### Materials

Nine trees were obtained from the nursery of Utsunomiya University, Japan (36°32’N and 139°54’E). The nine trees were regenerated through coppicing stem after cutting the stems once. The trees were planted at 1 − 2 m intervals. The genetic source was unknown. The stem diameter was measured at 1.3 m above the ground using a diameter tape. After felling the trees, tree height was measured using a tape measure. The mean stem diameter and tree height values were 16.9 cm and 12.2 m, respectively (Table 1) [18]. The number of annual rings at 1.3 m above the ground ranged from 9 to 14 (Table 1), suggesting that the tree age was around 10 years or more [18].

A disc with 2 cm in width was taken at 1.3 m above the ground from each tree for measurements of annual ring width and anatomical characteristics. In addition, logs with 50 cm long were obtained from 0.8 to 1.3 m above the ground for use in bending and compressive tests.

### Measurements

Bark to bark radial strips with the pith (5 cm in a tangential direction and 1 cm in a longitudinal direction) were prepared from the discs. The transverse surface of the radial strip was sanded, and a transverse image of the strip was obtained using an image scanner (GT-9300; Epson, Suwa, Japan) with 800 dpi. Annual ring width was measured from pith to bark in two directions using ImageJ software (National Institute of Health, Bethesda, Maryland, USA). Annual ring width at each cambial age was determined by averaging annual ring width values obtained from two directions in a strip.

Small stick samples (10 [L] × 1 [R] × 1 [T] mm) and small block samples (10 [L] × 10 [R] × 5 [T] mm) were collected from the radial strips at 1 cm intervals from the pith to the cambium. The stick samples were macerated with Schultze’s solution (100 mL of 35% nitric acid containing 6 g of potassium chloride). The macerated samples were placed on a slide glass and mounted with a coverslip and 75% glycerol. The lengths of 50 wood fibers and 30 vessel elements were then measured using a profile projector (V-12B; Nikon, Tokyo, Japan) and a digital caliper (CD-30C; Mitutoyo, Kawasaki, Japan). Transverse sections with 20 μm thickness were prepared from the block samples using a sliding microtome (REM-710; Yamato Kohki, Saitama, Japan). The sections were stained with 1% safranin, dehydrated with graded ethanol, and finally immersed in xylene. The sections were placed on glass slides and mounted using Bioleit (Oken Shoji, Tokyo, Japan) and coverslips. Digital images in each radial position were obtained using a microscope (BX-51; Olympus, Tokyo, Japan) equipped with a digital camera (DS-2210; Sato Shouji Inc., Kawasaki, Japan). Using the cross-sectional images at each radial position, vessel frequency, vessel diameter, wood fiber diameter, and wood fiber wall thickness were determined using ImageJ software. The number of vessels in the digital images was counted, while the vessel frequency was calculated by dividing the number of vessels by the area of each transverse sectional image. The diameters of wood fibers and wood fiber lumina were determined by averaging the major and minor radii, respectively. Each entire wood fiber wall region was regarded as a trapezoid, and the wood fiber wall thickness was calculated using the method described by Yoshinaga et al. [19]. In each radial position, 30 vessels and 50 wood fibers were measured.

Pith-to-bark radial boards with pith (2 cm width and 50 cm thickness) were collected from the logs. After air-drying in a laboratory at 20 ℃ and 65% relative humidity, the boards were planed so that they were 1 cm width. Finally, bending strength specimens (160 [L] × 10 [R] × 10 [T] mm) and compressive strength specimens (20 [L] × 10 [R] × 10 [T] mm) were successively prepared from the pith toward the bark of the boards. The static bending test was conducted using a universal testing machine (MSC-5/200-2; Tokyo Testing Machine, Tokyo, Japan). A load was applied to the center of the specimens on the radial surface with a 140 mm span and 4 mm/min load speed. The load and deflection were recorded using a personal computer. The modulus of elasticity (MOE) and modulus of rupture (MOR) were calculated using the following formulae:

$$mathrm{MOE} left(mathrm{GPa}right)=frac{{Delta Pl}^{3}}{4Delta Yb{h}^{3}}times {10}^{-3}$$

(1)

$$mathrm{MOR, (MPa)} =frac{3Pl}{2bh^2}$$

(2)

where Δ*P* (N) is the difference in the load between 10 and 40% values of the maximum load, *l* (mm) is the length of the span, Δ*Y* (mm) is deflection due to Δ*P*, *b* (mm) and *h* (mm) are the width and height of the specimen, and *P* (N) is the maximum load. After the static bending test, a block (10 [L] × 10 [R] × 10 [T] mm) without any visual defects was prepared from each specimen for measuring the moisture content and air-dry density. A compressive test was conducted using a universal testing machine with a load speed of 0.5 mm/min.

Compressive strength parallel to grain was calculated using the following formula:

$$text{Compressive strength} left(text{MPa}right)=frac{P}{A}$$

(3)

where *P* (N) is the maximum load and *A* (mm^{2}) is the cross-sectional area of the specimen. In the test, the mean ± standard deviation of the moisture content of the bending test specimens and compressive test specimens was 13.3 ± 0.3% and 10.9 ± 0.2%, respectively.

### Statistical analysis

Statistical analysis was conducted using R (Version 4.0.2, [20]). To evaluate radial growth increments and radial variations in wood properties, linear or nonlinear mixed-effects models were developed using the lmer package [21] or nlme package [22].

The estimated stem diameter (without bark) in relation to cambial age was regarded as twice the value of the cumulative annual ring width at 1.3 m above the ground in each tree. To evaluate radial growth increments, radial variations in estimated stem diameters at 1.3 m above the ground in relation to cambial age were determined using nonlinear mixed-effects models based on the Gompertz function (Table 2). In each model, individual tree was the random effect (Table 2). Among the three models, the most parsimonious model was selected based on the Akaike information criterion (AIC) [23]. In addition, the statistical significance of each fixed-effect parameter was evaluated in the selected model using the lmerTest package [21]. Based on the selected model, the CAI and MAI were calculated using the following formulae:

$$mathrm{CAI} left(mathrm{cm}/mathrm{y}right)={a}_{0}{a}_{2}mathrm{exp}left(-{e}^{{a}_{1}-{a}_{2}mathrm{CA}}right)times {e}^{{a}_{1}-{a}_{2}mathrm{CA}}$$

(4)

$$mathrm{MAI} left(mathrm{cm}/mathrm{y}right)=frac{{a}_{0}mathrm{exp}(-{e}^{{a}_{1}-{a}_{2}mathrm{CA}})}{mathrm{CA}}$$

(5)

where *a*_{0}, *a*_{1}, and *a*_{2} are the parameters obtained from the selected radial growth model, and CA is the cambial age. The equation of CAI is the first derivative equation of the radial growth model in Table 2. Based on Eqs. 4 and 5, the cambial ages at which CAI and MAI values were greatest were calculated. In addition, the ratio of the variance component of individual trees and residual to the total variance was calculated [24].

To evaluate radial variations in wood properties, linear or nonlinear mixed-effects models were developed based on linear (Models b-1 and b-2), logarithmic (Models c-1 and c-2), or quadratic functions (Models d-1 to d-3), with cambial age as the explanatory variable, wood properties as the response variable, and individual tree as the random effect (Table 3). Among the developed models, the model with the lowest AIC value was considered the most parsimonious model. In the selected model, the significance of the fixed-effect parameters and the ratios of the variance components of the random-effect parameters to the total variance were calculated [24].

The cambial age at which xylem maturation commenced was determined according to the modified method of Ngadianto et al. [10]. In the present study, the explanatory variable was considered cambial age instead of distance from pith in Ngadianto et al. [10]. Each wood property was estimated at 1-year intervals in the selected model containing only the fixed-effect parameters. The changing ratio of various wood properties at 1-year intervals were calculated as absolute values. An exponential model with a plateau was fitted to the data for changing the ratio of each wood property using the following formula:

$$mathrm{CR}_{1}={a}_{1}{{b}_{1}}^{mathrm{CA}_{1}}+{c}_{1}$$

(6)

where CR_{1} is the changing ratio of each wood property, CA_{1} is the cambial age, and *a*_{1}, *b*_{1}, and *c*_{1} are fixed-effect parameters. *c*_{1} is the plateau value in Eq. (6). An exponential model was then fitted to the data for the changing ratio using the following formula:

$$mathrm{CR}_{2}={a}_{2}{{b}_{2}}^{mathrm{CA}_{2}}$$

(7)

where CR_{2} is the changing ratio of each wood property, CA_{2} is the cambial age, and *a*_{2} and *b*_{2} are fixed-effect parameters. When CR_{2} in Eq. (7) equaled *c*_{1} in Eq. (6), CA_{2} was regarded as the cambial age at which xylem maturation commenced.

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