Understanding Effects of Competition and Shade Tolerance on Carbon Allocation with a Carbon Balance Model

Abstract

A carbon-balance model based on mechanistic and allometric relationships (CroBas) was used to assess the effects of competition in C allocation in jack pine (Pinus banksiana Lamb.), a shade-intolerant species, and black spruce (Picea mariana (Mill.) B.S.P.), a moderately shade-tolerant species. For both species, model efficiencies ranged from 36 to 99%. The average model bias was lower than 11% and 18% for jack pine and black spruce, respectively. For both jack pine and black spruce, the total tree C increased over the years, with greater increases noted for decreasing competition. When considering a C compartment as a ratio of the total tree C, decreasing competition resulted for both species in decreasing stem C and increasing C in branches and foliage. When considering the amount of C in a given compartment, for jack pine, decreasing competition led to greater C stem, branches, foliage, and roots, whereas, for black spruce, it also increased its stem C but lately shifted at about 20 years, following thinning; thus, the changing C allocation over time results from both “passive plasticity”, reflecting environmentally induced variations in growth, and “ontogenetic plasticity”, referring to variations in the ontogenetic trajectory of a trait. Overall, the C allocation to stem and foliage relative to the total tree C generally decreased as competition decreased, supporting the optimal partitioning theory. These C-allocation patterns were related to the species’ shade tolerance and illustrated how jack pine and black spruce maximize their competitive fitness.

1. Introduction

Carbon (C) allocation strategies allow plants to maximize their fitness. According to the optimal partitioning theory, biomass allocation increases towards a given plant organ if that organ is responsible for acquiring the most limiting resource [1]. This theory is based on the paradigm that evolutionary selection is likely to favor plants which maximize their net growth and energy capture through structural and/or physiological adaptations [2]. As a consequence, the compartment involved in the uptake of the limiting resource grows more relative to other organs, improving the uptake of the limiting resource [3]. For instance, empirical evidence has suggested that the C allocation to the root and foliage respectively increased in response to belowground competition and low light conditions [4], leading to a shift in tree allometry [5].

Although the importance of C allocation is well established and the mechanisms are fairly well theorized, empirical evidence depicting the mechanisms of C allocation is scarce [6], and the physiological processes governing medium- and long-term allocation changes are still poorly understood [7]. Consequently, there is little consensus on how to summarize allocation in a modeling structure [8]. A plethora of allocation models based on different assumptions have thus been proposed, resulting in differing predictions. Generally, C allocation models are based on empirical observations, and process-based models are based on our understanding of the plant physiological processes, which can be used to explain whole-plant behavior [8]. Empirical C allocation models (1) trace the carbon from the source (e.g., photosynthetically active leaves) to sinks (e.g., leaves, branches, stem, and roots) or (2) use differences in compartment growth rates [9,10]. In the latter case, the physiological rules underlying C partitioning are unknown, and the allocation coefficients are only valid for a limited range of environmental conditions [3], reducing the possibility to extend the use [11] of such models to other environmental conditions [12]. Mechanistic or process-based models account for translocation mechanisms by maximization of a fitness proxy [8] and have the advantage of being valid for a wide range of conditions different from those used for calibration. Referred to also as functional–structural models, they have received considerable attention [11,13,14]. In the current study, CroBas, a process-based carbon balance model initially developed for Scots pine [13], was adapted to jack pine (Pinus banksiana Lamb.) and black spruce (Picea mariana (Mill.) B.S.P).

Jack pine and black spruce are among the most important softwood species harvested in the Canadian boreal forest, and their regeneration is known to be favored by forest fire [14,15]. Shade-intolerant species, such as jack pine, are known to preferentially allocate growth to their stem, whereas shade-tolerant species, such as black spruce, prefer to attribute resources to their foliage [16]. Here we asked whether species’ shade tolerance influences C allocation in response to changes in forest stands’ conditions. Such an objective was addressed in earlier experiments in which jack pine and black spruce were shown to increase stem growth with decreasing competition, with the increase being more important for jack pine [10]. A consequence was that growth efficiency, defined here as the ratio of stemwood volume increment to foliage biomass, increased with decreasing competition for jack pine and did not change for black spruce [10]. It has also been shown that black spruce does not increase stem growth after partial release from competition [17]. These results were believed to be related to species autecology and different C allocation strategies. However, this hypothesis cannot be tested with empirical data. The use of models enables us to extend the scope of previously published results on aboveground compartments growth [10] to C allocation with the objective to explain differences in growth observed between jack pine and black spruce following commercial thinning.

The aim of this research was to provide insight into tree compartment C allocation for jack pine and black spruce, using CroBas, a functional–structural C balance model [13]. CroBas was preferred over other models for many reasons: (1) it considers an average individual of a stand, which is pertinent to even-aged stands as jack pine and black spruce; and (2) it requires, as inputs, information readily available, i.e., average stem diameter, tree height, crown length, number of stems per hectare, and site index. Patterns of C allocation were investigated for undisturbed stands and under changing competitive status. CroBas model is based on morphological and physiological aspects to predict tree growth, which is then allocated to the functional parts (stem, branches, foliage, fine roots, and transport roots). Stocking density is an integral part of the model that is used to account for competition through light availability. The models were parameterized with published information and data obtained from jack pine and black spruce stands subjected to commercial thinning [10,18].

2. Data Acquisition

The empirical data used for parameterization and validation of the models came from commercial thinning trials carried out in the Abitibi-Témiscamingue region of Northwestern Quebec [10,19]. The sites had average daily temperatures varying between 0.8 and 1.2 °C and yearly total precipitation between 670 and 900 mm [20]. All sites were post-fire naturally regenerated even-aged stands, with ages ranging from 48 to 82 years for jack pine and between 93 and 95 for black spruce (

Table 1. Jack pine and black spruce tree and stand characteristics in Canadian boreal forest of Northwestern Quebec, with ages ranging between 48 and 82 years for jack pine, and between 93 and 95 years for black spruce.

	Jack Pine					Black Spruce
					Mean (SD)					Mean (SD)
Gr	0%	1–31%	32–40%	41–66%		0%	1–31%	32–40%	41–66%
Nb	2625	2321	2838	2790	2000 (891)	2375	2283	2090	2364	2257 (521)
Na	2625	1250	1188	1050	1505 (800)	2375	1475	1260	1171	1435 (641)
Gb	27.5	23.2	20.2	18.5	21.6 (5.66)	38.85	33.43	34.24	29.29	32.6 (5.5)
Ga	27.5	16.9	13.1	11.7	19.0 (6.55)	38.85	27.9	28.01	21.59	26.7 (8.6)
Vb	121.4	112	101.4	101.1	101.3 (25.97)	187.1	164.1	174.4	140.1	159.5 (29)
Va	96.9	58.6	36.4	34.3	62.6 (27.46)	187.1	138.2	146.7	104.9	132.8 (43.6)
DBHb	11.3	10.5	9	8.7	11.6 (2.15)	14.4	13.4	13.7	11.9	13.1 (1.75)
DBHa	11.3	12.5	11.3	12	12.5 (1.75)	14.4	15.3	16.4	14.9	15.3 (1.72)
Htotb	13.7	17.3	20.5	23.6	16.2 (4.60)	15.3	15.9	15.9	15.3	15.6 (0.93)
Htota	11.5	11.3	9.6	9.8	10.7 (1.28)	15.3	15.9	16.6	15.2	15.7 (1.14)
Hcb	5.2	6.4	7.5	8.6	5.9 (1.82)	5.6	5.8	5.9	5.6	5.7 (0.34)
Hca	4.4	4.3	3.7	3.7	4.1 (0.47)	5.6	5.8	6.1	5.6	5.8 (0.41)
Vtotb	52.6	48.6	35.6	37.7	56.8 (24.24)	86	78.5	86.3	61.4	74.7 (23.65)
Vtota	40.7	48.5	30.2	35.3	44.3 (14.10)	86	97.7	117.7	90.9	98.0 (26.88)
Fma	4.76	5.62	5.50	6.50	5.54 (1.77)	4.94	3.63	5.14	5.89	5.32 (1.88)
Fmb	—	—	—	—	—	—	—	—	—	—

Note: G_r, relative basal area removed (%); N, number of stems per unit area (stems·ha⁻¹); G, basal area (m²); V, stand volume (m³); DBH, diameter at 1.30 m (cm); H_tot, tree height (m); H_c, crown length (m); V_tot, stem volume (dm³); F_m, foliage biomass (kg). Subscript “b” refers to conditions before thinning, and “a” is for the conditions after the thinning treatment. SD, standard deviation of the mean; —, not measured.

).

The experimental design followed a completely randomized block design, with five blocks for jack pine and four for black spruce. Stand density was reduced on 4 ha experimental units by removing primarily small, poor-quality, and low-vigor trees. The thinning intensity ranged from 0 (control) to 60% of initial stand basal area. Two to four 200 m² permanent plots were sampled in each experimental unit after thinning to establish thinning intensity [10,19]. Six years after thinning, two stems were felled per experimental unit, yielding 30 jack pine and 24 black spruce sample trees. Stem height (H_tot), diameter at 1.30 m (DBH), and crown length (H_c) were measured. Cross-sectional stem discs were obtained at 0, 1, 1.30, and 2 m, and at every meter thereafter. Ring widths were measured on each stem disk and used to estimate yearly volume increment (i_Vtot). Foliage was sampled from the crown of the felled trees, then used to estimate total tree foliage biomass, using regression analyses [10]. For each species, the dataset was randomly divided into two groups for model parameterization and validation, respectively.

3. Model Description and Parameterization

The CroBas model [13] adapted to jack pine and black spruce is based on: (1) a constant ratio of foliage biomass to cross-sectional sapwood area at the crown base, as implied by the pipe model theory [21]; (2) a functional balance, assuming a constant fine root to foliage biomass ratio [22]; and (3) an allometric relationship between crown surface area and foliage biomass (crown fractal dimension) [23]. The model considers an average individual of a stand and has a yearly time step. In the following, we are providing a summary of core equations used in CroBas. A detailed description of CroBas, including its parameters (

Table 2. Summary of jack pine and black spruce parameters and their provenance.

Symbol *	Meaning	Jack Pine	Black Spruce	Unit	References
φs	Form factor of stemwood in stem below crown	1.629	1.0	-	Based on pipe model assumption
φc	Form factor of stemwood in stem within crown	0.563	0.563	-	Based on conical form assumption
φ’b	Form factor of stemwood in branches	1.071	1.071	-	Estimated
φ’t	Form factor of stemwood in transport root	1	1	-	[24]
cb	Ratio of crown radius to crown length	0.20	0.15	-	[13,18]
ct	Ratio of transport root length to stem length	1	1	-	[13]
ρs, ρb, ρt	Density of wood	421	454	kg·m−3	[25]
αs	Sapwood area: foliage biomass ratio in stem	4.2 × 10−4	3.0 × 10−4	m2·kg−1	[18], stem sapwood area from Reference [26]
αb	Sapwood area: foliage biomass ratio in branches	1.03 × 10−3	2.13 × 10−3	m2·kg−1	[10]; branch sapwood area estimated from Reference [27]
αt	Sapwood area: foliage biomass ratio in transport roots	1.02 × 10−4	1.26 × 10−4	m2·kg−1	This paper; root sapwood area from Reference [26]
αr	Fine root: foliage biomass ratio	0.15	0.2	-	This paper; fine-root biomass [28]
β1	Parameter 1 for crown height estimation	0.5377	0.5948	-	Trial and error
β2	Parameter 2 for crown height estimation	−0.0659	−0.0248	-	Trial and error
β3	Parameter 3 for crown height estimation	0.5543	0.4252	-	Trial and error
2z	“Fractal dimension” of foliage in crown	1.121	1.7926	-	[18]
ξ	“Surface area density” of foliage	0.5139	0.2231	kg·m−2.7 (jack pine) kg·m−2.4 (black spruce)	[10], using Equation (5c) from Reference [13]
	Carbon use efficiency	0.587	0.37	kg·C·kg−1 DW	[29]
r1	Specific maintenance respiration rate of foliage + fine roots	0.31	0.09	kg·C·kg−1 DW·year−1	[30]
r2	Specific maintenance respiration rate of wood	0.02	0.07	kg·C·kg−1 DW·year−1	[29]
sf	Specific senescence rate of foliage	0.33	0.08	year−1	Based on needle lifetime of 13 years for black spruce [30] and 3 years for jack pine [31]
sr	Specific senescence rate of fine roots	3.3	3.3	year−1	[28]
ds0, db0, dt0	Specific sapwood area turnover rate per unit relative pruning	1	1	-	[13]
ds1	Specific stem sapwood area turnover rate in case of pruning	0.02	0.05	year−1	Estimated based on Reference [13]
db1	Specific branch sapwood area turnover rate in case of pruning	0.05	0.05		[13]
dt1	Specific transport root sapwood area turnover rate in case of pruning	0.05	0.05		[13]
ψs	Form factor of senescent sapwood in stem below crown	1.629	1.0	-	Implied by pipe model
ψc	Form factor of senescent sapwood in stem inside crown	0.5	0.5627	-	Trial and error
ψ’b	Form factor of senescent sapwood in branches	0.9	0.9	-	[13]
ψ’t	Form factor of senescent sapwood in transport roots	0.46	0.46	-	[13,24]
an	Specific leaf area	3.5	4.4	m3·kg−1	[18]
P0	Maximum rate of canopy photosynthesis per unit area	2.20	1.46	kg·C·m−2 year−1	Computed from Reference [10]
aσ	Decrease of photosynthesis per unit crown length	0.094	0.11	m−1	[32]
K	Extinction coefficient	0.53	0.52	-	[33]
Cmax	Crown coverage	1.52	1.91	-	Computed from Reference [10]
fe	Bark factor	0.225	0.737	-	This paper
φs.tot	Parameter for stem volume and basal area stem height	0.0578	0.3145	-	This paper
δ	Parameter for quadratic and arithmetic stem diameter at 1.30 m relationship	0.989	0.985	-	This paper
ε1	Parameter 1 related to quantum efficiency	0.0432	0.5948	-	Trial and error
ε2	Parameter 2 related to quantum efficiency	0.0012	0.0247	-	Trial and error
ε3	Parameter 3 related to quantum efficiency	0.0003	0.4252	-	Trial and error

Note: * model parameters have the same symbols as in Reference [13]; -, unitless.

), can be found in Reference [13].

3.1. Biomass of Compartments

The model distinguishes five tree compartments: foliage, branches, stem, transport, and fine roots. The conductive sapwood biomass of branches, stem, and transport roots compartments were computed as the product of the compartment length, its cross-sectional sapwood area at the base, a form factor, and their wood density. Due to differences in stem taper below and inside the crown, the stem was divided into 2 sections (below and above crown base), and a specific form factor was used for each section [34]. Foliage biomass was determined by using crown length, crown fractal dimension, and surface area density [13]. Fine root biomass was estimated based on functional balance [22].

3.2. Carbon Balance and Allocation

To estimate carbon balance, the model requires yearly photosynthesis and respiration, senescence of each compartment, crown self-pruning, and stem mortality.

3.2.1. Photosynthesis and Respiration

Tree photosynthesis (P) was estimated by reducing canopy maximum photosynthesis rate (P₀) per unit of ground area through self-shading, using the Beer–Lambert law and leaf area index (LAI). Landsberg and Waring [35] showed that P₀ depends on quantum efficiency (ε) and yearly photosynthetically active radiation per unit of ground square meter (φ_p). The later was estimated from yearly global solar radiation [36]. Average daily global solar radiation was computed on a monthly basis from temperature (°C) and precipitation (mm) averages [20] and atmospheric top solar radiation (MJ m⁻² d⁻¹) for the study sites. Daily global solar radiation was then integrated over the growing season (days with average daily temperature ≥ 5 °C [20]) to obtain an annual estimate. The fraction of photosynthetically active radiation absorbed by trees was then estimated to be 1/2 of the yearly global solar radiation [37].

Total respiration includes growth respiration, which is assumed to be proportional to total biomass and to be generic, and maintenance respiration, which varies with temperature. Annual respiration rates per unit of stand surface area of foliage, wood, transport, and fine roots were converted to tree levels, using tree compartment biomass and stand density [30]. Respiration values were then adjusted to our sites by using a Q₁₀ of 2.0 and 2.1 for jack pine and black spruce, respectively [30], and the average study site temperatures [20]. The difference between photosynthesis and respiration yields tree net productivity, which is allocated to tree compartments given compartment allometric relationships presented earlier (Section 3.1). For both jack pine and black spruce, yearly C biomass increment of a given tree compartment was obtained by multiplying the compartment yearly biomass increment by a conversion factor of 0.5.

3.2.2. Compartment Senescence and Stem Mortality

The foliage and fine-root specific senescence rates were assumed to be age-invariant. The foliage specific senescence rate was estimated based on maximum foliage retention (in years) and the time step of the model (e.g., 1 year). The fine root specific senescence rate was obtained from the literature [28] (Table 2). Total yearly stem, branch, and transport root sapwood-to-heartwood turnover rates were estimated by using Equation (12a–c) in Reference [13], defined as the product of wood density, cross-sectional sapwood area, a form factor of senescent sapwood, and a specific sapwood area turnover rate (Table 2). As stated earlier, there are 2 specific sapwood area turnover rates: one for the stem within the crown [13] error and the other for the stem below the crown implied by the pipe model theory (Table 2). Knowing that tree height increment is equal to crown increment without self-pruning, height to crown base was then estimated by subtracting total tree height from crown length, which was calculated as follows:

$${\mathrm{H}}_{\mathrm{c}}={\mathrm{H}}_{\mathrm{tot}}\left({\mathsf{\beta }}_1-{\mathsf{\beta }}_2\mathrm{LAI}\right)\exp \left(-{\mathsf{\beta }}_3{\mathrm{DBH}}_{}{\mathrm{H}}_{\mathrm{tot}}^{-1}\right),$$

(1)

where H_c is the crown height; H_tot the stem height; LAI the leaf area index; DBH the diameter at 1.3 m; and β₁, β₂, and β₃ are parameters (Table 2) estimated from our experimental dataset. For each plot of the experiment [10,19], we assigned, through trial and error, values to β₁, β₂, and β₃ and searched for a best fit between measured and estimated crown height.

Mortality was assumed to be driven by crown coverage (CC, Equation (32) [13]), so that maximum crown coverage (CC_max) coincided with maximum stand density (N_max). When C is about to exceed CC_max, tree mortality is triggered (N-N_max), so that CC_max is not exceeded.

CC = NπH_b² = Nπ c_b²H_c²

(2)

3.3. Stem Volume, Diameter, Basal Area, and Growth Estimate

In the CroBas model, the stem under bark biomass increment is equal to the stem sapwood biomass increment. The stem biomass increment was calculated by summing up net sapwood mass increment and yearly sapwood-to-heartwood turnover [13]. The stem volume increment is thus derived as follows:

$${\mathrm{i}}_{\mathrm{v}\mathrm{t}\mathrm{o}\mathrm{t}}=\frac{1}{{\mathsf{\rho }}_{\mathrm{s}}{\mathrm{f}}_{\mathrm{e}}}\left(\frac{\mathrm{D}{\mathrm{W}}_{\mathrm{s}}}{\mathrm{d}\mathrm{t}}+{\mathrm{S}}_{\mathrm{s}}\right),$$

(3)

where i_vtot is stemwood volume increment, ρ wood density, f_e a bark factor, DW_s/dt the net sapwood biomass growth, and S_s the sapwood biomass turning each year into heartwood.

The diameter increment was obtained with the time derivative of the stem volume equation. Stem volume (V_tot) is assumed to be proportional (φ, bark factor) to the basal area (g_1.3) and the height (H_tot):

$${\mathrm{V}}_{\mathrm{t}\mathrm{o}\mathrm{t}}={\mathsf{\phi }}_{\mathrm{s}.\mathrm{t}\mathrm{o}\mathrm{t}}{\mathrm{g}}_{1.3}{\mathrm{H}}_{\mathrm{t}\mathrm{o}\mathrm{t}}$$

(4)

The annual basal area increment was computed as the time derivative of Equation (4), as follows:

$${\mathrm{i}}_{\mathrm{g}}={\mathrm{g}}_{1.3}\left(\frac{{\mathrm{i}}_{\mathrm{V}\mathrm{t}\mathrm{o}\mathrm{t}}}{{\mathrm{V}}_{\mathrm{t}\mathrm{o}\mathrm{t}}}-\frac{{\mathrm{i}}_{\mathrm{H}\mathrm{t}\mathrm{o}\mathrm{t}}}{{\mathrm{H}}_{\mathrm{t}\mathrm{o}\mathrm{t}}}\right)$$

(5)

where i_g is the basal area increment at 1.3 m tree height, g_1.3 the basal area, i_vtot the volume increment, i_Htot the height increment, V_tot the total stem volume above bark, and H_tot the total stem height.

Foliage and fine roots are sensitive to soil fertility and affect the ratio of fine root to foliage biomass. Foliage is also sensitive to light and affects the ratio of fine root to foliage biomass. Because soil fertility is unknown, we only focused on light (quantum efficiency). Hence, a relationship was found between calibrated quantum efficiency, leaf area index, and site index, as follows:

$$\mathsf{\epsilon }={\mathsf{\epsilon }}_1+({\mathsf{\epsilon }}_2\times \mathrm{L}\mathrm{A}\mathrm{I})+\left({\mathsf{\epsilon }}_3\times \mathrm{L}\mathrm{A}\mathrm{I}\times \mathrm{S}\mathrm{I}\right),$$

(6)

where ε is the quantum efficiency used to estimate maximum photosynthesis; ε₁, ε₂, and ε₃ are parameters related to quantum efficiency (Table 2); LAI is the leaf area index, and SI is the site index [38]. To obtain ε₁, ε₂, and ε₃, the model was run for every single plot, using inputs (number of stems per hectare, stem diameter and height, and crown length) from the experiment [10,19]. We therefore proceeded by assigning values, through trial and error, to ε₁, ε₂, and ε₃, until we obtained a best fit between the measured and estimated basal area.

4. Model Validation and Tuning

For a simulation, the models require, as inputs, the following average stand variables: initial stand density (set to 6000 trees ha⁻¹ [13]), stem height (H_tot), diameter at 1.3 (DBH), and crown length (H_c). The model outputs include a component for basics forest variables, such as H_tot, DBH, stem volume (V_tot), and H_c, along with a C component as C allocation in foliage, branches, stem, and roots (structural and fine roots). For each simulated variable, the models also provide their yearly increments for a simulation horizon of 1–100 years.

For validation purposes, DBH, H_tot, and V_tot were contrasted against data collected in the field or picked up from the literature. A successful validation of these later implies realistic C component estimates, since both are linked. The predicted DBH, H_tot, and V_tot were compared with their counterparts from growth and yield tables developed for the province of Quebec [38]. As growth and yield tables are predictions, no formal comparison was carried out. Visual assessments were conducted instead. Yearly increments of stem height, diameter, and volume, along with foliage biomass, were validated by using empirical datasets [10,19] in which experimental units were subjected to different thinning intensities, including control (i.e., no thinning) and plots measured 6 years after thinning. The models were initialized and run for every plot, using its corresponding stand density, H_tot, DBH, and H_c; then the predicted and measured values were compared.

Fine-tunings of model parameters were performed in order to improve the relationships between predicted and measured data, and the final parameters are given in Table 2. This requires a good understanding of how the models work. Foliage biomass has positive relationships with fractal dimension (z) and foliage area density (ξ). Furthermore, z and ξ have a positive relationship with the stem diameter (DBH) and a negative relationship with both the stem height (H_tot) and crown length (H_c). In addition, DBH is positively related to the quantum efficiency (ε) and ratio of stem sapwood area to foliage biomass (α_s), while this later has a negative relationship with H_tot. Based on these relationships, adjustments of z, ξ, ε, and α_s were performed in order to obtain a best fit between predicted and empirical data.

Since yearly increments are more sensitive than their absolute counterparts, the average model bias and efficiency [39] were determined for predicted stem diameter, volume, and height increments.

5. Simulation Experiments

The simulations attempted to describe the dynamics of jack pine and black spruce C-allocation patterns under changing competitive status, for which patterns are lacking in the literature and could potentially contribute to refine current forest management practices. For both jack pine and black spruce, the models were calibrated with initial stand densities of 6000 stems ha⁻¹, indicating fully stocked stands. To test the effects of competition, the initial stands’ densities were reduced to rates based on thinning intensities, as conducted by the forest industry in Quebec [10,18]. For each species, three stand densities were simulated: (1) 6000 stems ha⁻¹, representing fully stocked stands; (2) 33% of stems removed (moderate thinning), approximately leaving 4000 stems ha⁻¹ in the stands; and (3) 50% of stems removed (heavy thinning), resulting in 3000 stems ha⁻¹ left in the stands.

6. Results

Jack pine and black spruce models were validated against experimental [10] and growth and yields data [38]. Once the validations and assessments were conclusive, we applied thinning intensities to produce simulated C allocation outputs.

6.1. Model Validation and Assessment

Very small differences were observed (Figure 1) when the model outputs of stem height, diameter, and volume were compared with the empirical growth and yield curves [38] over a 100-year period. The simulation outcomes showed consistent patterns: stem height and diameter increasing with time and reaching a plateau around 70 years, and stem volume also increasing with time before slowing down around 70 years and slightly tapered off. Although no experimental long-term data were available, crown-length predictions were generally within the range of measured data at the time of measurements (Table 1).

When contrasted with empirical data, simulated DBH, tree height and stem volume increments, and foliage biomass showed small differences (Figure 2), with overall high efficiencies (

Table 3. Jack pine and black spruce average model bias (MB) and efficiency (EF) for yearly diameter increment at 1.30 m (i_DBH), tree height (i_Htot), yearly stem volume increment (i_vtot), and total tree foliage biomass (F_m).

Variables	MB (%)	EF (%)
Jack Pine
iDBH	11	53
iHtot	6	55
ivtot	6	99
Fm	1	36
Black Spruce
iDBH	14	84
iHtot	10	69
ivtot	18	55
Fm	9	91

Note: The average model bias (MB) and model efficiency (EF) [39] are computed as follows—$\mathrm{A}\mathrm{M}\mathrm{B}=\frac{1}{\mathrm{n}}\sum ({\mathrm{y}}_{\mathrm{i}}-{\hat{\mathrm{y}}}_{\mathrm{i}})$ and $\mathrm{E}\mathrm{F}=1-\frac{\sum {({\mathrm{y}}_{\mathrm{i}}-{\hat{\mathrm{y}}}_{\mathrm{i}})}^2}{\sum {\left({\mathrm{y}}_{\mathrm{i}}-\mathrm{y}{\mathrm{m}}_{\mathrm{i}}\right)}^2},$ where n is the number of samples, y_i the measured variable, ${\hat{\mathrm{y}}}_{\mathrm{i}}$ the estimated variable, and ym_i the average of measured variables. For MB, a null value indicates no bias in the model, whereas EF ranges between 0 (model with poor fit) and 1 (model with excellent fit). Absolute values of MB are presented.

). The model biases were equal or lower than 11% for jack pine, and 18% for black spruce.

6.2. Model Competition Simulations and Effects on Carbon Allocation

For jack pine, the total tree C (C_tree) increased over the years, peaked at 4.02 kg·C tree⁻¹ at around 6 years, and then slightly tapered off (Figure 3). Both moderate and heavy thinning resulted in sharp C_tree increases to 5.58 kg·C tree⁻¹ and 6.43 kg·C tree⁻¹, respectively. They were followed by a plateau for the rest of the simulation period. For black spruce, the C_tree increased with each year to reach a maximum of about 10.68 kg·C tree⁻¹ at around 19 years, and then it decreased thereafter. The simulation experiments showed that, the higher the thinning intensity, the higher the C_tree. At their highest, C_tree values were 12.17 kg·C tree⁻¹ and 13.24 kg·C tree⁻¹ for moderate and heavy thinning, respectively. Despite differences noted in the magnitude of their peaks, all thinning intensities displayed similar patterns with their untinned counterpart over the simulation period.

Relative to the total tree C, the ratio of C in the stem (C_{stem_ratio}), branches (C_{branches_ratio}), foliage (C_{foliage_ratio}), and roots (C_{roots_ratio}) showed distinctive patterns (Figure 4). Irrespective to thinning intensities, the ranges of C_{stem_ratio} were about two-fold higher for jack pine relative to black spruce, while the opposite was true for C_{branches_ratio}. For both jack pine and black spruce, there was a clear negative relationship between C_{stem_ratio} and thinning intensity. By contrast, the C_{branches_ratio} and C_{foliage_ratio} showed a positive relationship with thinning intensity, while the C_{roots_ratio} seemed to not be affected by thinning for both species. For increasing thinning intensities, there were disproportionally higher C allocations to foliage, relative to the total tree C, for black spruce compared to jack pine.

Carbon allocation in the stem (C_stem), branches (C_branches), foliage (C_foliage), and roots (C_roots) for different thinning intensities showed different patterns according to thinning intensities (Figure 5). In the absence of thinning, the C allocation for jack pine was higher in the stem, followed by foliage. The lowest C allocations were in the branches and roots, which also showed similar ranges. Irrespective of the tree compartments, the C allocations increased with increasing thinning intensities, but their overall patterns remained quite consistent over the years.

For black spruce, and in the absence of thinning, there were higher C allocations in the stems. Foliage and branches came after and showed similar ranges (Figure 4). The lowest C allocation occurred in the roots. Meanwhile, the C allocation displayed a plateau in the stem and a peak, followed by a decrease over the years, in the foliage, branches, and roots. For increasing thinning intensities, a clear shift in the C allocation occurred in the stem, as shown by the negative relationship between thinning intensities and C allocation in stem, starting 20 years after thinning. However, for the branches, foliage, and roots, the C allocation increased with the increasing thinning intensities, and the patterns were overall quite consistent between thinning intensities.

7. Discussion

The CroBas model [13] was successfully adapted to jack pine and black spruce with the help of yield curves, and the predicted stem diameter, height, and volume seemed realistic, with low bias and high efficiency. In addition, the models yielded observed ranges of yearly height and volume increments following thinning. The CroBas model conceptually translates physiological rates and morphological ratios into growth rates and C allocation [40].

Simulation outcomes aiming at to provide insight into C-allocation patterns boiled down to three mains points: (1) for both jack pine and black spruce, the total tree C increased over the years, with greater increases for decreasing competition; (2) when considering a compartment C as a ratio of the total tree C, lower competition resulted for both species in decreasing stem C and increasing C in branches and foliage; and (3) when considering the amount of C in a given compartment, reduced competition resulted in jack pine to higher C stem, branches, foliage, and roots, whereas black spruce also displayed a higher stem C shifting to lower values from about 20 years following thinning until the 100 year simulation.

The total yearly C allocation at a tree scale represents tree net productivity. Foliage is responsible for tree C uptake through photosynthesis and therefore for tree productivity [18]. Decreasing competition, leading to the highest tree net productivity in jack pine and black spruce, agrees with the results from commercial thinning experiments [10]. Changing C allocation over time results from two mechanisms, ranging from “passive plasticity”, reflecting environmentally induced variations in plant traits, to “ontogenetic plasticity”, referring to variation in the ontogenetic trajectory of a trait [41]. “Passive plasticity” is the result of changes in the availability of resources, such as light, soil water, and nutrients, as trees growth taller. Conversely, C-allocation patterns over tree developmental stages (e.g., ontogenetic drift) [42] have been shown to be related to plant size, as larger plants will have to invest a larger fraction of their biomass in support structures [42,43]. As trees were released from competition, a greater total tree C can be interpreted as enhanced C uptake through photosynthesis, as tree foliage can enjoy greater light exposure due to the crown-coverage reduction following thinning; such findings agree with a previous experimental study [18].

Carbon allocation can be seen as a result of interplay between C source (foliage) and C sink (foliage, stem, branches, and roots). Carbon allocation is a process by which C assimilated or stored by leaves (assimilates) is transferred from this source (leaves) to foliage, stem, branches, and roots [3], where it is used for respiration or growth. Carbon allocation to different tree compartments is a key process by which trees adapt to changes in their environment. The current models focused on the C involved in growth. The models also tested the effects of aboveground competition on C allocation. Relative to the total tree C, the ratio of C allocated to the stem appeared to be higher for jack pine compared to black spruce, while the ratios of C allocated to foliage, branches, and roots were higher for black spruce. Competition even exacerbated the differences between species. It resulted that, for the 0–100-year simulation period, C allocated to stem increased with decreasing competition, contrasting with the decreasing C stem for decreasing competition noted for black spruce. Hence, stem growth is a priority for jack pine, whereas black spruce invests in foliage and branch growth. To support increasing stem and branch weights, C allocation to roots increased, as well, as shown by the simulation outputs. Increasing allocation to the roots secures access to the underground resources needed to sustain stem growth [44]. The simulated C allocation to foliage decreased as trees got older, presumably to follow the same pattern as the other tree compartments, knowing that foliage is responsible for tree C uptake. The shift of stem C allocation from 20 years following thinning observed for black spruce may be related to enhanced growth, making crown coverage reach its maximum value, thus triggering aboveground competition.

For black spruce, the higher C allocation to foliage relative to stem means more leaf area, thus allowing the foliage to take a greater advantage of the increase in available light following the thinning resulting in greater tree C. This contrasts with jack pine displaying higher C allocation to the stem as compared to foliage. Increasing C foliage for decreasing competition conflicts with the optimal partitioning theory, which predicts that foliage C allocation decreases with a decreasing aboveground competition [45], as light might not be limiting anymore.

Overall, the model outputs seemed to depict allocation rules that are consistent with species autecology. Jack pine is shade intolerant, while black spruce is moderately shade tolerant [46,47]. Jack pine’s C-allocation patterns are typical of shade-intolerant species known to maximize their stem growth rather than their branches or foliage. Although shade-tolerant species are less plastic than shade-intolerant species [16], current simulations showed that black spruce can have greater changes in allocation patterns than jack pine. Based on experimental data, allocation to branches was shown to be more sensitive to competition than allocation to foliage and stem [48], resulting in stronger allocation shifts following a change in the tree competitive status. Moreover, evergreen shade-tolerant species tend to minimize C loss through long leaf lifespans rather than maximizing C uptake and growth [49], as is the case for black spruce, which is known to retain its needles for up to 13 years [28,50]. Differences in C allocation with decreasing competition alter tree allometry in relation to the species shade tolerance [5].

Despite the successful adaptation of CroBas to jack pine and black spruce, we are still aware of the following limits. Tree competition involves aboveground resources, such as light, or belowground resources, such as soil water and nutrients [18]. However, the models only account for aboveground competition, using maximum crown coverage as a trigger to initiate mortality. In addition, simulated stem height, DBH, and volume were validated against growth and yield tables, which are themselves models [38] that are built by using forest inventory data. This added to our model’s uncertainty inherent to the growth and yield data. Our decision to use growth and yield data was dictated by the fact that growth and yield tables were readily available and we did not find any other alternative of such growth data. Another limit pertained to belowground tree compartment estimates, since they still need to be validated with experimental root data, which are currently lacking, mainly for mature trees. This seems to not be detrimental to the current study, since the models assume (1) a functional balance [22], implying a constant fine-root-to-foliage-biomass ratio; and (2) the pipe model principle [21], assuming a constant ratio between transport roots’ cross-sectional sapwood area and foliage. The ratio of foliage biomass and sapwood area may depend on hydraulic conductivity of woody tissue, known to vary among species, among trees of a same stand, or with age. Empirical data have shown about 20% variations in those ratios [51,52]. This generates uncertainties in the models; however, fine and structural roots are related to foliage, and any uncertainties to the latter would reflect on root predictions. Interestingly, simulated foliage biomasses have proven, with the help of experimental data, to be realistic, thus reinforcing our assumption of realistic root estimates.

Forest management studies generally concentrate on easily obtainable variables, such as diameter, basal area, and volume growth and yield [53]. The current models go beyond this limitation by offering the possibility to estimate short- and long-term C allocation, as well as C partitioning dynamics in stems, branches, foliage, and roots for different competitive status. Consequently, such models have far-reaching implications for forest management when it is about, for example, to optimize productivity and wood quality. The interests of such models appear obvious when empirical tree metrics are not readily available, not easily obtainable, or require long-term predictions.

8. Conclusions

This study focused on the impact of silviculture on tree growth and C allocation for two of the most important species of Eastern Canadian boreal forests. Simulation results provided insight into the influence of competition through stand density management, on tree productivity and C allocation and partitioning, in agreement with the species autecology. They also indicated that an approach based on tree C allocation dynamics is needed to better understand changes in observed tree growth. The holistic approach used here did indeed provide information not only on tree dimensions (diameter and height), but also on how trees allocate their C to different compartments in response to changes in their environment. The simulated allocation patterns were explained by strategies to increase the species competitive fitness. Belowground tree simulations still need to be validated with empirical root data, which are lacking.