# Evaluating the Ecological Integrity of Structural Stand Density Management Models Developed for Boreal Conifers

## Abstract

**:**

## 1. Introduction

#### SSDMMs and Their Evaluation

## 2. Experimental Section

Input Parameter | Denotations and (or) Value |
---|---|

Stand-type | Natural-origin Stands (n., subscripted by N) |

Natural Upland Black Spruce (PIm_{UN}) | |

Natural Jack Pine (PNb_{N}) | |

Natural Black Spruce and Jack Pine Mixtures (PImPNb_{N}) | |

Natural Lowland Black Spruce (PIm_{LN}) | |

Plantations (n., subscripted by M) | |

Managed Upland Black Spruce (PIm_{UM}) | |

Managed Jack Pine (PNb_{M}) | |

Site Index (S_{I}) | S_{I} ranging from 11 to 19 by 2 m intervals across all 6 stand-types. Note, Ontario-based stand-type-specific S_{I} models were used. For the upland black spruce stand-types (PIm_{UN} and PIm_{UM}), the S_{I} model developed by Carmean [22] was utilized. For the jack pine stand-types ( PNb_{N} and PNb_{M}), the S_{I} model developed by Carmean [23] was employed. For the mixed black spruce and jack pine stand-type (PImPNb_{N}), the S_{I} models developed by Carmean [22,23] were used in combination. Lastly, for the lowland black spruce stand-types (PIm_{LN}), the S_{I} model developed by Newton [24] was used. |

Rotation Age (R_{A}) | Varied by stand-type and S_{I}. Specifically, for natural-origin stands (PIm_{UN}, PNb_{N}, PImPNb_{N} and PIm_{LN}): (1) if S_{I} < 15 then R_{A} ranged from 100 to 120 by 10 year intervals; or (2) if S_{I} ≥ 15 then R_{A} ranged from 80 to 100 by 10 year intervals. For plantations (PIm_{M} and PNb_{M}): (1) if S_{I} < 15 then R_{A} ranged from 70 to 90 by 10 year intervals; or (2) if S_{I} ≥ 15 then R_{A} ranged from 50 to 70 by 10 year intervals. |

Initial Density (N_{I}) | Varied by stand-type. Specifically, for natural-origin stands (PIm_{UN}, PNb_{N}, PImPNb_{N} and PIm_{LN}), N_{I} ranged from 3000 to 10,000 stems/ha by 1000 stems/ha intervals. For plantations (PIm_{M} and PNb_{M}), N_{I} ranged from 1500 to 3500 stems/ha by 500 stems/ha intervals. |

Thinning | Varied by stand-type. |

Treatments | Specifically, for natural-origin stands (PIm_{UN}, PNb_{N}, PImPNb_{N} and PIm_{LN}), a single PCT treatment was applied with the following conditions: |

Time of Thinning (T_{A}) = 10 years | |

Thinning Type (T_{Y}) = PCT for Regimes 2 and 3 (T_{Y} =1) | |

Thinning Response Model: varied by Regime. Specifically, the maximum response model was used in Regime 2 whereas the minimum response model was used in Regime 3. | |

Thinning Removal: varied by the stand density existing at the time of thinning: residual target density post-PCT = 2000 to 3000 stems/ha. | |

For plantations (PIm_{M} and PNb_{M}), a single CT treatment was applied. | |

T_{A} = R_{A}-25 for Regimes 2 and 3 | |

T_{Y}: CT for Regimes 2 and 3 (T_{Y} = 2) | |

Thinning Units: %BA | |

Thinning Removal = 35% basal area | |

Merchantable | Length of pulplog (m) = 2.59 |

Specifications | Length of sawlog (m) = 5.03 |

Minimum small-end inside-bark diameter for pulplogs (cm) = 10 | |

Minimum small-end inside-bark diameter for sawlogs (cm) = 14 | |

Minimum small-end inside-bark diameter for merchantable volume (cm) = 4 | |

Operational | 0.01%/year |

Adjustment Factor | |

Genetic Worth | Plantations only. |

Effects | Genetic worth (G_{W}) and selection age (G_{A}): (1) for black spruce plantations (PIm _{M}), G_{W} was set at 10% and G_{A} at 15 years; and (2) for jack pine plantations (PNb_{M}), G_{W} was set at 7% and G_{A} at 20 years. |

Genetic worth response model: (1) Regimes 1 (Control) and 2 utilized a Type 1 response model initiating from the specified selection age; and (2) Regime 3 utilized a Type 2 response model initiating at the time of planting. |

## 3. Results and Discussion

_{UN}, PIm

_{UM}, PNb

_{N}, PNb

_{M}, PImPNb

_{N}and PIm

_{LN}refer to upland natural-origin black spruce, black spruce plantations, natural-origin jack pine, jack pine plantations, natural-origin black spruce and jack pine mixtures, and natural-origin lowland black spruce stand-types, respectively. Basic matrix notation using the conventional m rows × n columns configuration is used to identify each subgraph under discussion. Given space limitations an abridged set of the graphical output consisting of representative matrices for each stand-type are presented: Figure 1 for PIm

_{UN}and Figure A1, Figure A2, Figure A3, Figure A4 and Figure A5 in the Appendix for PIm

_{UM}, PNb

_{N}, PNb

_{M}, PImPNb

_{N}and PIm

_{LN}, respectively. Note, consistency is maintained throughout all the figures by using identical variables along both the x and y axis: Stand age (Age; year), quadratic mean diameter (QMD; cm), mean dominant height (H

_{d}; m), stand density (Density; stems/ha), and relative density (Relative Density; %/100) along the x-axis versus mean dominant height (H

_{d}; m), stand density (Density; stems/ha), stand basal area (BA; m

^{2}/ha), total stand volume (Volume; m

^{3}/ha), and total stand merchantable volume (Merch Volume; m

^{3}/ha) along the y-axis. Additionally, for reference purposes, the principal concept or relationship being evaluated is denoted in individual subgraphs using the following abbreviated subtitles (n., matrix position denoted in parentheses (row:column)): Site Curves (1:1), Site Form (1:2), Sukatschew Effect (2:1), Reineke (2:2), Spacing Percent (2:3), Stocking Guide (3:4). Yield Curves (4:1), Eichhorn’s Rule (4:3, 5:3), Yield-Density Effect (4:4), Yield-Rel (relative) Density Effect (4:5), Merch (merchantable) Yield Curves (5:1), merch (Merchantable) Yield-Density Effect (5:4) and Merch (merchantable) Yield-Rel (relative) Density Effect (5:5).

**Figure 1.**Bakuzis matrices for unthinned and precommercially thinned (PCT) upland black spruce (Sb) stands, which were established naturally (N) at an initial densities of 7000 stems/ha and grown on 5 site qualities (SI) over 100 year rotations: (

**a**) Regime 1 represented unthinned control stands; (

**b**) Regime 2 was initially identical to Regime 1 but the stands were subjected to a single PCT treatment at a stand age of 10 years in which stand densities were reduced to 2862 stems/ha and the maximum thinning response model setting was employed; and (

**c**) Regime 3 was identical to Regime 2 but the stands utilized the minimum thinning response model to account for accelerated growth arising from the PCT treatment.

#### 3.1. Principal Relationships Examined

#### 3.1.1. Mean Dominant Height–Age Developmental Patterns (1:1)

_{UN}, Figure A2b vs. Figure A2c for PNb

_{N}, Figure A4b vs. Figure A4c for PImPNb

_{N}, and Figure A5b vs. Figure A5c for PIm

_{LN}). Additionally, the post-thinning trajectories for the thinned stands employing the minimum thinning response model (Regime 3) were always greater than that calculated for the unthinned stand (Regime 1) (c.f., matrix position (1:1) in Figure 1a vs. Figure 1c for PIm

_{UN}, Figure A2a vs. Figure A2c for PNb

_{N}, Figure A4a vs. Figure A4c for PImPNb

_{N}and Figure A5a vs. Figure A5c for PIm

_{LN}). For a given stand-type, site class, rotation length and response model, the magnitude of the height increase varied directly with the number of trees removed during the PCT treatment, as expected.

_{UM}and Figure A3a and Figure A3b for PNb

_{M}). Conversely, a smooth continuous curve from establishment to rotation characterized the mean dominant height–age relationship when the genetic worth effect was described by the Type 2 response model (Regime 3): e.g., see matrix position (1:1) in Figure A1c for PIm

_{UM}and Figure A3c for PNb

_{M}. These patterns were consistent across all site classes, initial density levels and rotation lengths. Furthermore, irrespective of the model selected, the maximum height attained for a given site class and rotation length were equivalent. Basically, the height predicted for a given age by the Type 1 and Type 2 model specifications are only different during the initial period of development before the plantations reach the specified selection age. As expected, the height calculated for a given age using the unadjusted height–age function which did not account for genetic worth effects, was always less than the adjusted heights arising from the Type 1 response model during the post-selection age period, and from the Type 2 response model over the entire rotation (c.f., matrix position (1:1) in Figure 1a vs. Figure A1a–c for black spruce or Figure A2a vs. Figure A3a–c for jack pine).

#### 3.1.2. Site Form: Mean Dominant Height-Quadratic Mean Diameter Relationship (1:2)

_{UN}, PNb

_{N}, PImPNb

_{N}, PIm

_{LN}) or linear fashion (PIm

_{UM}, PNb

_{M}) with the site-specific relationship converging into a single common relationship, irrespective of initial density, rotation length, management intensity (control versus thinning), thinning response model where applicable (i.e., natural-origin stand) or genetic response model where applicable (i.e., plantations) (e.g., (1:2) in Figure 1 and Figure A1, Figure A2, Figure A3, Figure A4 and Figure A5). The convergence of the relationships among site indices, suggest the maintenance of a certain degree of structural uniformity within a given stand-type.

#### 3.1.3. Sukatsckew Effect: Density–Stand Age Relationship (2:1)

#### 3.1.4. Reineke’s Stand Density Index: Density–Quadratic Mean Diameter Relationship (2:2)

_{q}; quadratic mean diameter (cm)) and density (N (stems/ha)). This relationship is expressed as a power function: $N={k}_{1}{D}_{q}^{{k}_{2}}$ where k

_{1}is assumed to be a stand-type, regional-based and site-independent constant whereas k

_{2}is an universal constant empirically-determined to be equivalent to −1.605 (n., alternatively this relationship can be expressed in a linear form via a double logarithmic transformation). Thus accordingly, the density–quadratic mean diameter relationship for fully-stocked even-aged stands should be log-linear with (1) an invariant intercept for a given stand-type and region across a range of site qualities; and (2) a slope of approximately −1.6, which is invariant to stand-type, locality, species, and site differences.

_{UM}> PNb

_{M}> PIm

_{UN}> PNb

_{N}> PImPNb

_{N}>> PIm

_{LN}(c.f., matrix position (2:2) in Figure A1a, Figure A2a, Figure 1a, Figure A2a, Figure A4a and Figure A5a, respectively). Of note was the relationship for the lowland stand-type, which was quite different from the other stand-types. Specifically, the density-diameter relationships exhibited a significant degree of non-convergence in which the density for a given diameter decreased with declining site quality (e.g., (2:2) in Figure A5a).

_{1}). These patterns also infer that site quality may be influencing the occupancy level that a stand can achieve. Essentially, the patterns indicate that the greater the site quality, the more trees that a site can accommodate for a given mean tree size, and, hence, a greater level of occupancy is achievable. Similar findings have been reported for self-thinning coastal Douglas fir (Pseudotsuga menziesii var. menziesii (Mirb.) Franco), western hemlock (Tsuga heterophylla (Raef.) Sarg.) and red alder (Alnus rubra Bong.) stands in that the intercept parameter was affected by stand origin (natural-origin versus planted), degree of monospecificity (purity) and site quality [32].

#### 3.1.5. Spacing Percent: Density–Mean Diameter Height Relationship (2:3)

_{s}) is a species, age, and site independent index used to regulate stand densities and develop thinning schedules (e.g., Wilson [33,34]). It is based on the empirically-derived relationship between mean intertree spacing and mean dominant height (H

_{d}) and is expressed as a ratio: ${R}_{s}={(10000/N)}^{1/2}/{H}_{d}$ where N is stand density (stems/ha). The relationship is most applicable to stands with square spatial arrangements. It is also considered conceptually superior to diameter-based indices such as Reineke’s [31] SDI given that mean dominant height is not affected by density treatments and incorporates both site quality and age effects into a single variable. The temporal trend of R

_{s}within even-aged stands is governed by the relationship between mean dominant height increment and mortality. Hence, prior to the initiation of self-thinning, changes in R

_{s}can be attributed to height growth. During the post-crown closure period, however, both the mortality rate and height growth are simultaneously influencing the ratio. R

_{s}is hypothesized to follow a log-linear pattern and is expected to decline rapidly once stands approach the 10%–12% threshold values [14]. For a given stand-type, initial density, and rotation length, the SSDMMs produced density–height trajectories which were reversed-sigmoidal in shape (PIm

_{UN}; e.g., (2:3) in Figure 1a or negative exponential (PIm

_{UM}, PNb

_{N}, PNb

_{M}, PImPNb

_{N}and PIm

_{LN}; e.g., (2:3) in Figure A1a, Figure A2a, Figure A3a, Figure A4a and Figure A5a, respectively). The relationships also tended to inflect at a mean R

_{s}of approximately 10%. Post-thinning trends in R

_{s}within the natural-origin stands were characterized by a negative parabolic pattern of decline, irrespective of initial density, rotation length or thinning response model utilized (e.g., (2:3) in Figure 1b,c and Figure A2b,c, Figure A4b,c, and Figure A5b,c). The pattern of decline in R

_{s}within the plantation stand-types during the post-thinning period were largely negative exponential in form and convergent among site qualities, irrespective of initial density, rotation length or the genetic worth effect model used (e.g., (2:3) in Figure A1b,c and Figure A3b,c).

_{UN}> PNb

_{N}≈ PIm

_{UM}≈ PNb

_{M}> PImPNb

_{N}>> PIm

_{LN}(c.f., (2:3) in Figure 1a–c and Figure A2a–c, Figure A1a, Figure A3a, Figure A4a–c, and Figure A5a–c, respectively). The trajectories differentiated according to site quality with the more productive sites exhibiting a greater tolerance of density-stress as evident by a shift in the inflection point at which R

_{s}rapidly declined (e.g., moving from a minimum of 7%–8% on the poorest sites to a maximum of 13%–14% on the best sites). The site-dependent final R

_{s}values also increased with increasing site quality. These patterns are generally consistent with those reported for other species: e.g., loblolly (Pinus taeda L.) plantations in the Southern US where the lower asymptotic limit of R

_{s}was found to increase in a linear fashion with increasing site quality [35].

#### 3.1.6. Temporal Production Patterns: Basal Area (3:1), Total Volume (4:1) and Merchantable Volume (5:1)–Age

#### 3.1.7. Yield Interrelationships: Basal Area (3:2), Total Volume (4:2) and Merchantable Volume (5:2)—Quadratic Mean Diameter

_{q}) is inherently non-linear and density-dependent: $G\propto {D}_{q}^{2}N$. Similarly, for a given stage of stand development as defined by Lohey’s mean height (H

_{L}), total stand volume (V

_{t}) and merchantable stand volume (V

_{m}) vary directly with D

_{q}and N for a given H

_{L}: ${V}_{t,m}\propto G{H}_{L}\propto {D}_{q}^{2}N{H}_{L}$. For the untreated and treated natural-origin stand-types and unthinned plantations irrespective of initial density, rotation length and thinning model utilized, G, V

_{t}and V

_{m}increased with increasing D

_{q}(e.g., (3:2; 4:2; 5:2) in Figure 1a–c and Figure A1a, Figure A2a–c, Figure A3a, Figure A4a–c, and Figure A5a–c). For a given stand-type, initial density, rotation length, thinning treatment and response model, G, V

_{t}and V

_{m}initially followed identical concave non-linear trajectories until self-thinning commenced after which they diverged according to site quality. The basal area attained at the point of divergence directly varied with site quality. The post-divergence pattern could be characterized as a concave non-linear trend in which the asymptotic basal area attained and that achieved at rotation varied directly with site quality. The G-D

_{q}, V

_{t}-D

_{q}and V

_{m}-D

_{q}relationships for the thinned plantations exhibited similar site-dependent non-linear trajectories as did the natural-origin stand-types (e.g., (3:2; 4:2; 5:2) in Figure A1b,c and Figure A3b,c)). However, there was a higher degree of convergence among site qualities for a given initial density, rotation length, genetic worth effect model and thinning regime. Furthermore, the post-thinning trajectories shared a common developmental pathway where the asymptotic values attained at rotation varied directly with site quality. This convergence is likely attributed to the effect of the CT treatments which reduced stand basal areas by 35% (Table 1) resulting in the absence of self-thinning effects as opposed to that observed for the natural-origin stands and unthinned plantation trajectories.

#### 3.1.8. Eichhorn’s Rule: Basal Area (3:3), Total Volume (4:3) and Merchantable Volume (5:3)–Mean Dominant Height

_{d}, V

_{t}-H

_{d}and V

_{m}-H

_{d}trajectories for a given stand-type, initial density, rotation length, thinning regime, and thinning or genetic worth effect response model, should (1) converge and exhibit a single site-independent sigmoidal trajectory (Eichhorn’s rule or equivalently, Assmann’s (1961a, as cited in Pretzsch [36]) common yield level hypothesis); or (2) diverge into multiple sigmoidal trajectories differentiated by broad site quality groupings (Assmann’s, 1961a, as cited in Pretzsch [36]) special yield level hypothesis).

#### 3.1.9. Reciprocal Yield Effect Relationships: Basal Area (3:4), Total Volume (4:4) and Merchantable Volume (5:4)—Stand Density

_{t}-N and V

_{m}-N trajectories (right to left along the x-axis) for a given stand-type, initial density, rotation length, thinning regime, and thinning or genetic worth effect response model, revealed similarities: site-dependent linear (lower site qualities) to polymorphic (higher site qualities) increases in production as density declined (e.g., (3:4; 4:4; 5:4) in Figure 1a–c and Figure A1a–c, Figure A2a–c, Figure A3a–c, Figure A4a–c and Figure A5a–c). These declines are attributable to self-thinning and density-independent causal mortality agents. The asymptotic yields achieved varied directly with site quality whereas the final densities surviving at rotation were inversely related to site quality. This latter observation combined with the fact that the trajectories differentiated on the basis of site quality are partially attributed to the Sukatsckew effect (i.e., mortality rates increased with increasing site quality).

#### 3.1.10. Density-dependent Effects on Volumetric Production: Total Volume (4:5) and Merchantable Volume (5:5)–Relative Density Index.

_{r}; V

_{t}-P

_{r}and V

_{m}-P

_{r}trajectories) for each stand-type, initial density, rotation length, thinning regime, and thinning or genetic worth effect response model, indicated that the patterns observed for the natural-origin stand-types and the unthinned plantations, were not consistent with expectation (e.g., (5:4; 5:5) in Figure 1a–c), Figure A1a, Figure A2a–c, Figure A3a, Figure A4a–c, and Figure A5a–c)). Specifically, a site-dependent density effect was clearly evident in terms of the maximum level of volumetric production achieved as density-stress increased. Essentially, the inference is that stands on better sites can withstand greater levels of density-stress before incurring production declines and are able to get closer to their biological maximum levels of production than stands on poorer sites. Furthermore, once stands experience their site-dependent maximum level of density-stress, the subsequent trajectories were also contrary to that predicted by self-thinning theory (i.e., relative density indices declined). Although the patterns for the CT plantations exhibit similar trends, the trajectories did not exhibit the same degree of site-dependency as observed for the other stand conditions (e.g., (5:4; 5:5) in Figure A1b,c and Figure A3b,c). Most plausibly because the thinning treatments occurred before stands achieved their site-dependent maximum density-stress levels and hence the asymptotic effects were not fully manifested.

#### 3.2. Site-Dependent Occupancy Effects on Productivity

_{q})-density (N) relationship underlying Reineke’s [31] SDI $\left(N\right)={\text{\alpha}}_{1}{D}_{q}^{{\text{\alpha}}_{2}}$ where α

_{1}is a species-specific constant and α

_{2}is an empirically-determined universal constant equal to −1.6), and the mean volume $\left(\overline{v}\right)$-density relationship underlying Yoda’s [17] self-thinning rule $\left(\overline{v}\right)={\mathrm{\beta}}_{1}{N}^{{\mathrm{\beta}}_{2}}$ here β

_{1}is a species-specific constant and β

_{2}is an empirically-determined universal constant equal to −1.5): (1) Weiskittel [32] reported that the intercept (α

_{1}) of the asymptotic D

_{q}-N relationship for self-thinning coastal Douglas fir (Pseudotsuga menziesii var. menziesii (Mirb.) Franco), western hemlock (Tsuga heterophylla (Raef.) Sarg.) and red alder (Alnus rubra Bong.) stands was positively correlated with site quality for all three species; (2) similarly, Zhang [38] found that the intercept (α

_{1}) of the asymptotic D

_{q}-N relationship for self-thinning ponderosa pine (Pinus ponderosa Lawson and C. Lawson) stands varied directly with site index; and (3) Bi’s [39] re-analysis of Yoda’s [17] classical experiments which were used to establish the generality of the original self-thinning rule, revealed that the intercept parameter (β

_{1}) of the asymptotic $\overline{v}-N$ relationship increased with increasing site fertility. In relation to the site-dependent nature of the density–mean dominant height (H

_{d}) relationship $\left(N\propto {H}_{d}^{-2}\right)$ underlying Wilson’s [33,34] relative spacing index, Zhao [35] reported the lower asymptotic limit of relative spacing within loblolly (Pinus taeda L.) plantations varied directly with site quality, and hence was similar to the trends observed in this study.

_{e}N and assuming that $\overline{v}={k}_{1}{D}_{q}^{1.6}$ [40], yields the approximation: ${\mathrm{log}}_{e}N={\mathrm{log}}_{e}{k}_{1}-\frac{2}{3}{\mathrm{log}}_{e}\overline{v}\simeq {\mathrm{log}}_{e}{k}_{1}-\frac{2}{3}{\mathrm{log}}_{e}{D}_{q}^{2.4}$ where ${k}_{1}={\left({\mathrm{\beta}}_{1}^{-1}\right)}^{1/{\mathrm{\beta}}_{2}}$ which, when retransformed to an arithmetic formulation, approximates Reineke’s [31] underlying N-D

_{q}relationship: $N\simeq {k}_{1}{\left({D}_{q}^{2.4}\right)}^{-2/3}\simeq {k}_{1}{D}_{q}^{-1.6}$. Likewise, assuming the height-diameter allometric relationship for excurrent forest tree species is ${H}_{d}={k}_{2}{D}_{d}^{0.8}$ [41] within the context of Wilson’s [33,34] relative spacing underlying relationship $N={k}_{3}{H}_{d}^{-2}$, yields the approximation, $N\simeq {k}_{3}{\left({k}_{2}{D}_{q}^{0.8}\right)}^{-2}\simeq {k}_{4}{D}_{q}^{-1.6}$ where ${k}_{4}={k}_{2}^{-2}{k}_{3}$. Hence, it is plausible to find similarities among the three indices in terms of their site dependences at asymptotic occupancy levels given the intrinsic functional relationships that exists among them.

#### 3.3. Ecological Integrity of SDMD-Type Models: A Broader Discussion

## 4. Conclusions

## Acknowledgments

## Appendix

**Figure A1.**Bakuzis matrices for genetically-improved unthinned and commercially thinned (CT) upland black spruce (Sb) plantations (P) which were established at an initial densities of 2500 stems/ha and grown on 5 site qualities (SI) over 70 year rotations: (

**a**) Regime 1 represented unthinned plantations in which genetic worth effects were described by the Type 1 response model; (

**b**) Regime 2 was initially identical to Regime 1 and employed the same response model, however, the plantations were subjected to a single CT treatment at a stand age of 45 years in which the basal areas were reduced by 35%; and (

**c**) Regime 3 was identical to Regime 2 but used the Type 2 response model to account for genetic worth effects.

**Figure A2.**Bakuzis matrices for unthinned and precommercially thinned (PCT) jack pine (Pj) stands which were established naturally (N) at an initial densities of 7000 stems/ha and grown on 5 site qualities (SI) over 100 year rotations: (

**a**) Regime 1 represented unthinned control stands; (

**b**) Regime 2 was initially identical to Regime 1 but the stands were subjected to a single PCT treatment at a stand age of 10 years in which stand densities were reduced to 2862 stems/ha and the maximum thinning response model setting was employed; and (

**c**) Regime 3 was identical to Regime 2 but the stands utilized the minimum thinning response model to account for accelerated growth arising from the PCT treatment.

**Figure A3.**Bakuzis matrices for genetically-improved unthinned and commercially thinned (CT) jack pine (Pj) plantations (P) which were established at an initial densities of 2500 stems/ha and grown on 5 site qualities (SI) over 70 year rotations: (

**a**) Regime 1 represented unthinned plantations in which genetic worth effects were described by the Type 1 response model; (

**b**) Regime 2 was initially identical to Regime 1 and employed the same response model, however, the plantations were subjected to a single CT treatment at a stand age of 45 years in which the basal areas were reduced by 35%; and (

**c**) Regime 3 was identical to Regime 2 but used the Type 2 response model to account for genetic worth effects.

**Figure A4.**Bakuzis matrices for unthinned and precommercially thinned (PCT) black spruce and jack pine mixed stands which were established naturally (N) at an initial densities of 7000 stems/ha and grown on 5 site qualities (SI) over 100 year rotations: (

**a**) Regime 1 represented unthinned control stands; (

**b**) Regime 2 was initially identical to Regime 1 but the stands were subjected to a single PCT treatment at a stand age of 10 years in which stand densities were reduced to 2862 stems/ha and the maximum thinning response model setting was employed; and (

**c**) Regime 3 was identical to Regime 2 but the stands utilized the minimum thinning response model to account for accelerated growth arising from the PCT treatment.

**Figure A5.**Bakuzis matrices for unthinned and precommercially thinned (PCT) lowland black spruce (Sb) stands which were established naturally (N) at an initial densities of 7000 stems/ha and grown on 5 site qualities (SI) over 100 year rotations: (

**a**) Regime 1 represented unthinned control stands; (

**b**) Regime 2 was initially identical to Regime 1 but the stands were subjected to a single PCT treatment at a stand age of 10 years in which stand densities were reduced to 2862 stems/ha and the maximum thinning response model setting was employed; and (

**c**) Regime 3 was identical to Regime 2 but the stands utilized the minimum thinning response model to account for accelerated growth arising from the PCT treatment.

## Conflicts of Interest

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**MDPI and ACS Style**

Newton, P.F.
Evaluating the Ecological Integrity of Structural Stand Density Management Models Developed for Boreal Conifers. *Forests* **2015**, *6*, 992-1030.
https://doi.org/10.3390/f6040992

**AMA Style**

Newton PF.
Evaluating the Ecological Integrity of Structural Stand Density Management Models Developed for Boreal Conifers. *Forests*. 2015; 6(4):992-1030.
https://doi.org/10.3390/f6040992

**Chicago/Turabian Style**

Newton, Peter F.
2015. "Evaluating the Ecological Integrity of Structural Stand Density Management Models Developed for Boreal Conifers" *Forests* 6, no. 4: 992-1030.
https://doi.org/10.3390/f6040992