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From equation (4.1), the maximum value of Y was considered to be TA.

The intersection point of the two lines considered as TA is calculated as follows:

Sampling height and stand density

Estimation of the juvenile wood proportion

where RW_{h} is the ring width at cambial age h.

Then, the JW proportion in volume was calculated from equations (4.10) and (4.11) in equation (4.12).

(4.12)

The profiles of RW, RD and MFA at 2.4 m sampling height from pith to bark are presented in Figure 4-3. The JW boundary is not defined as clearly as in Figure 4-2. As mentioned above, although RW presents a maximum at ring 4 which suggests a transition between two types of wood, it does not point out the JW boundary. According to the MFA profile, a first transition at about ring 10 and a second at about ring 25 are consistent with the presence of three zones in wood as described previously (Clark and Saucier 1989). Finally, the RD profile shows a minimum at about ring 10, also revealing a transition between two zones, but this can not be considered as the JW to MW transition.

According to Figures 4-2 and 4-3, TA was estimated to occur at about ring 4 to 5 with RW, ring 10 with RD, ring 10-25 with MFA, ring 20 with RA and ring 25 with MD. As a first consequence, the results suggest that RD and RW are not appropriate traits to determine the transition age. As the TA is expected to occur in the 11-37 years range in Douglas fir (Abdel-Gadir and Krahmer 1993a) and 11-21 years in black spruce (Yang and Hazenberg 1994), RA and MD were selected as the best traits to determine TA and MFA was used as a comparison trait. As a second remark, Figure 4-2 shows that MD leads to a later TA in comparison to RA. Nevertheless, their radial patterns are similar (Figure 4-4).

The efficiency of RA to determine the JW boundary should be emphasized. Indeed, both RW and RA refer to tree growth (Clark and Saucier 1989). However, RA provides information about the radial and tangential growth of the annual rings, and about the increasing tree diameter. From this point of view, ring area can be considered as a better indicator of growth rate than RW.

**Figure 4-3. Average ring width (RW), ring density (RD) and microfibril angle (MFA) profiles at 2.4 m sampling height.**

*Variation of transition age with traits and method*

The transition age for each tree was calculated from RA and MD, using polynomial and segmented linear regression as described above. These two methods applied to the two traits, RA and MD, led to four different results for TA at the 2.4 m sampling height (Table 4-2). The difference between the methods was significant while the difference between stand density was not (Table 4-1). The results also show that TA determined from MD is higher than TA determined from RA as it was already noticed in the preliminary visual analysis. Moreover, the methods of linear regression and polynomial regression led to two significantly different results. The segmented linear regression method, as shown in Table 4-2, results in an earlier TA when compared to the polynomial regression. The segmented linear regression method was selected because it gave results closer to the results found with MFA (Table 4-2).

The analysis confirms that the determination of TA is dependent on the trait considered. Although RA and MD have similar radial patterns, the TA value found by the two traits is significantly different.

**Table 4-1. ANOVA of transition age at a sampling height of 2.4 m. Comparison of four approaches (MOD) (2 traits x 2 methods) and three stand density groups (SD).**

**Table 4-2. Average transition age estimated by third-order polynomial, segmented linear regressions and derivative function, for three stand density groups at 2.4 m sampling height. Ring area (RA), maximum ring density (MD) and microfibril angle (MFA) profiles are used. Results with different letters are statistically different (Duncan test, 0.05 probability level).**

Variation of TA with sampling height

**Table 4-3. ANOVA of transition age at three stand densities (SD) and at three sampling heights (SH).**

Variation of TA with stand density

**Table 4-4. Average transition age at three sampling heights and in three stand density groups. Results with different letters are significantly different at 0.05 probability level (Duncan test, read in column). **

Estimation of the juvenile wood proportion

The results of this study lead to the following conclusions:

No significant differences in transition age were found between the three stand density groups.