Potential Utility of a Climate-Sensitive Structural Stand Density Management Model for Red Pine Crop Planning

Abstract

The objectives of this study were to evaluate and exemplify the potential utility of a climate-sensitive modular-based structural stand density management model (SSDMM) developed for red pine (Pinus resinosa Aiton) in crop planning decision making. Firstly, the model’s predictive ability was assessed using a retrospective validation approach without consideration of climate change effects. Although limited in scope and applicability, the preliminary results revealed that the magnitude of the mean prediction error for the principal determinates governing stand development did not exceed ±15%. Secondly, the potential utility of the model was illustrated within a spatial-based forest management planning context for a range of climate change scenarios. These exemplifications included three conventional crop plan simulations (initial spacing (IS), IS plus one commercial thinning (CT) treatment, and IS plus two CTs) developing under three climate change scenarios (1971–2000 climate norms, and 4.5 and 8.5 representative concentration pathways) over 75-year rotations (2022–2097) at three geographically diverse locales (north-eastern (Kirkland Lake), north-central (Thessalon), and north-western (Thunder Bay) Ontario, Canada). Resultant developmental indices and (or) productivity metrics were contrasted in terms of (1) regional-specific differences in temporal stand dynamical patterns and rotational yields with increasing climatic change severity, and (2) silvicultural effectiveness of the crop plans within and across locales for each climate change scenario. Climate-wise, although the results revealed marginal regional differences across a multitude of rotational outcome metrics, declines in mean tree size and merchantable volume productivity, and most importantly utility pole production within unthinned plantations, were among the most consequential and consistent negative outcomes associated with climate-induced site productivity declines. Silviculturally, crop plans that included thinning treatments relative to their counterparts that did not, yielded trees of greater mean size and were able to maintain utility pole production status while not achieving similar levels of site occupancy or volumetric productivity. Management-wise, maintenance of pole production status along with concurrent increases in fiscal worth even in light of climate change outweighed the marginal decline in volumetric productivity that was associated with the thinning regimes. In summary, the validation results provided a measure of predictive performance relative to the underlying calibration data set whereas the exemplifications illustrated the model’s potential operational utility in spatial-based forest management planning. For managers aspiring to maintain the historical productivity legacy of red pine through optimal density management decision making while acknowledging prediction uncertainty when forecasting stand development trajectories under climate change, the SSDMM provides an optional decision-support tool for designing climate-smart crop plans during the Anthropocene.

1. Introduction

Red pine (Pinus resinosa Aiton) is an important contributor to the regional forest products supply chains throughout the north temperate and southern boreal forest regions of central North America. This species produces a wide variety of commercially-relevant end-products including high value utility poles extensively used in constructing electrical transmission and distribution networks, and rustic residential log structures, veneer widely deployed in home and office furniture manufacturing, appearance-based boards, flooring, decking and wall panelling employed in numerous interior and exterior carpentry applications, dimensional lumber and engineered wood composites frequently used in constructing and retrofitting residential and commercial buildings, and raw fibre residuals utilized in the production of pulp and paper products and more recently in the production of biofuel derivatives [1]. Ecologically, red pine is a shade intolerant, genetically uniform and fire-adapted species that exhibits a wide range of phenotypic plasticity in response to site occupancy regulation (sensu [2]). Resultantly, density management has been widely practiced throughout the species range. Crop plans that include both initial spacing (IS) and subsequent commercial thinning (CT) treatment(s) are representative of red pine silvicultural efforts, particularly when volumetric yield maximization and end-product objectives are paramount (e.g., [2,3]).

Conceptually, density management consists of regulating site occupancy in a manner that concentrates the finite growth-determinate resources on selected crop trees, thus enabling the realization of specified stand-level management objectives (e.g., attaining early stand operability status, maximizing end-product value and (or) optimizing carbon sequestration potential). Ecologically, this involves controlling the intensity and asymmetry of interspecific and intraspecific competitive interactions for environmental resources and physical growing space, minimizing negative allelopathic effects, and (or) promoting positive facilitative relationships. Logistically, the principal site occupancy control mechanisms have included (1) manipulating initial stand composition and structure (species, planting density and spatial arrangement) at the time of plantation establishment via IS treatments, and (2) regulating stand structures (species composition, spatial patterns and vertical and horizontal size distributions) and site occupancy levels (crop tree density) at the sapling or semi-mature stages of development via precommercial thinning (PCT) or CT treatments, respectively.

Historically, apart from universal forest production axioms (e.g., [4,5,6]), generic silvicultural guides (e.g., spacing indices [7,8]) and static stand density management diagrams (e.g., SDMDs; [9]), the availability of comprehensive decision-support models and associated tools required for designing optimal crop plans for red pine plantations has been limited, particularly in relation to addressing stand-level volumetric yield, end-product production and (or) ecosystem service objectives. Furthermore, this limitation has been exacerbated with climate change given that most density management decision-support aids that are currently available, lack the ability to account for such effects. Consequently, the recently introduced modular-based climate-sensitive structural stand density management model (SSDMM) for red pine which attempts to address a wide array of forest management objectives while simultaneously accounting for site productivity changes arising from climate change ([10]), may have potential currency in addressing this ongoing and operationally-critical deficiency.

Briefly, the climate-sensitive SSDMM for red pine evolved from the modelling approaches introduced in the development of the static, dynamic and structural stand density management diagrams (e.g., [11,12,13] and [14], respectively). More precisely, the red pine SSDMM employed the generalized parameterization framework and overall hierarchical model structure advanced in the development of the SSDMM for jack pine (Pinus banksiana Lamb.) [14]. Additionally, the resultant red pine model and associated algorithmic analogue integrated a number of more recently introduced innovations advanced within this modelling domain. These advancements included: (1) numerically ensuring mathematical compatibility in merchantability volumetric predictions and sawmill-based product volumes (e.g., constraining the cumulative chip and lumber volume estimate to be no greater than to the stand-level merchantable volume estimate (e.g., [15]); (2) accounting for density-independent mortality arising from extraneous factors such as insects and disease through the deployment of an end-user-specified operational adjustment factor (e.g., [15]); (3) integrating a crown occupancy algorithm to account for the temporal response delay that occurs when trees within recently thinned stands are adjusting to their newly allocated growing space and site resources (e.g., [15]); (4) accommodating genetic worth and thinning release effects on growth and stand dynamical processes through a functional adjustment to the site-based height-age equation (e.g., [16] and [17], respectively); (5) incorporating a geographical-referencing biophysical site index function for accounting for site productivity changes and resultant effects on stand dynamical processes over three continuous 30-year commitment periods arising from a given climate change scenario [18]; and (6) integrating fibre attribute models to enable the prediction of a suite of wood quality determinates which underlie end-product potential (e.g., [19]). In addition, a new consequential end-product group was recognized and accommodated within this red pine model variant: i.e., utility poles [10].

Although the model specification, parameterization and computational pathways have been extensively documented [10], exemplification of the model’s utility in spatial-based crop planning under climate change has not yet been demonstrated. Likewise, validation metrics in terms of the model’s predictive accuracy have yet to be presented. Consequently, the objectives of this study were to address these outstanding deployment prerequisites. Although limited in analytical scope with respect to climate change effects, the validation objective was realized by presenting mean error metrics for a key set of mensurational-based determinates underlying temporal stand dynamics and structural development. The applicability of one of the principal ecological axioms underlying this modeling approach was also examined: the self-thinning rule [20]. The exemplification objective was realized by presenting a comparative evaluation of 75 year rotational outcomes for a triple-set of conventional crop plans (i.e., IS, IS plus one CT treatment, and IS plus two CT treatments) growing under each of the climate change scenarios (i.e., historical climatic norms from the 1971–2000 period; RCP 4.5 ([21]) and RCP 8.5 ([21]); henceforth denoted NC, RCP4.5 and RCP8.5, respectively) spanning three commitment periods (i.e., present–2040, 2041–2070, 2071–2100) at three geographically distinct localities in central Canada (i.e., north-eastern (Kirkland Lake), north-central (Thessalon), and north-western (Thunder Bay) Ontario). Collectively, the realization of these objectives aspired to provide the prerequisite performance metrics required for the model’s potential operational deployment, reconfirm the model’s underlying ecological integrity, and demonstrate its potential utility in spatial-based crop planning decision-making.

2. Materials and Methods

2.1. The Red Pine SSDMM: Structure and Formulation

Similar to the analytical structure used in the previous SSDMMs developed for boreal conifers [14,15,22,23], the hierarchical-based red pine SSDMM consisted of six sequentially linked prediction modules: Module A—Dynamic SDMD; Module B—Diameter and Height Recovery; Module C—Taper Analysis and Pole, Log and Stem Volume Estimation; Module D—Biomass and Carbon Estimation; Module E—Mill-specific Product Recovery and Value Estimation; and Module F—Fibre Attribute Estimation. A schematic illustration of the structure of the SSDMM including the interrelationships and sequential flow of computations among the individual modules along with generic input requirements and resultant output metrics is provided in Figure 1 of the companion contribution ([10]). Analytically, Module A involved the development of a climate-sensitive red pine dynamic SDMD via the parameterization and integration of a broad array of static and dynamic yield–density relationships employing the traditional SDMD modelling framework along with the introduction of a biophysical site-specific height–age function to account for climate change effects on site productivity [18] and a set of sub-models to address genetic worth and thinning response effects (sensu [16,17,24,25]). Module B consisted of the development of a (1) Weibull-based parameter prediction equation system (PPES) for diameter distribution recovery, and (2) composite height-diameter prediction equation for diameter-class-specific height estimation. Module C deployed a dimensional compatible taper equation developed for red pine by Sharma [26] in the estimation of stem product yields (number of pulp and saw logs, and utility poles) and stem volumes at the individual tree, diameter class and stand levels. Module D entailed the employment of a set of allometric-based biomass equations developed for red pine by Lambert et al. [27] to estimate above-ground total and component-specific (periderm, stem, branch and foliage) biomasses and associated carbon mass equivalents, also calculated at the individual tree, diameter class and stand levels. Module E utilized sawmill-specific product and value equations for generating chip and lumber volumes and associated monetary values at the diameter-class and stand levels (i.e., virtual stud and random length mill processing configurations). Note, fiscal worth estimates for recovered utility poles were arithmetically added to the chip and lumber values in order to generate a total revenue estimate at the stand level, i.e., cumulative chip and lumber inflation-adjusted fiscal worth estimates for the log-producing diameter classes (10–32 cm) incremented by the fiscal value of the poles extractable from the pole-producing diameter classes (34+ cm). Module F encompassed the employment of a suite of Silviscan-based attribute prediction models specific to red pine in order to estimate a key set of end-product-based fibre determinates [28], i.e., wood density, microfibril angle, modulus of elasticity, fibre coarseness, tracheid wall thickness, tracheid radial diameter, tracheid tangential diameter and specific surface area.

An algorithmic analogue of the resultant modular-based SSDMM was also developed and subsequently deployed to exemplify the model’s potential utility. Specifically, by simultaneously contrasting stand development trajectories and associated rotational outcomes for triple-sets of crop plans growing under varying climate change scenarios (i.e., NC (nil case; i.e., 1971–2000 climate norms), RCP4.5 and RCP8.5) at three distinct geographical localities (north-eastern, north-central and north-western Ontario, Canada). The crop plans were consistent with conventional density management protocols in terms of IS and thinning treatments and adhered to current regulatory guidelines issued for the Province of Ontario [3]. The rotational outcome measures included overall productivity metrics, log and pole product distributions, biomass production and carbon sequestration yields, quantity of recoverable mill-based end-products, duration of optimal site occupancy and structural stability indicators, operability status indices, estimates of fibre-based wood quality determinates, and economic performance measures.

In summary, the red pine SSDMM was constructed via the collective integration of the six parameterized modules deploying the hierarchical structure as presented in Figure 1 of [10]. The computational pathway as explicitly presented in the Supplementary Material section of [10], was also encapsulated within a Fortran coded algorithmic variant. This program reduced computational effort and complexity, and enabled iterative-based simulations in which locale and scenario specific candidate crop plans could be readily contrasted and evaluated across a wide array of management-relevant performance metrics. The only notable change from these initial relationships was the deployment of an updated survivorship model (i.e., Equation S-11 in [10]). Specifically, in order to better reflect survivorship patterns during the post-thinning phase of plantation development, an enlarged portion of the initial data set which included survivorship observations from both unthinned and thinned plantations, was used to reparameterize the net density change function (Equation S-11 [10]), resulting in the revised parameter estimates: −0.76 × 10⁻⁹, −1.398753, 2.036377 and 2.358288 for ${\phi }_0,{\phi }_1,{\phi }_2\mathrm{and}{\phi }_3$, respectively. The relationship, based on 390 observations of which approximately 65% were from thinned plantations, explained most of the variation (99%) with a standard error of estimate of 21 stems/ha/year. Statistically, the regression relationship was in general compliance with the underlying constant error variance and normality assumptions as inferred from graphical-based residual analyses.

2.2. The Red Pine SSDMM: Evaluation of Predictive Ability

Realistically, the likelihood of acquiring adequate testing data sets from either inventory-based censuses (e.g., permanent sample plot (PSP) systems) or density-control experiments for a comprehensive full-model evaluation is minimal given the diversity of output variables produced by the SSDMM. For example, estimates of biomass and carbon outcomes, recoverable end-product volumes and fibre attributes are not commonly available from such PSP systems or experimental measurements. However, focusing on the prediction accuracy of the temporal mean volume–density trajectories and associated mean tree-level (e.g., mean dominant height, quadratic mean diameter, mean volume and mean live crown ratio) and stand-level (e.g., basal area, total and merchantable volumes, total density and relative density) predicted metrics generated within Module A, can be constructive given their consequential role as predictor variables within the downstream subordinate-based modules (sensu [29]). For example, the Weibull-based PPES, composite height-diameter, taper, biomass and end-product recovery functions, and the hierarchical fibre attribute equations, are all dependent on such predictors (see Figures 1 and SM2-1 and accompanying Table SM2-1, in [10]). Thus such an approach was utilized in this study. Specifically, the predictive accuracy of the key driving variables produced within Module A were evaluated using the mean prediction error statistic [30]: mean dominant height (H_d (m)), density (N (stems/ha)), mean volume ($\overline{v}$ (dm³)), total volume (V_t (m³/ha)), merchantable volume (V_m (m³/ha)), quadratic mean diameter (D_q (cm)), basal area (G (m²/ha)), relative density index (P_r (%/100)) and live crown ratio (L_r (%)).

2.3. The Red Pine SSDMM: Exemplifications in Crop Planning Decision-Making

In order to demonstrate the potential utility of the algorithmic analogue of the red pine SSDMM, three conventional crop plans for a medium-to-good site quality (site index of 23 m at a breast-height age of 50 year) were simulated for three climate change scenarios (NC (1971–2000 climate norms), RCP4.5 and RCP8.5) spanning three commitment periods (present-2040, 2041–2070, and 2071–2100) at three geographically distinct locales in central Canada (north-east (Kirkland Lake), north-central (Thessalon) and north-west (Thunder Bay) Ontario). The SSDMM simulations consisted of inputting the relevant bioclimatic variables unique to each commitment period, climate change scenario, and locale (

Table 1. Bioclimatic variables by commitment period, climate change scenario and geographical locale: observed historical climate norms (1971–2000; NC) and projected values consistent with the RCP4.5 and RCP8.5 climate change scenarios.

Input Parameter (Unit)	NC	RCP4.5			RCP8.5
	1971–2000	2011–2040	2041–2070	2071–2100	2011–2040	2041–2070	2071–2100
Location a: Thunder Bay, Ontario (north-western)
Mean temperature during growing season (°C)	11.3	14.19	14.74	15.41	14.21	15.56	17.27
Total precipitation during growing season (mm)	455.4	485.2	549.7	544.2	545	532	565.3
Location a: Thessalon, Ontario (north-central)
Mean temperature during growing season (°C)	13.5	14.36	15.05	15.73	14.49	15.85	17.76
Total precipitation during growing season (mm)	503.3	586.6	666.8	635.7	600	634.8	620.8
Location a: Kirkland Lake, Ontario (north-eastern)
Mean temperature during growing season (°C)	11.2	14.14	14.67	15.38	14.29	15.9	17.78
Total precipitation during growing season (mm)	482.3	516.9	579	576.8	537.6	566.1	579.3

All forecasted values for climatic parameters were generated from the second-generation Canadian Earth System Model (CanESM2) which consisted of a physical atmosphere–ocean model (CanCM4) coupled to a terrestrial carbon model (CTEM) and an ocean carbon model (CMOC) [31]. Locale-specific estimates for all three locations were indirectly provided by a customized spatial climatic algorithm that was based on the CanESM2 ([32]). The only exception was that of the 1971–2000 climate norms for the Thessalon site which had to be obtained from the tabular data records documented for the Mississagi Ontario Hydro Station. (https://climate.weather.gc.ca/climate_norms/index_e.html; accessed on 1 June 2021). Specifically, over the April to September period for the 1971–2000 calendar years, monthly mean daily temperatures and monthly total rainfall amounts were extracted from such and seasonal means subsequently generated. ^a Longitude and latitude in decimal degrees for Thunder Bay, Ontario (north-western), Thessalon, Ontario (north-central) and) Kirkland Lake, Ontario (north-eastern) locales were respectively: −89.2500 and 48.3833; −83.6888 and 46.3519; and −80.0333 and 48.1500.

) and subsequently generating stand development trajectories over 75-year rotations (2022–2097). Note, (1) all 3 crop plans assumed a site preparation treatment that preceded the planting of 2000 genetically-improved seedlings per hectare, and (2) density management treatments, rotation length, merchantable specifications, operability targets and economic assumptions were all consistent with management practices and regulatory frameworks currently applicable within the Ontario region.

Table 2. Input parameters for the SSDMM simulations for red pine plantations growing on medium-to-good quality sites.

Parameter (Units) a	Regime 1	Regime 2	Regime 3
	(IS)	(IS+1CT)	(IS+2CTs)
Rotation age (year)	75	75	75
Planting year	2022	2022	2022
Simulation years	2022–2097	2022–2097	2022–2097
Initial planting density (stems/ha)	2000	2000	2000
Genetic worth (%)/selection age (year)	8/15	8/15	8/15
1st CT: stand age (year)/basal area removal (%)	-	55/35	40/20
2nd CT: stand age (year)/basal area removal (%)	-	-	55/20
Operational adjustment factor (%)	0.01	0.01	0.01
Merchantable Specifications
Pulp log length (m)	2.59	2.59	2.59
Pulp log minimum diameter (inside bark; cm)	10	10	10
Saw log length (m)	5.03	5.03	5.03
Saw log minimum diameter (inside-bark; cm)	14	14	14
Merchantable top diameter (inside-bark cm)	10	10	10
Minimum utility pole length (m)	12.2	12.2	12.2
Minimum pole upper diameter (inside-bark; cm)	19.9	19.9	19.9
Minimum pole diameter class (outside-bark; cm)	34	34	34
Product degrade (%)	10	10	10
Minimum Operability Targets
Piece-size (merchantable stems/merchantable m3)	10	10	10
Merchantable volumetric stand yield (m3/ha)	200	200	200
Economic Parameters
Interest rate (%)	2	2	2
Discount rate (%)	4	4	4
Mechanical site preparation (CAD/ha)	300	300	300
Planting (CAD/seedling)	0.8	0.8	0.8
1st CT costs: variable (CAD/m3 of merchantable volume removed)/fixed (CADha)	-	75/300	75/300
2nd CT costs: variable (CAD/m3 of merchantable volume removed)/fixed (CAD/ha)	-	-	65/300
Rotational harvesting+stumpage+renewal+ transportation+manufacturing variable costs (CAD/m3 of merchantable volume harvested)	75	65	55
Current net pole value (CAD(K)/pole)	0.3	0.3	0.3

^a A medium-to-good quality site was nominally defined as having a site index value of 23 m (i.e., mean dominant height of 23 m at a breast-height age of 50 [18]). Genetic worth is the percentage increase in dominant height growth expected to occur at the specified selection age (see Appendix B of [10] and [16] for more specifics). Operational adjustment factor is the annual mortality rate attributed to non-density-dependent abiotic and biotic causes. Product degrade is an end-user-specified allowance for correcting for the potential over-estimation arising from the use of product prediction functions derived from virtual sawmill-based simulations (sensu [33]). Note, all fiscal input variable values are informed approximations. Computationally: (1) variable cost estimates for thinning treatments include all on-site equipment operating costs, stumpage payments, renewal fees, transportation expenses and manufacturing costs and are collectively expressed as a function of merchantable volume removed (sensu [34]); (2) fixed cost estimates for thinning included forest management fees (e.g., tree marking) and equipment movement costs (to and from the site); and (3) rotational variable cost estimates for final harvesting include all those associated with operating harvesting equipment, statutory stumpage payments and renewal fees, transportation expenses and manufacturing processing costs, and are collectively expressed as a function of the quantity of merchantable fibre harvested.

provides a complete list of the specific input variables and model parameter settings deployed for each crop plan.

3. Results and Discussion

3.1. Synopsis of the Climate-Sensitive Modular-Based SSDMM and Algorithmic Analogue Deployed: Hierarchical Structure, Computational Pathway, Software Design and Performance Indices Produced

Briefly, as illustrated in Figure 1 and explicitly described in the Supplementary Materials section of [10] (Figure SM2-1 and accompanying Table SM2-1), the sequential integration of the six individual modules within the hierarchical-based modelling framework yielded the computational pathway utilized within the red pine SSDMM. Subsequently, translating and coding this pathway into the Fortran programming language resulted in an algorithmic analogue capable of readily generating locale-specific SSDMMs and associated annual and rotational estimates of mensurational metrics (mean tree dimensions and site occupancy measures), volumetric yields, log and pole product distributions, biomass and carbon sequestration outcomes, end-product recovery volumes and associated fiscal worth values, wood quality indicators and ecosystem service performance measures, for any end-user-specified crop plan and climate change scenario [10]. Furthermore, in order to maintain numeric equivalency among the various volumetric yield and product-based estimates, the program also embedded a number of internal computations and associated validation tests. These included ensuring approximate equivalence between the (1) quadratic mean diameter value generated from the yield–density relationship and that generated from the corresponding recovered diameter distribution (e.g., recovery of the diameter distribution is negated for a given rotation year if the estimates differ by more than ±25%), (2) dominant height estimates derived from the site-specific height–age function and that derived from the recovered height distribution (e.g., rescaling the recovered height distribution to attain equivalence with the site-based dominant height estimate [15]), and (3) merchantable stem volume estimate and the additive sum of the mill-specific lumber and chip volumes (e.g., adjusting the product volume estimates to comply with the merchantable volume estimate when the former was greater than the latter [15]). Additionally, enhanced input options where included within the crop planning graphical user interface (GUI) that enabled the end-user to introduce or modify various assumptions that could affect yield and end-product outcomes, and resultant performance indicators. These included the ability to define the (1) operational adjustment factors for density-independent mortality, (2) merchantability specifications for logs and poles in order to dynamically respond to changes in harvesting thresholds or market requirements as they occur, (3) type and rate of growth responses for genetic worth effects, and (4) product degrade levels, inflation and discount rates, and fixed and variable cost estimates. For the climate-sensitive simulations, input for the geo-referenced temperature and precipitation values specific to each commitment period for the selected climate change scenario (e.g., NC, RCP4.5, RCP8.5) are also required. Procedurally, these values can be either inputted manually by the end-user or auto-populated by the program when crop planning for one of the three representative Ontario-centric locations (north-east (Kirkland Lake), north-central (Thessalon) or north-western (Thunder Bay), Ontario, e.g., Table 1).

Ultimately, the computational sequence yields an extensive array of output for each specified crop plan. More comprehensively, for each rotation year along the size–density trajectory predicted for a given crop plan, the program recovers the grouped-diameter frequency distribution. For each diameter class recovered, the program then provides an estimate of total tree height. Thus, given diameter class, tree height and class density information, the number of pulp-logs, saw-logs and utility poles extractable (according to merchantability specifications inputted by the end-user), merchantable and total volumetric stem yields, component-specific biomasses and associated carbon masses, sawmill-specific recoverable chip and lumber volumes and associated fiscal worth values, and breast-height-positioned wood quality attributes, can be predicted. Cumulative total stand-level values are subsequently generated for each output variable. The output is presented in both tabular and graphical formats inclusive of the size–density trajectories displayed in the traditional SDMD graphic, regime-specific annual estimates at the individual diameter-class and stand levels, regime-specific thinning treatment yields and rotational summaries, and regime-based rotational contrasts across a subset of crop planning performance metrics.

These latter rotational performance indices were considered key determinates underlying optimal crop plan selection: i.e., (1) overall volumetric, biomass and carbon sequestration productivity as measured by mean annual merchantable volume increment (R_MAI; m³/ha/year), mean annual biomass increment (R_BMI; t/ha) and mean annual carbon increment (R_CAI; t/ha), respectively; (2) percentage of saw logs produced (R_SL; %); (3) mill-based end-product production expressed as the percentage of lumber volume recovered via the stud sawmill processing protocol (R_LV(s); %); (4) number of utility poles produced (N_up; poles/ha); (5) relative land expectation value (E_(s); %); (6) duration of optimal site occupancy (S_O; %); (7) stand stability as quantified by the mean height/diameter ratio for the dominant crown classes (S_S; m/m); (8) time to operability status as measured by the number of years that a plantation requires to reach harvestable status as defined by end-user-specified piece size (number of merchantable stems per cubic metre of merchantable volume harvestable; stems/m³) and overall stand-level merchantable yield (merchantable volume per unit area; m³/ha) thresholds (O_T; year); and (9) suite of Silviscan-based end-product-based attribute determinates: mean basal-area weighted fibre attribute values for wood density (${\overline{W}}_{d(T)}$), microfibial angle (${\overline{M}}_{a(T)}$), modulus of elasticity (${\overline{M}}_{e(T)}$), fibre-coarseness (${\overline{C}}_{o(T)}$), tracheid wall thickness (${\overline{W}}_{t(T)}$), tracheid radial diameter (${\overline{D}}_{r(T)}$), tracheid tangential diameter (${\overline{D}}_{t(T)}$) and specific surface area (${\overline{S}}_{a(T)}$). Refer to Table SM3-1 within the Supplementary Materials section of [10] for the complete computational details underlying these performance indices.

3.2. Predictive Performance of Temporal Stand Dynamic Determinates

The predictive ability of the principal relationships within Module A were examined. These collectively govern temporal stand development and drive the majority of the downstream modules inclusive of their module-specific embedded relationships (refer to Figures 1 and SM2-1 in [10] for complete details). Analytically, the assessment consisted of (1) extracting a subset of sequential plot measurements from individual density management experiments within the parameterization data set, (2) given (1), deploying the non-climate-sensitive algorithmic analogue to simulate their temporal size–density trajectories based on their stand configurations (e.g., stand age, initial density and site quality) across three differential density-independent mortality rates (i.e., operational adjustment factors), and (3) given (2), quantifying the magnitude of the resultant absolute and relative errors using the mean prediction error statistic [30] for nine of the principal driving variables (e.g., H_d, N, $\overline{v}$, V_t, V_m, D_q, G, P_r and L_r). Appendix A provides a complete account of the analytics and results obtained. In summary, the results based on 256 plot measurements derived from 65 experimental and monitoring plots, revealed adequate predictive ability. Specifically, the validation results indicated that the red pine SSDMM produced relatively accurate predictions for all of the variables evaluated: i.e., within ±15% of their true values. This magnitude of predictive error across all nine variates is within the threshold recommended for operational growth and yield projection systems [30] (i.e., ±20%). Furthermore, the magnitude of the relative prediction errors was similar to those reported for the SSDMMs developed for boreal conifers (e.g., less than ±20% (Appendix A in [29])). However, given the limited inferential utility of assessing predictive ability when deploying a validation data set that is not independent of the parameterization data set, as presented in this study, a cautionary approach should be exercised when interpreting the results. Specifically, the reported magnitude of the resultant error metrics should be considered as preliminary and tentative approximations pending the availability of large, regional-wide and independent validation data sets.

It is also acknowledged that these results pertain to model performance with respect to the calibration data sets and hence without consideration of climate change effects. Consequently, the inability to accommodate such effects within this assessment limits the utility of the error metrics in terms of their applicability regarding future forecasts during the Anthropocene. Overall however, the results are nevertheless useful in assessing the underlying quantitative axioms deployed in the SSDMM or when non-climatic sensitive crop planning is warranted. In this regard, the results largely confirmed the applicability of a number of these axioms in terms of their quantitative performance when integrated within the SSDMM (e.g., collective ability of the yield–density relationships to precisely describe site-dependent crop plan trajectories as reflected in the accuracy of the derived yield estimates [10]).

Numerically, these validation results are also consistent with those reported for the dynamic structural SDMDs developed using a state-space modelling approach by Stankova and Diéguez-Aranda [35] for natural-origin English oak (Quercus robur L.) and Downy birch (Betula pubescents Ehrh.) stand-types and Radiata pine (Pinus radiata D. Don) and Scots pine (Pinus sylvestris L.) plantations, in Europe. Specifically, error metrics for these dynamic structural model variants with respect to quadratic mean diameter, stand density, total volume and biomass projections were within ±20% of their true values for three of the stand-types (English oak and downy birch, Radiata pine,) and within ±40% for Scots pine plantations. It was concluded that the larger errors associated with the Scot pine model arose principally from the marginal prediction performance of the underlying dominant height model. This inference is of consequence given that the dynamic and structural model variants, similar to most other stand-level growth and yield models, deploy the site-specific mean dominant height–age function as the principal determinate underlying temporal stand dynamics. For example, it is the main driver underlying the rate of progression of the size–density trajectory as it transverses a species-specific size–density space, as illustrated within the traditional SDMD graphic. Additionally, the function is commonly employed to account for genetic worth, thinning or climate change effects on forest productivity through a rate parameter modification approach (sensu [36]). For example, the site-specific height–age model is re-specified by the inclusion of rate parameter modifiers for precipitation and temperature in order to reflect changing temporal dynamics arising from anthropogenic climate change (e.g., [18,37]). Thus, imprecise descriptions of the site-specific height–age development patterns will have consequential effects on overall predictive precision.

3.3. Applicability of a Principal Ecological Axiom Shared among SDMD Model Variants: The Self-Thinning Rule

The static, dynamic and structural SDMD model variants all share commonalities in terms of their underlying ecological and functional foundation, particularly with respect to resource competition axioms, self-thinning theory, reciprocal yield–density relationships, site occupancy-forest productivity constructs, and stand dynamic determinates (e.g., site quality effects on stand dynamics and self-thinning processes). Among these shared commonalities, the asymptotic size-density relationship as quantified by the self-thinning rule, is arguably one of the most consequential relationships employed given its empirical applicability, analytical utility and universal ecological theoretical worth (sensu [13,29,38,39]). More precisely, the relationship quantitatively bounds a species size-density space, yields an asymptotic reference to quantify relative site occupancy which is used to inform stand-level density regulation decisions, and provides density-dependent mortality likelihoods as self-thinning proceeds. The relationship also represents a direct conceptual linkage to plant biology population, stand dynamics and forest production axioms (e.g., density–dependency and site determinates underlying structural change, survival and allometric relationships within plant populations). This linkage contributes substantially to the overall ecological integrity of the SDMD modelling approach which largely differentiates it from the more commonly used empirical-based approaches used in traditional stand-level growth and yield modelling. Thus given its analytical and theoretical importance across all of the SDMD model variants including the red pine SSDMM evaluated and exemplified in this study, an examination of its underlying conceptual formulation initially proposed by Yoda et al. [20] along with subsequent alternative reformulations proposed for forest tree populations, as they relate to red pine, is warranted.

Briefly, Yoda et al. [20] proposed the first conceptual explanation for the repeatedly and consistently observed relationship between mean plant size and population density within numerous natural and cultured plant populations undergoing self-thinning. Quantitatively, this universally observed relationship was one that could be described by a power law specification with a reoccurring common exponent, or slope when expressed in logarithmic terms, of −3/2, irrespective of species, population structure or site quality (e.g., as observed within a wide range plant populations consisting of annual cereal crop species to long-lived forest tree species growing in pure stands and bivariate mixtures of varying fertility). In order to provide a more functional explanation of this generic empirical relationship, Yoda et al. [20] proposed a geometrical deviation based on the assumptions that (1) self-thinning occurs only when the total coverage of a stand exceeds 100% and so operates as to maintain 100% cover, and (2) plants of the same species are always geometrically similar in shape irrespective of growth stage or habitat conditions. Consequently, (1) mean volume or biomass ($\overline{v}$) per surviving plant can be expressed as a function of the cube of some unspecified linear plant dimension (l), thus yielding $\overline{v}\propto l^3$, (2) mean ground area occupied by a plant (s) can be expressed as a function of the square of this linear dimension, thus yielding $s\propto l^2$, (3) s can be expressed as an inverse proportional function of population density (N), thus yielding $s\propto N^{-1}$, and (4) combining (1), (2) and (3), therefore yields $s\propto l^2\propto {\left(l^3\right)}^{2/3}\propto {\overline{v}}^{2/3}\propto N^{-1}$ and hence the proportionality $\overline{v}\propto N^{-3/2}$ with the power exponent of −1.5.

Given the considerable debate on the relative merits and applicability of this derivation particularly as it relates to self-thinning forest tree populations, numerous alternative formulations have been proposed since the pioneering work of Yoda and colleagues (e.g., [40,41,42,43,44,45]). Representative examples of the resultant allometric and mechanical reformulations include those proposed by Enquist et al. [44] and Newton [45], respectively. Specifically, Enquist et al. [44] proposed a reformulation derived from the universal scaling law [46]. This deviation was based on three key assumptions: (1) sessile plants compete for spatially-limiting environmental resources; (2) the rate of resource use per individual plant $\left(Q\right)$ scales with size according to the proportionality $v^{3/4}$$\left(Q\propto v^{3/4}\right)$; and (3) plants grow until they are limited by resource supply. Thus the maximum number of plants that can be supported per unit area is related to the rate of resource supply per unit area (R) and the average rate of resource use per individual $\left(\overline{Q}\right)$, i.e., $R\approx N\cdot \overline{Q}\approx N\cdot {\overline{v}}^{3/4}$. Hence, when the rate of resource use approximately equals the rate of resource supply within a given environment, R becomes a constant yielding the proportionality $N\propto {\overline{v}}^{-3/4}$, ultimately giving a conceptual derived self-thinning exponent of −1.3 when solved for mean biomass or volume.

The empirical mean volume—density relationship for self-thinning red pine plantations along with the conceptual-based reformulations proposed by Yoda et al. [20] and Enquist et al. [44] are graphically illustrated in Figure 1. Specifically, the conceptually-derived relationships were parameterized deploying the selected interval data set (2.95–3.75 log₁₀(N) range with n_max = 50 (42)) used to establish the self-thinning relationship as described in Newton [10]. The resultant logarithmic intercept and self-thinning exponent estimates were respectively 7.797 and −1.5 for Yoda’s fixed slope derivation, and 7.196 and −1.333 for Enquist’s allometric-based derivation. The approximate equivalence between self-thinning exponents proposed by the Enquist conceptual model (−1.333) and the actual empirical result determined by bisector regression analysis (−1.322), provides a measure of empirical validity to this allometric-based deviation.

Although the value predicted by the reformulation proposed by Yoda et al. [20] (−1.5) was within the 95% confidence interval of the resultant empirical exponent value for red pine, its was markedly different in terms of its absolute value. Likewise, so is the self-thinning exponent for red pine plantations previously reported by Smith and Woods [9] (i.e., −1.587).

The approximate equivalence between the empirically determined self-thinning relationship and the allometric model proposed by Enquist et al. [44], not only provides a measure of supplemental support for the deployment of the self-thinning rule within the red pine SSDMM but also for the species-specific applicability of this allometric-based reformulation, as derived from the universal scaling law [46]. Additionally, the red pine exponent is approximately equivalent to the meta-like empirical-based mean exponent reported by Enquist et al. [44] for a wide range of plant types, sizes and species (e.g., ranging from the smallest annual crop species (e.g., radish (Raphanus sativus L.)) to the largest long-lived tree species (e.g., giant Sequoia (Sequoiadendron giganteum Lindl. [Buchholz])): −1.341 as determined from 251 self-thinning plant populations.

The mechanical deviation was based on dimensional relationships and space competition assumptions among neighbouring trees within structurally unstratified, monospecific and even-aged self-thinning stands [45]. More specifically, reformulation as similarly presented previously [45] utilizes allometric, geometric and dimensional relationships specific to excurrent coniferous tree species. Although considerably less general than that of Enquist et al. [44], this reformulation acknowledges the species and allometric specificity of the rule (sensu [47,48]) in terms of stem and crown characteristics and competitive interaction mechanisms. For example, the spatially non-contiguous nature of crown cover (crown shyness) combined with the numerous crown collisions commonly observed at high wind velocities within density-stressed conifer populations suggests that physical competition for space may be partially responsible for self-thinning behaviour. Wind-induced crown abrasion among individual trees within density-stressed stands resulting in the loss of branches and associated leaf area has been documented for a number of coniferous species (e.g., balsam fir (Abies balsamea (L.) Mill; [49]) and lodgepole pine (Pinus contorta var. latifolia; [50])). Although the resultant crown shyness is a predictable structural outcome of repeated crown collisions, the cumulative effect of the continuous loss of photosynthetic biomass is largely unknown, particularly in terms of its effects on tree survival. Conceptually, however, the continuous loss of foliar mass, principally among the smaller trees, may potentially produce mortality patterns analogous to those observed within a light-based dominance–suppression competitive relationship. This latter relationship is one that has been characterized as an asymmetrical resource pre-emption competitive process in which the smaller individuals do not receive sufficient solar radiation due to passive shading from the larger individuals, eventually resulting in declining growth rates and their subsequent mortality (e.g., [51]). Hence, given the observational evidence obtained from ocular assessments of crown sway dynamics, it is suggested that wind-induced crown friction among individuals within density-stressed pine stands may also be a plausible determinate underlying the self-thinning process.

Quantitatively, this hypothesis can be postulated through the following mechanical-based reformulation ([45]): (1) assuming that within density-stressed stands during wind events, trees sway in a manner in which their mean spatial volume requirement $\left({\overline{s}}_v\right)$ can be approximated by a conical geometric solid (inverted neiloid), and hence yielding the proportionality,

$$s\propto a_s\propto r_s{}^2\propto h^{2\varphi }\propto N^{-1}\mathrm{where}{r}_s\propto h^{\varphi }\left\{\varphi =1.5\left(\mathrm{neiloid}\right)\right.$$

where a_s is the crown sway area at the apex of the tree (top of the inverted neiloid), r_s is the radius of a_s, and h is the height of the tree which is equivalent to the vertical dimension of ${\overline{s}}_v$; (2) assuming that the (i) mean stem volume of a excurrent tree resembles a conical geometric solid, and (ii) tree height scales with basal radius $\left(r_B\right)$ in order to maintain physical stability according to the geometric and elastic similarity axioms (e.g., [52]), yields the proportionality,

$$\overline{v}\propto r_B^{2}h\propto h^{2\phi +1}\mathrm{where}{r}_B\propto h^{\phi }\left\{\begin{array}{l}\phi =1.0\left(\mathrm{geometric}\mathrm{similarity}\mathrm{model}\right)\\ \phi =1.5\left(\mathrm{elastic}\mathrm{similarity}\mathrm{model}\right)\end{array}\right.$$

and (3) given (1) and (2), therefore yields the combined relationship,

$$s\propto {\left(h^{2\phi +1}\right)}^{2\varphi /\left(2\phi +1\right)}\propto {\overline{v}}^{2\varphi /\left(2\phi +1\right)}\propto N^{-1}.$$

Hence yielding the reformulated self-thinning proportionality: $\overline{v}\propto N^{-\left(2\phi +1\right)/2\varphi }$

Thus assuming that $\varphi$ is approximately equivalent to 1.5 (neiloid assumption for crown occupancy when swaying), and $\phi$ ranges in value from 1.0 to 1.5 (physical stability requirement), the self-thinning exponent would be expected to vary between −1.00 and −1.33. Furthermore, based on the empirically determined exponent for red pine observed in this study (−1.322) and tentatively accepting that $\varphi$ is approximately equivalent to 1.5, it is indicated that the predicted scaling exponent ($\phi$) for red pine would be equivalent to 1.5 (1.483). This hypothesized result suggests that the mechanical height scaling pattern of red pine is most consistent with elastic similarity model. Thus in summary, the self-thinning exponent predicted by this mechanical reformulation is largely in numeric compliance with the observed empirical value of −1.322 when assuming an elastic allometric relationship. Although further investigations are required to confirm the generality of this reformulation, the presentation of this alternative mechanical-based explanation with respect to jack pine [45] and red pine (this study) may provide additional insights into the potential mechanisms underlying self-thinning behaviour within these Pinus stand-types.

More universally, the overwhelming empirical evidence in support of the applicability of the self-thinning rule across the plant kingdom along with the associated functional explanations of self-thinning behaviour, has yielded one of the principal axioms of plant ecology (sensu [53]). The analytical results and associated geometric, allometric and mechanical explanations of the rule as exemplified in this study. provides additional confirmatory support in terms of its theoretical worth and empirical utility, not only for the red pine SSDMM but also for all the SDMD model variants. Furthermore, recent evidence suggesting the invariant nature of the self-thinning exponent with changing growing environments [54] bodes well for its continued deployment within climate-sensitive models including SSDMMs.

3.4. Exemplification of the Red Pine SSDMM in Crop Planning

Three conventional crop plans for plantations established on medium-to-good site qualities (site index of 23 m at a breast-height age of 50 year) were simulated for three climate change scenarios (NC, RCP4.5 and RCP8.5) spanning three commitment periods (present–2040, 2041–2070, 2071–2100) over a 75-year rotation (2022–2097) at three different locales in the Province of Ontario (north-east (Kirkland Lake), north-central (Thessalon), and north-west (Thunder Bay)). The SSDMM simulations consisted of inputting the required locale-specific bioclimate variables (Table 1) and the crop planning details (Table 2) for each of the three climate change scenarios and locales via the algorithm’s input GUI input screen. Ultimately, this yielded nine crop plan sets each consisting of three silviculturally distinct density management regimes for a combined total of 27 crop plans, i.e., 3 silviculturally distinct density management regimes (IS; IS + 1 CT; and IS + 2 CTs) × 3 climate change scenarios/regime (NC; RCP4.5; and RCP8.5) × 3 locales (Thessalon, Kirkland Lake, and Thunder Bay). The actual values for the climate variables used in conjunction with the biophysical site-specific height–age function for each of the three scenarios by commitment period and geographic locale (Table 2) were derived from a spatial-referencing climatic algorithm [32]. This climatic algorithm produced output based on the embedded second-generation Canadian Earth System Model (CanESM2) which consisted of a physical atmosphere–ocean model (CanCM4) coupled to a terrestrial carbon model (CTEM) and an ocean carbon model (CMOC) [31].

The exemplified crop plans were designed in accordance with a net production maximization objective in terms of allowing plantations to attain an optimal level of site occupancy before the initiation of the first thinning treatment (0.35 ≤ P_r ≤ 0.50) while also encouraging individual tree development during the post-thinning phase (e.g., maximizing individual tree growth in order to yield larger sized trees with greater end-product potential by maintaining relative densities below 0.35). Consequently, the following three crop plans were considered at each locale for each of the climate change scenarios: (1) initial planting of 2000 seedlings/ha (2.2 × 2.2 m spacing; Regime 1); (2) initial planting of 2000 seedlings/ha with one subsequent CT treatment at a stand age of 55 years in which 35% of the basal area is removed (Regime 2); and (3) initial planting of 2000 seedlings/ha with two subsequent CT treatments, the first one at a stand age of 40 years in which 20% of the basal area is removed, and the second one at a stand age of 55 years during which 20% of the basal area is also removed (Regime 3). These specific thinning ages and thinning-induced basal area reductions were selected from multiple iterative simulations of the model under the climate normal scenario for a medium-to-good site quality. Overall, the deployed thinning prescriptions, rotation ages, merchantable specifications, genetic worth effects, operability targets and economic parameters were consistent with current management practices and expectations within the chosen locales. Furthermore, the CT treatments complied with regulatory defined guidelines with respect to pre-treatment stand conditions and removable thresholds [3], i.e., mean live crown ratio of ≥35%, basal area of ≥25 m²/ha, and basal area removals of ≤35% of the pre-treatment level. A complete account of the initial model parameter settings inclusive of thinning treatment specifics for each crop plan is given in Table 2.

In order to graphically exemplify the temporal mean volume–density trajectories for a crop plan set, the resultant traditional SDMD graphic is presented for each climate scenario. Specifically, crop plans growing under the (1) NC scenario at the north-central locale (Thessalon, Ontario) are illustrated in Figure 2, (2) RCP4.5 scenario at the north-eastern locale (Kirkland Lake, Ontario) are illustrated in Figure 3, and (3) RCP8.5 scenario at north-western locale (Thunder Bay, Ontario) are illustrated in Figure 4. Additionally, in order to demonstrate the interpretation utility of the graphic in terms of manually interpolating yield estimates and inferring stand dynamical patterns, the following numerical account of the crop plan set developed under the NC scenario is given. Specifically, as inferred by the intersection of the size–density trajectories with the crown closure isoline for the NC simulations (Figure 2), initial crown closure status was attained at age 15 for all three regimes. For Regime 1, the size–density trajectory adhered to the self-thinning expectations as it approached a relative density value of 0.5. The interpolated yield estimates at rotation for the 690 crop trees indicated an optimal stocked condition (basal area (derived from quadratic mean diameter and density) and relative density values of 48 m²/ha and 0.43, respectively) with lower overall mean tree sizes relative to the thinned regimes (i.e., mean tree volume of 825 dm³ versus 1386 dm³ (Regime 2) and 1457 dm³ (Regime 3); and quadratic mean diameter values of 30 cm versus 38 cm (Regime 2) and 39 cm (Regime 3). For Regime 2, the size–density trajectory at the time of the CT treatment (age 55) was approximately intersecting the 24 m dominant height (Hd), 22 cm quadratic mean diameter (Dq), 0.4 relative density (Pr) and 35% live crown ratio (Lr) isolines and hence was in general compliance with the CT guidelines proposed by Kayahara et al. [55] and endorsed by the regulator [3]. The corresponding interpolated mean volume, density and basal area values at age 55 were 405 dm³, 1211 stems/ha and 48 m²/ha, respectively. The CT treatment resulted in reducing the basal area by 35% (17 m²/ha) and yielded an interim merchantable volume harvest of 162 m³/ha from the 772 thinned trees. For Regime 3, the size–density trajectory at the time of the first CT treatment (age 40) was approximately intersecting the 20 m dominant height (Hd) isoline, directly below the 18 cm quadratic mean diameter (Dq) and 0.35 relative density (Pr) isolines, and slight below the 40% live crown ratio (Lr) isoline. Similarly, at the time of the second CT treatment (age 55), the trajectory was approximately intersecting the 24 m dominant height (Hd) isoline, 26 cm quadratic mean diameter (Dq) isoline, 0.3 relative density (Pr) isoline, and 40% live crown ratio (Lr) isoline. The basal area values of the pre-treatment plantations were 39 m²/ha (first CT) and 38 m²/ha (second CT). Collectively, these pre-treatment conditions also met the regulatory guidelines issued for CT candidate stands [3]. The first CT treatment resulted in a reduction of 20% (8 m²/ha) in basal area and yielded an interim merchantable volume harvest of 62 m³/ha from the 646 thinned trees. The second CT treatment resulted in reducing the basal area also by 20% (8 m²/ha) and yielded an interim merchantable volume harvest of 75 m³/ha from the 294 thinned trees. The duration of the post-CT response delay period in which density-dependent mortality was assumed to be inconsequential while crop trees rebuilt their crowns and regained full occupancy of their newly allocated growing spaces lasted approximately 8 years for the single thinning in Regime 2, and 3 and 5 years, respectively, for the first and second thinning in Regime 3 (n., occurrence and duration inferred from the initial vertical-like post-thinning size-density trajectories). By rotation, the thinned plantations had attained approximate equivalence in terms of mean tree size (quadratic mean diameters of 38 and 39 cm for Regime 2 and 3, respectively), and site occupancy (relative densities of 0.26 and 0.25 for Regime 2 and 3, respectively) irrespective of differences in the number, timing or intensity of the CT treatments.

Although the traditional SDMD graphic can be extremely useful in examining stand developmental pathways and resultant yield consequences of specified crop plans as just described, the computation burden of simultaneously extracting the full range of estimable yield metrics and performance measures when deploying the analytically complex SSDMM variants dictates the development of algorithmic analogues. Consequently, a Fortran 95/90/77-compliant red pine software program was developed using the Lahey/Fujitsu Fortran 95 compiler (Lahey Computer Systems Inc., Incline Village, NV, USA; [10]). Note, this red pine algorithm will be eventually translated into the more user-friendly Visual Basic^® (VB.NET; Microsoft Corp., Redmond, WA, USA) programing language and subsequently integrated into the CP_DSS (CroPlanner Decision-support Software Suite) suite, that was previously presented (i.e., [56]).

Thus, deploying the red pine algorithm for the scenario and locale specific crop plan simulations as defined in Table 2 produced a broad array of volumetric yield rotational metrics (e.g., mean tree size, site occupancy, and volumetric yield outcomes;

Table 3. Effects of climate change on SSDMM-derived rotational yield estimates for three red pine crop plans of increasing silviculture intensity at three geographic locales (north-central (Thessalon), north-eastern (Kirkland Lake) and north-western (Thunder Bay) Ontario): (1) initial spacing (IS) with no thinning (Regime 1); (2) IS with one commercial thinning (CT) treatment (Regime 2); and (3) IS with two CT treatments (Regime 3).

Index a	Locale b	Crop Plan c
(Unit)		Regime 1: IS					Regime 2: IS+1 CT					Regime 3: IS+2 CT
		Climate Change Scenario d					Climate Change Scenario d					Climate Change Scenario d
		NC	RCP4.5		RCP8.5		NC	RCP4.5		RCP8.5		NC	RCP4.5		RCP8.5
				∆		∆			∆		∆			∆		∆
$H_d$ (m)	C	28.7	28.5	−0.7	27.5	−4.2	28.7	28.5	−0.7	27.5	−4.2	28.7	28.5	−0.7	27.5	−4.2
	E	29.3	28.5	−2.7	27.2	−7.2	29.3	28.5	−2.7	27.2	−7.2	29.3	28.5	−2.7	27.2	−7.2
	W	29.2	28.4	−2.7	27.3	−6.5	29.2	28.4	−2.7	27.3	−6.5	29.2	28.4	−2.7	27.3	−6.5
$D_q$ (cm)	C	29.6	29.5	−0.3	28.5	−3.7	38.2	38.0	−0.5	36.5	−4.5	39.1	38.9	−0.5	37.2	−4.9
	E	30.0	29.5	−1.7	28.3	−5.7	38.9	37.9	−2.6	35.9	−7.7	39.7	38.8	−2.3	36.9	−7.1
	W	29.9	29.4	−1.7	28.3	−5.4	38.7	37.6	−2.5	36.0	−6.8	39.5	38.4	−2.8	36.9	−6.6
$G$ (m2/ha)	C	47.6	47.1	−1.1	45.0	−5.5	33.0	32.7	−0.9	31.5	−4.5	31.8	31.6	−0.6	30.6	−3.8
	E	49.5	47.0	−5.1	44.4	−10.3	33.9	32.6	−3.8	31.3	−7.7	32.9	31.4	−4.6	30.2	−8.2
	W	49.0	46.6	−4.9	44.6	−9.0	33.6	32.6	−3.0	31.4	−4.7	32.7	31.6	−3.4	30.3	−7.3
$\overline{v}$ (dm3)	C	825.3	811.8	−1.6	735.2	−10.9	1386.1	1362.5	−1.7	1216.9	−12.2	1456.9	1431.8	−1.7	1269.5	−12.9
	E	860.2	808.6	−6.0	715.5	−16.8	1468.0	1355.6	−7.7	1171.5	−20.2	1528.9	1426.0	−6.7	1234.0	−19.3
	W	848.1	801.2	−5.5	719.8	−15.1	1445.0	1327.7	−8.8	1180.5	−18.3	1503.5	1389.7	−7.6	1240.8	−17.5
$V_t$ (m3/ha)	C	569.2	560.3	−1.6	517.5	−9.1	566.9	558.8	−1.4	524.6	−7.5	528.3	521.5	−1.3	493.3	−6.6
	E	602.5	557.0	−7.5	505.8	−16.0	588.1	557.3	−5.2	517.1	−12.1	546.0	520.6	−4.7	485.0	−11.2
	W	593.4	551.0	−7.1	509.1	−14.2	581.6	556.1	−4.4	519.5	−10.7	540.8	521.9	−3.5	487.0	−9.9
$V_m$ (m3/ha)	C	555.6	546.7	−1.6	504.6	−9.2	552.8	544.7	−1.5	510.9	−7.6	514.8	508.1	−1.3	480.2	−6.7
	E	588.5	543.6	−7.6	493.0	−16.2	573.7	543.3	−5.3	503.4	−12.3	532.2	507.2	−4.7	472.0	−11.3
	W	579.5	537.7	−7.2	496.2	−14.4	567.4	542.2	−4.4	505.7	−10.8	527.2	508.4	−3.6	474.0	−10.1
$N$ (stems/ha)	C	690.0	690.0	0.0	704.0	2.0	288.0	289.0	0.3	302.0	4.9	265.0	266.0	0.4	281.0	6.0
	E	700.0	689.0	−1.6	707.0	1.0	285.0	289.0	1.4	309.0	8.4	266.0	265.0	−0.4	283.0	6.4
	W	700.0	688.0	−1.7	707.0	1.0	286.0	294	2.8	308.0	7.7	267.0	272.0	1.9	283.0	6.0
$P_r$ (%/100)	C	0.4	0.4	0.0	0.4	0.0	0.3	0.3	0.0	0.3	0.0	0.3	0.3	0.0	0.2	−0.1
	E	0.5	0.4	−0.1	0.4	−0.1	0.3	0.3	0.0	0.3	0.0	0.3	0.3	0.0	0.2	−0.1
	W	0.4	0.4	0.0	0.4	0.0	0.3	0.3	0.0	0.3	0.0	0.3	0.3	0.0	0.2	−1.0

Note: For within crop plan (regime) relative comparisons, ∆ denotes the (1) percentage difference relative to the NC scenario for indices expressed in absolute units, or (2) absolute percentage or proportional difference from the NC scenario for indices expressed in proportional or percentage units (e.g., relative density index). ^a Predicted rotational values. Denotations: $H_d$ is predicted mean dominant height; $D_q$ is predicted quadratic mean diameter; $G$ is predicted basal area per stand; $\overline{v}$ is predicted mean volume per tree; $V_t$ and $V_m$ are predicted total and merchantable volume per stand inclusive of thinning yields, respectively; and $N$ and $P_r$ are predicted total absolute and relative density, respectively. ^b C, E and W denote north-central (Thessalon, Ontario), north-eastern (Kirkland Lake, Ontario) and north-western (Thunder Bay, Ontario) locales, respectively (n., longitude and latitude coordinates provided in Table 1). ^c Crop plan specifics are provided in Table 2. ^d Locale-specific climate change scenario specifics are provided in Table 1.

). The relative multitude of climate change effects on these rotational metrics for each crop plan at each local is also presented in Table 3. Examining these values revealed systematic declines at rotation in attained mean heights, diameters and volumes, stocking levels and cumulative volumetric yields, with increasing climate change severity irrespective of crop plan or locale. Specifically, relative to the NC scenario for a given crop plan, consequential declines for the RCP4.5 and RCP8.5 scenarios were respectively in the order of 1%–3% and 4%–7% for mean dominant height, 0%–3% and 3%–8% for quadratic mean diameter, 1%–5% and 4%–10% for stand basal area, 2%–27% and 11%–20% for mean stem volume, 1%–8% and 7%–16% for total stand volume, and 2%–8% and 7%–16% for merchantable stand volume. Furthermore, for a given scenario, the smallest declines were consistently at the north-central locale.

These rotational yield projections can also be used to evaluate the relative silvicultural effectiveness of the specified crop plans under each of the three climate change scenarios, as demonstrated in the comparisons presented in

Table 4. Climate-specific silvicultural effectiveness comparisons among the selected red pine crop plans for plantations situated in north-central (Thessalon), north-eastern (Kirkland Lake) and north-western (Thunder Bay) Ontario: SSDMM-derived rotational yield comparisons for three crop plans growing under three climate change scenarios.

Index a	Locale b	Climate Scenario c
(Unit)		Climate Normal			RCP4.5			RCP8.5
		Crop Plan Comparison d			Crop Plan Comparison d			Crop Plan Comparison d
		IS+1CT vs. IS	IS+2CT vs. IS	IS+2CT vs. IS+1CT	IS+1CT vs. IS	IS+2CT vs. IS	IS+2CT vs. IS+1CT	IS+1CT vs. IS	IS+2CT vs. IS	IS+2CT vs. IS+1CT
		∆	∆	∆	∆	∆	∆	∆	∆	∆
$D_q$ (cm)	C	29.1	32.1	10.3	28.8	31.9	2.4	28.1	28.1	1.9
	E	29.7	32.3	8.9	28.5	31.5	2.4	26.9	26.9	2.8
	W	29.4	32.1	8.9	27.9	30.6	2.1	27.2	27.2	2.5
$G$ (m2/ha)	C	−30.7	−33.2	−5.3	−30.6	−32.9	−3.4	−30.0	−30.0	−2.9
	E	−31.5	−33.5	−4.1	−30.6	−33.2	−3.7	−29.5	−29.5	−3.5
	W	−31.4	−33.3	−3.7	−30.0	−32.2	−3.1	−20.2	−20.2	−3.5
$\overline{v}$ (dm3)	C	68.0	76.5	1.0	67.8	76.4	5.1	65.5	65.5	4.3
	E	70.7	77.7	0.8	67.6	76.4	5.2	63.7	63.7	5.3
	W	70.4	77.3	0.8	65.7	73.5	4.7	64.0	64.0	5.1
$V_t$ (m3/ha)	C	−0.4	−7.2	−1.2	−0.3	−6.9	−6.7	1.4	1.4	−6.0
	E	−2.4	−9.4	−1.2	0.1	−6.5	−6.6	2.2	2.2	−6.2
	W	−2.0	−8.9	−1.2	0.9	−5.3	−6.1	2.0	2.0	−6.3
$V_m$ (m3/ha)	C	−0.5	−7.3	−1.2	−0.4	−7.1	−6.7	1.2	1.2	−6.0
	E	−2.5	−9.6	−1.2	−0.1	−6.7	−6.6	2.1	2.1	−6.2
	W	−2.1	−9.0	−1.2	0.8	−5.4	−6.2	1.9	1.9	−6.3
$N$ (stems/ha)	C	−58.3	−61.6	−0.5	−58.1	−61.4	−8.0	−57.1	−57.1	−7.0
	E	−59.3	−62.0	−0.4	−58.1	−61.5	−8.3	−56.3	−56.3	−8.4
	W	−59.1	−61.9	−0.4	−57.3	−60.5	−7.5	−56.4	−56.4	−8.1
$P_r$ (%/100)	C	−0.1	−0.1	0.0	−0.1	−0.1	0.0	−0.1	−0.2	−0.1
	E	−0.2	−0.2	0.0	−0.1	−0.1	0.0	−0.1	−0.2	−0.1
	W	−0.1	−0.1	0.0	−0.1	−0.1	0.0	−0.1	−0.2	−0.1

Note: ∆ denotes the (1) relative percentage difference between crop plans for indices expressed in absolute units, or (2) absolute proportional difference between crop plans for indices expressed in proportional units (e.g., relative density index). ^a,b As defined in Table 3. ^c See Table 1 for climate change scenario specifics. ^d See Table 2 for crop plan specifics.

. Examination of these relative metrics revealed: (1) thinning regimes yielded increases in mean tree sizes but declines in site occupancy, irrespective of climate change scenario or locale; and (2) relative to the once-thinned plantations, the twice-thinned plantations exhibited marginal negative declines in stand-level volumetric yields irrespective of climate change scenario or locale. More precisely, relative to the no-thinning IS-only regimes (Regime 1), the plantations that received a single and heavy late rotation commercial thinning treatment (35% basal area reduction at 55 years; Regime 2) and the plantations that received two lighter mid and late rotational commercial thinning treatments (20% basal area reductions at the 40 and 55 years; Regime 3), yielded much larger sized trees (mean increases of 27%–32% and 64%–78% in quadratic mean diameter and mean stem volume, respectively) but lower overall stocking levels (means decreases of 20%–33%, 56%–62% and 10%–20% declines in stand basal area, absolute density and relative density, respectively). These relative trends were consistent across all scenarios and locales. Marginal scenario and locale specific differences were evident in the stand-level volumetric yield outcomes with the twice-thinned plantations growing under the NC and RCP4.5 scenarios exhibiting the largest declines (5%–9% and 5%–10% declines in total and merchantable volume, respectively).

Enhanced and potentially more informative climate relevant metrics and comparisons can also be extracted from the SSDMM. For example, from a climate change impact perspective, such metrics for each scenario-specific set of the exemplified crop plans at each of the three distinct geographic locales are presented in

Table 5. SSDMM-derived rotational stand-level performance indices for three crop plans growing under three climate change scenarios for red pine plantations situated in north-central (Thessalon), north-eastern (Kirkland Lake) and north-western (Thunder Bay) Ontario.

Index a	Locale b	Crop plan c
(Unit)		Regime 1: IS					Regime 2: IS+1CT					Regime 3: IS+2CT
		Climate Change Scenario d					Climate Change Scenario d					Climate Change Scenario d
		NC	RCP4.5		RCP8.5		NC	RCP4.5		RCP8.5		NC	RCP4.5		RCP8.5
				∆		∆			∆		∆			∆		∆
RMAI (m3/ha/year)	C	7.4	7.3	−1.4	6.7	−9.5	7.4	7.3	−1.4	6.8	−8.1	6.9	6.8	−1.4	6.4	−7.2
	E	7.8	7.2	−7.7	6.6	−15.4	7.6	7.2	−5.3	6.7	−11.8	7.1	6.8	−4.2	6.3	−11.3
	W	7.7	7.2	−6.5	6.6	−14.3	7.6	7.2	−5.3	6.7	−11.8	7	6.8	−2.9	6.3	−10.0
RBAI (m3/ha/year)	C	3.8	3.8	0.0	3.5	−7.9	4.6	4.6	0.0	4.4	−4.3	4.6	4.5	−2.2	4.4	−4.3
	E	4.1	3.8	−7.3	3.5	−14.6	4.8	4.6	−4.2	4.3	−10.4	4.6	4.5	−2.2	4.3	−6.5
	W	4	3.7	−7.5	3.5	−12.5	4.8	4.6	−4.2	4.3	−10.4	4.8	4.5	−6.2	4.3	−10.4
RCAI (m3/ha/year)	C	1.9	1.9	0.0	1.8	−5.3	2.3	2.3	0.0	2.2	−4.3	2.3	2.3	0.0	2.2	−4.3
	E	2	1.9	−5.0	1.7	−15.0	2.4	2.3	−4.2	2.1	−12.5	2.3	2.3	0.0	2.1	−8.7
	W	2	1.9	−5.0	1.7	−15.0	2.4	2.3	−4.2	2.2	−8.3	2.3	2.3	0.0	2.1	−8.7
RSL (%)	C	72	71.6	−0.4	68.5	−3.5	50	49.7	−0.3	49.6	−0.4	34.3	34.3	0	32.2	−2.1
	E	76	71.6	−4.4	67.5	−8.5	49.5	49.9	0.4	49.6	0.1	36.3	34.8	−1.5	31.9	−4.4
	W	80.3	71.3	−9	67.7	−12.6	49.5	50.1	0.6	49.6	0.1	34.9	35	0.1	31.7	−3.2
RLV(s) (%)	C	89.6	89.4	−0.2	87.9	−1.7	77.4	77.2	−0.2	76.2	−1.2	73.8	73.7	−0.1	72.8	−1
	E	90.2	89.4	−0.8	87.5	−2.7	77.3	77.3	0	75.9	−1.4	73.4	73.8	0.4	72.6	−0.8
	W	90	89.2	−0.8	87.6	−2.4	77.3	77.3	0	75.9	−1.4	73.5	73.9	0.4	72.6	−0.9
Nup (poles/ha)	C	44	35	−20.5	0	[−44]	286	287	0.3	300	4.9	263	263	0.0	279	6.1
	E	73	0	[−73]	0	[−73]	282	287	1.8	308	9.2	264	264	0.0	281	6.4
	W	63	0	[−63]	0	[−63]	283	292	3.2	305	7.8	264	270	2.3	282	6.8
E(s) ($k/ha)	C	11.1	10.8	−2.7	10.2	−8.1	21	21.1	0.5	22.4	6.7	21.8	21.8	0.0	23.4	7.3
	E	11.5	9.8	−14.8	10.1	−12.2	20.4	21.2	3.9	23.1	13.2	21.4	21.9	2.3	23.6	10.3
	W	11.6	9.8	−15.5	10.1	−12.9	20.5	21.5	4.9	22.9	11.7	21.5	22.4	4.2	23.6	9.8
$S_O$ (%)	C	48	46.7	−1.3	46.7	−1.3	21.3	20	−1.3	20	−1.3	1.3	0	−1.3	0	−1.3
	E	45.3	48	2.7	46.7	1.4	18.7	21.3	2.6	20	1.3	0	1.3	1.3	0	0
	W	45.3	48	2.7	46.7	1.4	18.7	21.3	2.6	20	1.3	0	1.3	1.3	0	0
SS (m/m)	C	99.6	99.4	−0.2	100	0.4	76.7	76.4	−0.3	76.5	−0.2	82.4	82.3	−0.1	82.4	0
	E	100.3	99.6	−0.7	99.5	−0.8	76.8	76.4	−0.4	76.5	−0.3	82.5	82.2	−0.3	82.2	−0.3
	W	101.2	99.6	−1.6	100.5	−0.7	76.8	76.6	−0.2	76.6	−0.2	82.4	82.5	0.1	82.2	−0.2
OT (year)	C	31	30	−3.2	30	−3.2	31	30	−3.2	30	−3.2	31	30	−3.2	30	−3.2
	E	33	30	−9.1	30	−9.1	33	30	−9.1	30	−9.1	33	30	−9.1	30	−9.1
	W	33	30	−9.1	30	−9.1	33	30	−9.1	30	−9.1	33	30	−9.1	30	−9.1
${\overline{W}}_{d(T)}$ (kg/m3)	C	458.7	458.7	0.0	458.8	0.0	461.1	461	−0.0	460	−0.2	461.8	461.7	−0.0	460.5	−0.3
	E	458.7	458.7	0.0	458.9	0.0	461.6	460.9	−0.2	459.8	−0.4	462.2	461.6	−0.1	460.2	−0.4
	W	458.7	458.7	0.0	458.9	0.0	461.5	460.7	−0.2	459.8	−0.4	462.1	461.3	−0.2	460.3	−0.4
${\overline{M}}_{a(T)}$ (°)	C	16.4	16.3	−0.6	15.7	−4.3	21.7	21.6	−0.5	20.7	−4.6	22.3	22.1	−0.9	21.2	−4.9
	E	16.6	16.2	−2.4	15.5	−6.6	22.1	21.5	−2.7	20.4	−7.7	22.6	22.1	−2.2	20.9	−7.5
	W	16.5	16.2	−1.8	15.6	−5.5	22	21.4	−2.7	20.5	−6.8	22.5	21.8	−3.1	21	−6.7
${\overline{M}}_{e(T)}$ (GPa)	C	10.4	10.4	0.0	10.7	2.9	8.6	8.6	0.0	8.8	2.3	8.4	8.5	1.2	8.7	3.6
	E	10.3	10.4	1.0	10.7	3.9	8.5	8.6	1.2	8.9	4.7	8.4	8.5	1.2	8.8	4.8
	W	10.3	10.5	1.9	10.7	3.9	8.5	8.6	1.2	8.9	4.7	8.4	8.5	1.2	8.7	3.6
${\overline{C}}_{o(T)}$ (µg/m)	C	502.8	502.5	−0.1	500.1	−0.5	527.1	526.5	−0.1	522	−1.0	530.3	529.6	−0.1	524.5	−1.1
	E	503.6	502	−0.3	499.5	−0.8	529.5	526.3	−0.6	520.5	−1.7	532	529.4	−0.5	523.2	−1.7
	W	503.3	501.8	−0.3	499.6	−0.7	528.9	525.4	−0.7	520.8	−1.5	531.5	528	−0.7	523.3	−1.5
${\overline{W}}_{t(T)}$ (µm)	C	3	3	0.0	3	0.0	3	3	0.0	3	0.0	3	3	0.0	3	0.0
	E	3	3	0.0	3	0.0	3	3	0.0	3	0.0	3	3	0.0	3	0.0
	W	3	3	0.0	3	0.0	3	3	0.0	3	0.0	3	3	0.0	3	0.0
${\overline{D}}_{r(T)}$ (µm)	C	34	34	0.0	33.8	−0.6	35.5	35.4	−0.3	35.2	−0.8	35.7	35.6	−0.3	35.3	−1.1
	E	34.1	34	−0.3	33.8	−0.9	35.6	35.4	−0.6	35.1	−1.4	35.7	35.6	−0.3	35.3	−1.1
	W	34	34	0.0	33.8	−0.6	35.6	35.4	−0.6	35.1	−1.4	35.7	35.5	−0.6	35.3	−1.1
${\overline{D}}_{t(T)}$ (µm)	C	31.6	31.5	−0.3	31.4	−0.6	32.6	32.5	−0.3	32.4	−0.6	32.7	32.7	0.0	32.5	−0.6
	E	31.6	31.5	−0.3	31.4	−0.6	32.7	32.5	−0.6	32.3	−1.2	32.8	32.7	−0.3	32.4	−1.2
	W	31.6	31.5	−0.3	31.4	−0.6	32.6	32.5	−0.3	32.3	−0.9	32.7	32.6	−0.3	32.4	−0.9
${\overline{S}}_{a(T)}$ (m2/kg)	C	282.1	282.1	0.0	282.5	0.1	278.9	279	0.0	279.5	0.2	278.6	278.7	0.0	279.2	0.2
	E	282	282.2	0.1	282.5	0.2	278.7	279	0.1	279.7	0.4	278.4	278.7	0.1	279.4	0.4
	W	282	282.2	0.1	282.5	0.2	278.7	279	0.1	279.7	0.4	278.4	278.8	0.1	279.4	0.4

Note, for each silvicultural regime (crop plan), ∆ denotes the (1) percentage difference relative to the NC scenario for indices expressed in absolute units, or (2) absolute percentage or proportional difference from the NC scenario for indices expressed in proportional or percentage units (e.g., lumber volumes, site occupancy, height/diameter ratio). Additionally, where no percentage comparison is possible, the absolute index value for the NC regime is included within a square bracket (i.e., number of poles per hectare at rotation). ^a Predicted rotation values. Denotations: R_MAI is the mean annual merchantable volume; R_LV(s) is the percentage of lumber volume recovered via a stud sawmill processing protocol; N_up is the number of utility poles produced per unit area; S_o is the percentage of the rotation in which the regime was maintained within the optimal relative density management window; S_s is the mean height/diameter ratio; O_T is the time to operability status as defined by the specified piece-size and merchantability thresholds; and mean basal-area weighted fibre attribute values for wood density (${\overline{W}}_{d(T)}$), microfibial angle (${\overline{M}}_{a(T)}$), modulus of elasticity (${\overline{M}}_{e(T)}$), fibre-coarseness (${\overline{C}}_{o(T)}$), tracheid wall thickness (${\overline{W}}_{t(T)}$), tracheid radial diameter (${\overline{D}}_{r(T)}$), tracheid tangential diameter (${\overline{D}}_{t(T)}$) and specific surface area (${\overline{S}}_{a(T)}$). Refer to Table SM3-1 within the Supplementary Materials section of [10] for the computational details). ^b As defined in Table 3. ^c Crop plan specifics provided in Table 2. ^d Climate change scenario specifics provided in Table 1.

. These include rotational summaries and contrasts for a set of critical stand-level performance indices related to productivity, log production, recoverable end-products inclusive of utility pole production, economic worth, optimal site occupancy, stand structural stability, operability status attainment, and wood quality fibre determinates underlying end-product potential. Examination of these comparisons revealed: (1) systematic declines in volumetric, biomass and carbon sequestration production with increasing climate change severity across all three crop plans with the plantations established at the north-central locale exhibiting the lowest declines overall (e.g., declines ranging 1%–8% and 7%–15% in merchantable volume productivity under the RCP4.5 and RCP8.5 scenarios, respectively); (2) marginal differences in sawlog and recoverable lumber proportions under the RCP8.5 scenario with the western locale exhibiting somewhat larger declines; (3) dramatic and systematic declines in utility pole productivity with increasing climate change severity for unthinned plantations with those established at the eastern and western locales unable to even achieve pole production status; (4) declines in economic worth with increasing climate change severity for unthinned plantations; (5) inconsequential climate effects on stand stability and most of the wood fibre attributes with the possible exception of a marginal climate-induced decline in microfibril angle and increase in modulus of elasticity values for the twice-thinned plantations; and (6) accelerated operability status with increasing climate change severity irrespective of crop plan or locale. Attainment of earlier operability status is most plausibly caused by the increased rates of stand development during the first two commitment periods (2022–2040 and 2041–2070) given the more conducive growing conditions (e.g., generally, concurrent increases in growing season temperatures and precipitation rates relative to historical climate norms; Table 1). However, these advantageous growing conditions dissipated and were subsequently replaced with less conducive ones, particularly with respect to warmer seasonal mean temperatures as the plantations approached rotation age during the third commitment period (2071–2100; Table 1). Resultantly, rotational mean tree sizes and merchantable volumetric productivity in both unthinned and thinned plantations, and utility pole production within unthinned plantations, exhibited consequential declines with increasing climate change severity, irrespective of geographic locale. Although these exemplifications are limited in scope with respect to site quality variation, diversity of crop plans and geographic locales, the resultant contrasts demonstrate the overall utility of the SSDMM for assessing the spatial and temporal consequences of increasing climate change severity on red pine productivity.

Similar to the rotational yield comparisons presented in Table 4, the relative silvicultural effectiveness of the selected crop plans for a given climate change scenario and locale can also be evaluated using the rotational performance metrics. For example,

Table 6. Climate-specific silvicultural effectiveness comparisons among the selected red pine crop plans for plantations situated in north-central (Thessalon), north-eastern (Kirkland Lake) and north-western (Thunder Bay) Ontario: SSDMM-derived rotational yield comparisons for three crop plans growing under three climate change scenarios.

Index a	Locale b	Climate Scenario c
		Climate Normal			RCP4.5			RCP8.5
		Crop Plan Comparison d			Crop Plan Comparison d			Crop Plan Comparison d
		IS+1CT vs. IS	IS+2CT vs. IS	IS+2CT vs. IS+1CT	IS+1CT vs. IS	IS+2CT vs. IS	IS+2CT vs. IS+1CT	IS+1CT vs. IS	IS+2CT vs. IS	IS+2CT vs. IS+1CT
		∆	∆	∆	∆	∆	∆	∆	∆	∆
RMAI (m3/ha/year)	C	0.0	−6.8	−6.8	0.0	−6.8	−6.8	1.5	−4.5	−5.9
	E	−2.6	−9.0	−6.6	0.0	−5.6	−5.6	1.5	−4.5	−6.0
	W	−1.3	−9.1	−7.9	0.0	−5.6	−5.6	1.5	−4.5	−6.0
RBAI (m3/ha/year)	C	21.1	21.1	0.0	21.1	18.4	−2.2	25.7	25.7	0.0
	E	17.1	12.2	−4.2	21.1	18.4	−2.2	22.9	22.9	0.0
	W	20.0	20.0	0.0	24.3	21.6	−2.2	22.9	22.9	0.0
RCAI (m3/ha/year)	C	21.1	21.1	0.0	21.1	21.1	0.0	22.2	22.2	0.0
	E	20.0	15.0	−4.2	21.1	21.1	0.0	23.5	23.5	0.0
	W	20.0	15.0	−4.2	21.1	21.1	0.0	29.4	23.5	−4.5
RSL (%)	C	−22	−37.7	−15.7	−21.9	−37.3	−15.4	−18.9	−36.3	−17.4
	E	−26.5	−39.7	−13.2	−21.7	−36.8	−15.1	−17.9	−35.6	−17.7
	W	−30.8	−45.4	−14.6	−21.2	−36.3	−15.1	−18.1	−36	−17.9
RLV(s) (%)	C	−12.2	−15.8	−3.6	−12.2	−15.7	−3.5	−11.7	−15.1	−3.4
	E	−12.9	−16.8	−3.9	−12.1	−15.6	−3.5	−11.6	−14.9	−3.3
	W	−12.7	−16.5	−3.8	−11.9	−15.3	−3.4	−11.7	−15	−3.3
Nup (poles/ha)	C	550.0	497.7	−8.0	720.0	651.4	−8.4	[300]	[279]	−7.0
	E	286.3	261.6	−6.4	[287]	[264]	−8.0	[308]	[281]	−8.8
	W	349.2	319.0	−6.7	[292]	[270]	−7.5	[305]	[282]	−7.5
E(s) ($k/ha)	C	89.2	96.4	3.8	95.4	101.9	3.3	119.6	129.4	4.5
	E	77.4	86.1	4.9	116.3	123.5	3.3	128.7	133.7	2.2
	W	76.7	85.3	4.9	119.4	128.6	4.2	126.7	133.7	3.1
$S_O$ (%)	C	−26.7	−46.7	−20	−26.7	−46.7	−20	−26.7	−46.7	−20
	E	−26.6	−45.3	−18.7	−26.7	−46.7	−20	−26.7	−46.7	−20
	W	−26.6	−45.3	−18.7	−26.7	−46.7	−20	−26.7	−46.7	−20
SS (m/m)	C	−22.9	−17.2	5.7	−23	−17.1	5.9	−23.5	−17.6	5.9
	E	−23.5	−17.8	5.7	−23.2	−17.4	5.8	−23	−17.3	5.7
	W	−24.4	−18.8	5.6	−23	−17.1	5.9	−23.9	−18.3	5.6
OT (year)	C	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	E	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	W	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
${\overline{W}}_{d(T)}$ (kg/m3)	C	0.5	0.7	0.2	0.5	0.7	0.2	0.3	0.4	0.1
	E	0.6	0.8	0.1	0.5	0.6	0.2	0.2	0.3	0.1
	W	0.6	0.7	0.1	0.4	0.6	0.1	0.2	0.3	0.1
${\overline{M}}_{a(T)}$ (°)	C	32.3	36.0	2.8	32.5	35.6	2.3	31.8	35.0	2.4
	E	33.1	36.1	2.3	32.7	36.4	2.8	31.6	34.8	2.5
	W	33.3	36.4	2.3	32.1	34.6	1.9	31.4	34.6	2.4
${\overline{M}}_{e(T)}$ (GPa)	C	−17.3	−19.2	−2.3	−17.3	−18.3	−1.2	−17.8	−18.7	−1.1
	E	−17.5	−18.4	−1.2	−17.3	−18.3	−1.2	−16.8	−17.8	−1.1
	W	−17.5	−18.4	−1.2	−18.1	−19.0	−1.2	−16.8	−18.7	−2.2
		4.8	5.5	0.6	4.8	5.4	0.6	4.4	4.9	0.5
${\overline{C}}_{o(T)}$ (µg/m)	C	5.1	5.6	0.5	4.8	5.5	0.6	4.2	4.7	0.5
	E	5.1	5.6	0.5	4.7	5.2	0.5	4.2	4.7	0.5
	W	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
${\overline{W}}_{t(T)}$ (µm)	C	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	E	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	W	4.4	5.0	0.6	4.1	4.7	0.6	4.1	4.4	0.3
${\overline{D}}_{r(T)}$ (µm)	C	4.4	4.7	0.3	4.1	4.7	0.6	3.8	4.4	0.6
	E	4.7	5.0	0.3	4.1	4.4	0.3	3.8	4.4	0.6
	W	3.2	3.5	0.3	3.2	3.8	0.6	3.2	3.5	0.3
${\overline{D}}_{t(T)}$ (µm)	C	3.5	3.8	0.3	3.2	3.8	0.6	2.9	3.2	0.3
	E	3.2	3.5	0.3	3.2	3.5	0.3	2.9	3.2	0.3
	W	−1.1	−1.2	−0.1	−1.1	−1.2	−0.1	−1.1	−1.2	−0.1
${\overline{S}}_{a(T)}$ (m2/kg)	C	−1.2	−1.3	−0.1	−1.1	−1.2	−0.1	−1.0	−1.1	−0.1
	E	−1.2	−1.3	−0.1	−1.1	−1.2	−0.1	−1.0	−1.1	−0.1
	W	−1.0	−1.1	−0.1	−1.0	−1.1	−0.0	−1.0	−1.1	−0.0

Note: For each climatic-specific crop plan set, ∆ denotes the (1) percentage difference relative to the NC scenario for indices expressed in absolute units, or (2) absolute percentage or proportional difference from the NC scenario for indices expressed in proportional or percentage units (e.g., lumber volumes, site occupancy, height/diameter ratio). Additionally, where no percentage comparison is possible, the absolute index value for the thinned regime is included within a square bracket (i.e., number of poles per hectare at rotation). ^a As defined in Table 5. ^b As defined in Table 3. ^c Crop plan specifics provided in Table 2. ^d Climate change scenario specifics provided in Table 1.

provides such relative-based comparisons among the selected set of crop plans for each climate change scenario and locale. Examination of these comparisons revealed that relative to the unthinned plantations established at the same initial spacing, growing on the same site quality and under the same climate change scenario, the thinned plantations exhibited: (1) mostly negligible differences in merchantable volumetric productivity for the once-thinned plantations compared to more moderate declines evident for the twice-thinned plantations (5%–9%) irrespective of scenario or locale; (2) increases in above-ground biomass productivity and carbon sequestration potential; (3) declines in saw log production and recoverable lumber proportions across all locales and scenarios with the twice-thinned plantations illustrating substantially higher rates of reduction (36%–45% versus 18%–30% for sawlog proportions and 15%–17% versus 12%–13% for lumber volume proportions); note, the increase in the number of smaller-size trees arising from the thinning treatment(s) and attainment of pole production status indirectly contributed to these reduced proportions; (4) consequential increases in economic worth arising from thinning with the twice-thinned plantations exhibiting the largest increases (85%–134% versus 77%–119%); (5) declines in the duration of optimal site occupancy across all locales and scenarios with the twice-thinned plantations illustrating substantially higher rates of reduction (45%–47% versus 27%–28%); (6) declines in height/diameter ratios and hence increased stand stability across all locales and scenarios; (7) virtually no change in the time required to attain stand operability status for a given locale and scenario; and (8) although changes were minimal for six of the eight wood quality fibre attributes examined, thinning elicited substantial relative-based increases in microfibial angle and declines in wood stiffness (modulus of elasticity) across all locales and scenarios; thus potentially yielding lower quality solid-wood end-products.

Although these specific simulation results and associated inferences suggest that the crop plans which included thinning treatments were marginally less productive in terms of merchantable volumetric productivity and produced wood fibre of slightly lower quality in terms of solid wood end-product potential, they generated consequential increases in mean tree sizes, stand stability, and most importantly, enabled the plantations to achieve pole production status and maintain that status even with increasing climate change severity. The differences between the thinning regimes for a given scenario and locale were marginal for most of the performance metrics; however, the once-thinned regime generated slightly lower economic worth outcomes but were slightly better in terms of merchantable volumetric production and the proportion of sawlogs and lumber volume produced. With respect to pole production, the results indicated that the thinned plantations were well capable of yielding pole products with the twice-thinned plantations out-producing the once-thinned plantation across all locales irrespective of scenario. Given that the achievement of pole production status represents a consequential milestone for most red pine managers, these simulations clearly demonstrate the continued utility of thinning in terms of attaining this milestone even in the face of increasing climate change severity. More generally, although these exemplifications, numeric comparisons and resultant management inferences are unique to the selected crop plan sets, regional locales and scenarios considered, they demonstrate the potential applicability of the red pine SSDMM in optimal crop plan selection under climate change.

3.5. SDMD-Based Crop Planning for Red Pine: Past, Present and Future

Historically, similar to other Canadian conifers, red pine crop planning has largely been informed by (1) theoretical forest production constructs arising from European research results (e.g., [4,5,6]), (2) empirically derived site-invariant spacing indices and guides (e.g., Wilson’s mean dominant height/intertree spacing index [7,8]), (3) variable-density empirical yield tables (e.g., [57,58]), (4) empirical observations, analytical summaries and associated inferences derived from numerous individual experimental and operational field trials investigating the magnitude, pattern and duration of volumetric yield responses to IS, PCT and CT treatments at the individual-tree and (or) stand levels (e.g., [59,60,61,62]), and (5) static stand density management diagrams (e.g., [9,63]). Although these approaches have found consequential utility in density management decision making in terms of determining the likelihood of realizing volumetric yield objectives, they have limited applicability when managing for end-product potential or ecosystem service outcomes nor are they able to account for the effects of anthropogenic climate change when formulating crop plans. Hence, the resultant requirement for enhanced stand-level decision-support tools that can simultaneously forecast rotational outcomes for these diverse objectives under a range of plausible climate change scenarios, has become more acute among red pine managers ([64,65,66,67,68]). The modular-based SSDMM as validated and exemplified in this study, aspired to address this demand-driven forest management operational requirement. Furthermore, explicitly including pole production as an integral part of the crop planning decision making process, represented a consequential addition to the end-product and economic based criteria deployed when designing, evaluating and ultimately selecting optimal red pine crop plans (sensu [69]).

However, even with these advantageous forecasting capabilities, the degree of climate change uncertainty with respect to its future severity and associated effects (sensu [70]) will likely render future model forecasts as informed approximations. Thus, similar to other stand-level forecasting models and decision-support systems, a cautionary approach should be exercised when explicitly interpreting model predictions and associated crop planning inferences. For example, although climate change mitigation policies (actual and pledged) suggest that the range of plausible RCPs would be in the order of 1.9 to 6.0 (sensu [71]), the lack of certainty suggests that candidate crop plans be simulated across a range of potential climate change scenarios. As demonstrated in this study, this provides a basis for evaluating the range of plausible outcomes in terms of realizing a stated management expectation (e.g., declining ability of well managed unthinned plantations to produce utility poles across currently projected climate change scenarios). Concurrent monitoring of actual plantations which mirror the selected crop plan would also be constructive in terms of confirming the validity of the assumed climate change scenario deployed.

Analytically, the climate-sensitive red pine SSDMM increments the growing list of structural yield decision-support models developed for boreal and temperate forest tree species, e.g., structural SDMD models by Newton [14,15,22,23] for Canadian boreal conifers and by Stankova and Diéguez-Aranda [35] for European conifers and broadleaf species. As exemplified in this study, the ability to account for a wide spectrum of climate change scenarios and geo-referencing their effects on crop plan performance can facilitate optimal crop plan selection. Likewise, enabling regional comparisons across the species range could have currency in terms of informing reforestation and afforestation decision making, particularly given that these silvicultural practices are increasingly being recognized as essential components in natural-based climate mitigation strategies ([72]).

Consequential progress towards climate-sensitive spatial-based crop planning with respect to Canadian conifers has been challenging given the paucity of stand-level decision-support models that can account for localized climate change effects. Although empirical inventory-based carbon budget models have found utility in providing estimates of carbon pools and fluxes at regional and national scales particularly for accounting and national reporting purposes (e.g., [73]), they have limited utility in spatial-based forest management planning given their inability to provide climate-sensitive crop-plan-specific forecasts by site or geographic locale. However, as exemplified in this study, the advent of climate-driven biophysical site index models along with their integration into growth and yield forecasting systems provides a plausible analytical pathway for spatially-explicit crop planning under climate change.

Respectively, however, the pattern of declining site productivity with increasing climate change severity irrespective of locale or crop plan as reflected within the site index model predictions, represents only a single, albeit important, stand development determinate. Quantifying climate change effects via the use of a single stand development determinate in isolation has at times provided mixed results. For example, red pine model-based projections arising from climate-induced changes in seasonal (vegetative) total precipitation and mean temperature have projected consistent declines in dominant height development with increasing RCP [18] (i.e., site productivity declines). Conversely, however, similar climatic-induced effects have elicited both a positive and negative effect on individual-tree diameter growth [74]. More generally, development of climate-sensitive models is currently limited by necessity given that most of the underlying correlative relationships are retrospectively extracted from past climate-growth trends observed during mostly steady-state climatic conditions. Additionally, the potential consequential effects on pine forest productivity arising from climate-induced changes in other known growth drivers are not addressed in the model presented in this study (i.e., only localize moisture and temperature induced site productivity changes are considered). For example, such omitted determinates include potential increases in the duration of the vegetative growing season and photosynthesis inputs (CO₂). Furthermore, the model does not address other climate change consequences such as those related to locale and regional specific biotic and abiotic disturbances (e.g., increased mortality arising from the increased incidence of insect attacks, disease occurrence, wind-throw, and episodic drought events). One overarching photosynthetic element not considered is the potential changes arising from ambient atmospheric CO₂ enrichment. Recently, CO₂ enrichment arising from climate change has been identified as a plausible environmental determinate underlying the large, documented increases in the carrying capacity of loblolly pine (Pinus taeda L.) throughout the southeastern forests of the United States of America [75]. Analytically, this suggests that the inclusion of a CO₂ concentration covariate within future site productivity models may be worthy of consideration. Hence, given the current level of climate change uncertainty in terms of its severity and associated impacts on stand developmental processes, model predictions inclusive of those presented in this study are likely to evolve as the certainty of climate change effects becomes more definitive. Acknowledging these modelling shortcomings and their potential effect on the precision of future productivity forecasts, requires accommodation when interpreting model-based outputs.

In summary, the validated climate-sensitive red pine SSDMM exemplified in this study incrementally contributes to the SDMD-modelling legacy established over the past 60 years ([29]). As demonstrated, the SSDMM can be used to address operational prerequisites arising from the paradigm shift towards climate-smart crop planning and silvicultural decision making for this commercially important species (sensu [76]). Deploying multiple climate change scenarios across a set of crop plan candidates and geographic locales provides a measure of variability of the range of plausible rotational outcomes that could be expected. However, crop planning predictions derived from the red pine SSDMM should be considered as informed expectations given incomplete knowledge in terms of the severity of climate change and its resultant effects across a multitude of stand developmental processes and productivity determinates. Acknowledging such will be an essential element to crop planning decision making during the Anthropocene.

4. Conclusions

Red pine is an intensely managed species throughout central North America. Although the species responds readily to site occupancy regulation, the lack of stand-level decision-support tools that can account for localized climate change effects and provide quantitative insights of their potential consequences in terms of achieving stated volumetric yield, end-product and ecosystem service objectives, has hindered crop planning. The climate-sensitive SSDMM, validated and exemplified in this study, aspired to fill this analytical void, specifically by providing red pine managers with a crop planning decision-support tool that attempts to address a wide array of stand-level management objectives while accounting for climate change effects. The overall compliance of the model in terms of the primary underlying ecological construct (self-thinning rule) along with acceptable forecasting precision, contributes to the prerequisite evidentiary foundation required for its potential use in operational crop planning. Furthermore, the simultaneous prediction of rotational volumetric yield, end-product and ecosystem service outcomes by geographic location and climate change scenario, demonstrated the model’s applicability for assessing locale-specific crop plan candidates. Particularly in terms of evaluating their silvicultural effectiveness and determining the likelihood of achieving stated management objectives. In summary, as the complexities of density management intensify during the Anthropocene, the SSDMM offers red pine managers a potential analytical platform for designing, evaluating and ultimately selecting the optimal climate-smart crop plan required for the realization of a specified stand-level management objective (e.g., maximizing volumetric productivity, enhancing end-product potential (utility pole production) or diversifying ecosystem service outcomes (carbon sequestration)).