_{ij}}\right)+{e}_{ij}\)

Slope

293.66

  1. Dij, estimated stem diameter at 1.3 m above the ground at the ith cambial age of the jth individual tree; CAij, ith cambial age of the jth individual tree; a0, a1, and a2, fixed-effect parameters; Tree0j, Tree1j, and Tree2j, random-effect parameters at the jth individual tree level; eij, residuals; − , the model failed to converge. The bold value represents the minimum AIC value