Understanding changes in black (Picea mariana) and white spruce (Picea glauca) foliage biomass and leaf area characteristics

Abstract

Key message

Growth conditions related to inter-tree competition greatly influence black and white spruce foliage biomass and projected leaf area characteristics.

Abstract

Foliage characteristics such as biomass and area are important among other reasons because they can be related to tree growth. Despite their economic and ecologic importance, equations to characterize foliage biomass and projected area of black (Picea mariana (Miller) BSP) and white (Picea glauca (Moench) Voss) spruces are sparse. Total foliage biomass and projected leaf area, foliage biomass and leaf area density, and relative vertical distribution of black and white spruces foliage biomass and leaf area were modelled with linear and nonlinear mixed effect models. A total of 65 white spruces and 57 black spruces were destructively sampled at four different locations in Alberta, Québec, and Ontario, Canada. Our results show that for each species, total tree foliage biomass and projected leaf area is proportional to stem diameter, total height, and crown length. The addition of crown length in the equations improved the precision of the predictions of total foliage biomass for both species and diminishes greatly the site level random effect. An increase in DBH for black spruce and in the DBH to total height ratio for white spruce skewed the relative vertical foliage biomass distribution toward the base of the living crown. According to our results, growth conditions or tree development stage influence both foliage biomass and leaf area characteristics of black and white spruces. Our results emphasize the importance of inter-tree competition on foliage biomass characteristics.

Appendix

Branch foliage biomass estimation

Foliage biomass at the branch level was predicted with a species-specific nonlinear mixed-effects equation for black spruce (Eq. A1) and white spruce (Eq. A2). The random effects at the site-, plot-, and tree-level were added to the predictions.

$$\begin{gathered} {\text{Wfb}}_{l(ijk)} = 0.3725{\text{Gb}}_{l(ijk)}^{1.095} + 0.59{\text{Cd}}_{l(ijk)} - \hfill \\ (0.3056 + b_{i} + b_{j(i)} + b_{k(ij)} ){\text{Gb}}_{l(ijk)} \times {\text{Cd}}_{l(ijk)} + \varepsilon_{l(ijk)} \hfill \\ \end{gathered}$$

(A1)

$$\begin{gathered} {\text{Wfb}}_{l(ijk)} = 0.3962{\text{Gb}}_{l(ijk)}^{1.037} + 11.62{\text{Cd}}_{l(ijk)} - \hfill \\ (0.308 + b_{i} + b_{j(i)} + b_{k(ij)} ){\text{Gb}}_{l(ijk)} \times {\text{Cd}}_{l(ijk)} + \varepsilon_{l(ijk)} \hfill \\ \end{gathered}$$

(A2)

where Gb is branch basal area (cm²); Cd is the relative crown depth that has a value of 0 at the top of the tree and 1 at crown base; the b are random parameters; ijkl are the subscripts for the lth branch in tree k in plot j in site i; and ε represents the random error.

White spruce branch-specific leaf area estimation

Specific leaf area at the branch level for white spruce was predicted with a linear mixed-effects equation (Eq. A3). The random effects at the plot- and tree-level were added to the predictions.

$${\text{Sla}}_{l(ij)} = (b_{j} + b_{k(j)} + 27.83){\text{Cd}}_{l(jk)} + \varepsilon_{l(jk)}$$

(A3)

where Sla is the estimated specific leaf area (cm²/g); Cd is the relative crown depth that has a value of 0 at the top of the tree and 1 at crown base; the b are random parameters; jkl are the subscripts for the lth branch in tree k in plot j; and ε represents the random error.

Crown radii estimation

To estimate crown radius, the length of all sample tree living branches (Bl) was estimated with a nonlinear mixed model. Models for each species were fitted separately and random effects at the site-, and plot- and tree-level were added to the predictions to obtain tree-specific branch length. Equations A4 and A5 show the branch length model for black and white spruce, respectively, as reproduced from Power et al. (2012).

$${\text{Bl}} = 8.9515{\text{Bd}}^{{(0.6768 + b_{i} + b_{j(i)} + b_{k(ij)} )}} \times {\text{Cd}}^{0.4605} \times {\text{SI}}^{0.3401} + \varepsilon_{l(ijk)}$$

(A4)

$${\text{Bl}} = 17.5727{\text{Bd}}^{{(0.7561 + b_{i} + b_{j(i)} + b_{k(ij)} )}} \times {\text{Cd}}^{0.3068} + \varepsilon_{l(ijk)}$$

(A5)

where Bl is the branch length (cm); Bd is branch basal diameter (cm); Cd is relative crown depth, which has a value of 0 at the top of the tree and 1 at crown base; SI is the site index (m); ijkl are the subscripts for the lth branch in tree k in plot j in site i; b are random effects parameters; and ε is the random error.

Following branch length estimation, we calculated the horizontal distance (Hl) between the tree bole and the tip of the living branch using the estimated Bl and the measured branch angle (θ) (Eq. A6).

$${\text{Hl}} = {\text{Bl}} \times \sin \,\theta$$

(A6)

For each sample tree, crown radius was calculated as the average of the four longest estimated horizontal branch lengths within each crown section. Height of each crown radius was defined as the height of the tip of the largest branch used to calculate the crown radius value.