# Variation in Wood Quality in White Spruce (Picea Glauca (Moench) Voss). Part I. Defining the Juvenile–Mature Wood Transition Based on Tracheid Length

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## Abstract

**:**

## 1. Introduction

Acronym | Description |
---|---|

BA | Basal area |

CA | Cambial age |

JW | Juvenile wood |

JWP | Juvenile wood proportion |

JWV | Juvenile wood volume |

JWR (JWR_{h}) | Juvenile wood radius (at a given height h) |

M_Q_L | Maximum-quadratic-linear |

MW | Mature wood |

RMSE | Root-mean-squared error |

TA | Transition age |

TL | Average ring tracheid length |

WQA | Wood quality attributes |

Main Transition Method | Transition Age Value (Years) | Species | Source |
---|---|---|---|

Piecewise | 18 | Lodgepole pine | Mansfield, et al. [34] |

Piecewise | 14 | Jack pine | Fujiwaraand Yang [35] |

Piecewise | 20 | Balsam fir | Fujiwaraand Yang [35] |

Piecewise | 12–19 | White spruce | Fujiwaraand Yang [35], Yang [36] |

Piecewise | 11–21 | Black spruce | Fujiwaraand Yang [35], Yang [36], Yangand Hazenberg [37] |

Piecewise | 10–18 | Loblolly pine | Bendtsenand Senft [4], Loo, Tauerand McNew [10] |

Visual | 16–18 | Scots pine | Fries, Ericssonand Morling [33] |

Visual | 18–20 | Norway spruce | Kučera [15] |

Visual | 15 | Douglas-fir | Ericksonand Harrison [38] |

## 2. Material and Methods

#### 2.1. Sample Collection

^{2}/ha, respectively. For each target BA, three thinning operations had been conducted, in 1962, 1972, and 1982. In 2002, the BA in the control plot was 44 m

^{2}/ha. Eight trees (two dominant, four codominant, and two suppressed) were randomly selected in the heavy and light thinning intensities. Seven trees (two dominant, four codominant, and one suppressed) were randomly selected in the medium thinning intensity, and seven trees (two dominant, three codominant, and two suppressed) were randomly selected in the control plot, for a total of 30 trees. Sampled trees were limited to those with undamaged crowns [39]. Trees were felled in July 2008 and pruned once on the ground. Discs were collected at 1.3 m (breast height, BH) from all sampled trees. A subset of five trees (one dominant, three codominant, and one suppressed) felled from the whole plantation was also sampled at 1.3 m, 4.3 m, 7.3 m, 10.3 m, and 13.3 m for longitudinal description of TL and TA estimation. The limited size of this longitudinal sample was due to TL measurement issues. Although this sampling size is not representative of the trend for the entire tree species, we believe that it provides a good idea of the variations that can occur in measured and estimated properties. The mean tree height of the sampled trees was 21.1 m (15.0–32.9 m), and diameter at breast height below the bark, measured with an electronic digital caliper, was 26.8 cm (15.0–39.4 cm). Tree characteristics are presented in Table 3.

Tree ID | Tree Age (Years) | Tree Height (m) | Clear Bole Length (m) | Crown Length (m) | Diameter at Breast Height (cm) |
---|---|---|---|---|---|

Stand averages | |||||

All trees (mean) | 72 | 21.1 | 14 | 7 | 26.8 |

Subset of five trees sampled longitudinally | |||||

1 | 72 | 25.1 | 16.2 | 8.9 | 39.4 |

2 | 72 | 23 | 16.3 | 6.7 | 28.3 |

3 | 72 | 20 | 12.1 | 7.9 | 23.4 |

4 | 72 | 19.3 | 13.5 | 5.8 | 21.5 |

5 | 72 | 21.8 | 15.8 | 6 | 23.2 |

#### 2.2. Sample Preparation and Wood Quality Attributes

_{i}L

_{i}

^{3}/Σn

_{i}L

_{i}

^{2}(where i = 1, 2, 3 …n categories; n = fiber count in the (ith) category; L = contour length). Using this method, the estimated tracheid lengths were similar to true tracheid length measurements, that is, were controlled for the bias caused by the large number of fines generated during preparation [33]. Average ring tracheid length (TL) was computed by weighting the tracheid length for each wood zone with the relative ring width.

#### 2.3. Transition Age Modeling

Model | Juvenile Wood | Mature Wood | Transition Age |
---|---|---|---|

Piecewise | TL = a_{1} + b_{1}·
x + ε_{i} | TL = a_{2} + b_{2}·
x + ε_{i} | TL = a_{1} + TA·(b_{1} − b_{2}) + b_{2}·
x + ε_{i} |

M_Q_L | TL = a_{1} + b_{1}·
x + c·x^{2} + ε_{i} | TL = a_{2} + b_{2}·
x + ε_{i} | TA = −b/2c + ε
_{i} |

MIXED | TL = a + b·
x + c·x^{2} + d·x^{3} + ε_{i} | TA = (−b ± (b^{2} − 4a·c)^{−0.5})/2a + ε
_{i} |

#### 2.3.1. Segmented Models

^{®}(SAS Institute Inc., Cary, NC, USA) [44].

#### 2.3.2. Third-Order Polynomial Model

^{®}was used to fit the third model, it was called the MIXED model. We included the repeated structure age in this model to improve the inference. Indeed, not accounting for the correlation between measurements results in an underestimation of the variance [45], resulting, among other, in higher type I error rates (incorrectly rejecting a true null hypothesis) for tests of intergroup differences. For the MIXED model, TA was determined by setting the derivative of the third-degree function equal to zero and solving for age. For third-degree polynomials, two solutions were obtained, but only one was of biological significance and hence retained [13].

#### 2.4. Comparison between Models

^{®}. Model fit was measured using the root-mean-squared error (RMSE). Paired t-tests with Bonferroni adjustment to account for multiple testing [44] were used to compare estimates of TA, JW radius (JWR), JW proportion (JWP), and TL at the time of transition for each tree between paired models.

#### 2.5. Juvenile Wood Proportion, Volume, and Shape

^{2}), TR: whole tree radius in 2007 (mm), TAR: whole tree basal area (mm

^{2}), and JWP: juvenile wood proportion in tree basal area (%).

_{h}) (Equation (6)) and tree basal area (TAR

_{h}) (Equation (7)) were computed at the five-abovementioned heights. JW volume (JWV) (Equation (8)) and tree volume (TV) (Equation (9)) were computed from the juvenile wood basal area and tree basal area. Because it obtains less bias in the volume determination and does not depend on the bole shape [47], Newton’s formula was preferred to others for section scaling. The first Section S1 included 1.3 m (base), 4.3 m (half height), and 7.3 m (top) and the second Section S2 included 7.3 m (base), 10.3 m (half height), and 13.3 m (top). The truncated cone formula (Equation (10)) was used for both juvenile wood volume and whole tree volume whenever it was impossible to compute Newton’s formula for section scaling. JWP in volume (JWPV) (Equation (11)) was computed from the results of Equations (8)–(10). JW shape was determined from the JWR and whole tree radius in 2007 for the abovementioned heights using Matlab

^{®}(MathWorks Inc., Natick, MA, USA) [48].

_{h}: juvenile wood basal area at height h (mm

^{2}); JWR

_{h}: juvenile wood radius at height h (mm), TAR

_{h}: tree basal area at height h (mm

^{2}), TR

_{h}: whole tree radius in 2007 at height h (mm), JWV: JW volume (m

^{3}), TV: tree volume (m

^{3}), V: JWV (m

^{3}) or TV (m

^{3}) according to the tree zone considered and computed with the truncated cone formula, L: length of the sampled tree section (m), and JWPV: JWP in volume (%) computed with Newton’s or the truncated cone formula.

## 3. Results

#### 3.1. Tracheid Length Radial and Longitudinal Variation

**Figure 1.**Radial and longitudinal variations in tracheid length (TL): (

**a**) radial variation in tracheid length at breast height (1.3 m); (

**b**) radial variation in tracheid length from 1.3 to 13.3 m; (

**c**) longitudinal variation in average (cambial age 3–30) tracheid length; and (

**d**) longitudinal variation in juvenile (cambial age 3) and mature (cambial age 30) tracheid length. Bars indicate standard errors.

#### 3.2. Transition Age, Juvenile Wood Width, Juvenile Wood Proportion, and Tracheid Length Estimates at Breast Height

**Figure 2.**Mean and standard deviation of the estimates for the piecewise, maximum-quadratic-linear (M_Q_L), and MIXED model at breast height: (

**a**) transition age (TA); (

**b**) juvenile wood radius (JWR); (

**c**) juvenile wood proportion (JWP); and (

**d**) tracheid length (TL) at the time of transition.

**Figure 3.**Graphical representation of the average transition ages determined with the piecewise, maximum-quadratic-linear (M_Q_L), and MIXED model, and average tracheid length at breast height.

**Table 5.**Mean, standard deviation (SD), and range for transition age (TA, years), tracheid length at the time of transition (TL, mm), juvenile wood radius (JWR, mm), and juvenile wood proportion (JWP, %) estimated using the three transition age models at breast height (30 trees) with root-mean-squared error (RMSE) as a measure of goodness of fit.

Model | TA | TL | JWR | JWP | |||||
---|---|---|---|---|---|---|---|---|---|

Mean (± SD) | Range (min–max) | RMSE | Mean (± SD) | Range (min–max) | Mean (± SD) | Range (min–max) | Mean (± SD) | Range (min–max) | |

Piecewise | 11 ± 2 | 6–17 | 0.1548 | 2.6 ± 0.2 | 2.1–2.9 | 44.1 ± 11.8 | 24.1–75.3 | 15.3 ± 9.3 | 3.5–52.5 |

M_Q_L | 22 ± 8 | 9–40 | 0.1433 | 3.1 ± 0.3 | 2.4–3.6 | 70.4 ± 25.6 | 32.0–149.2 | 37.9 ± 19.9 | 6.1–86.3 |

MIXED | 27 ± 7 | 15–41 | 0.1127 | 3.3 ± 0.2 | 2.8–3.6 | 82.4 ± 25.9 | 41.8–154.5 | 47.5 ± 14.4 | 22.0–84.7 |

**Table 6.**Average and standard error (SE) for differences at breast height (30 trees) in transition age, juvenile wood proportion, and tracheid length at the time of transition between each of the three-paired models. Estimates for each tree were compared across paired models using paired t-tests with Bonferroni adjustment (p < 0.05/30 = 0.0016).

Model Pair | DF | Transition Age (Years) | Juvenile Wood Proportion (%) | Tracheid Length (mm) | |||
---|---|---|---|---|---|---|---|

Mean (± SE) | t-Value (p-Value) | Mean (± SE) | t-Value (p-Value) | Mean (± SE) | t-Value (p-Value) | ||

MIXED vs. Piecewise | 28 | 16.6 (1.09) | 15.2 (<0.0001) | 32.9 (1.98) | 16.6 (<0.0001) | 0.69 (0.03) | 21.8 (<0.0001) |

M_Q_L vs. Piecewise | 27 | 11.1 (1.44) | 7.8 (<0.0001) | 22.8 (3.12) | 7.3 (<0.0001) | 0.49 (0.05) | 9.9 (<0.0001) |

MIXED vs. M_Q_L | 28 | 5.4 (1.37) | 3.9 (0.0005) | 9.7 (2.80) | 3.5 (0.0018) | 0.19 (0.05) | 3.9 (0.0006) |

#### 3.3. Juvenile Wood Volume, Proportion, and Shape

**Figure 4.**Longitudinal patterns of variation in transition age (years) with tree height (m) using the piecewise, maximum-quadratic-linear (M_Q_L), and MIXED models. Bars indicate standard errors.

**Figure 5.**Graphical representation of juvenile wood (interior dark cone) and mature wood (exterior grey mesh) with transition age determined using piecewise, maximum-quadratic-linear (M_Q_L), and MIXED models.

**Table 7.**Tree volume, juvenile wood volume, and juvenile wood proportion from 1.3 to 13.3 m obtained from five trees using the piecewise, maximum-quadratic-linear (M_Q_L), and MIXED models.

Tree ID | Tree Volume (m^{3}) | Juvenile Wood Volume (m^{3}) | Juvenile Wood Proportion (%) | ||||
---|---|---|---|---|---|---|---|

Piecewise | M_Q_L | MIXED | Piecewise | M_Q_L | MIXED | ||

1 | 0.86 | 0.07 | 0.25 | 0.44 | 7.7 | 28.7 | 50.8 |

2 | 0.35 | 0.04 | 0.07 | 0.17 | 11.7 | 19.8 | 47.7 |

3 | 0.32 | 0.04 | 0.14 | 0.17 | 13.2 | 43.7 | 52.5 |

4 | 0.21 | 0.06 | 0.14 | 0.12 | 26.8 | 67.4 | 58.9 |

5 | 0.20 | 0.11 | 0.15 | 0.15 | 53.2 | 71.4 | 72.7 |

## 4. Discussion

#### 4.1. Tracheid Length Radial and Longitudinal Variation

#### 4.2. Transition Age, Juvenile Wood Proportion, and Tracheid Length at the Time of Transition at Breast Height

#### 4.3. Juvenile Wood Volume, Proportion, and Shape

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Mvolo, C.S.; Koubaa, A.; Beaulieu, J.; Cloutier, A.; Mazerolle, M.J.
Variation in Wood Quality in White Spruce (*Picea Glauca* (Moench) Voss). Part I. Defining the Juvenile–Mature Wood Transition Based on Tracheid Length. *Forests* **2015**, *6*, 183-202.
https://doi.org/10.3390/f6010183

**AMA Style**

Mvolo CS, Koubaa A, Beaulieu J, Cloutier A, Mazerolle MJ.
Variation in Wood Quality in White Spruce (*Picea Glauca* (Moench) Voss). Part I. Defining the Juvenile–Mature Wood Transition Based on Tracheid Length. *Forests*. 2015; 6(1):183-202.
https://doi.org/10.3390/f6010183

**Chicago/Turabian Style**

Mvolo, Cyriac Serge, Ahmed Koubaa, Jean Beaulieu, Alain Cloutier, and Marc J. Mazerolle.
2015. "Variation in Wood Quality in White Spruce (*Picea Glauca* (Moench) Voss). Part I. Defining the Juvenile–Mature Wood Transition Based on Tracheid Length" *Forests* 6, no. 1: 183-202.
https://doi.org/10.3390/f6010183