Value-added forest management planning: A new perspective on old-growth forest conservation in the fire-prone boreal landscape of Canada

Forest Ecology and Management 429 (2018) 44–56

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Value-added forest management planning: A new perspective on old-growth forest conservation in the fire-prone boreal landscape of Canada

T

⁎

Baburam Rijala,b, , Luc LeBela, David L. Martellc, Sylvie Gauthierd, Jean-Martin Lussierd, Frédéric Rauliera,b a

Faculté de foresterie, de géographie et de géomatique, Université Laval, 2405 rue de la Terrase, Québec, QC G1V 0A6, Canada Centre d’étude de la forêt, Faculté de foresterie, de géographie et de géomatique, Université Laval, Canada c Faculty of Forestry, University of Toronto, Toronto, ON M5S 3B3, Canada d Natural Resources Canada, Canadian Forest Service, Laurentian Forestry Centre, 1055 du P.E.P.S., P.O. Box 10380, Stn. Sainte-Foy, Québec, QC G1V 4C7, Canada b

A R T I C LE I N FO

A B S T R A C T

Keywords: Fire Linear programming Revenue Risk Simulation Timber supply

The maintenance of old-growth stands is important for sustaining natural forest ecosystems, but fire disturbances and commonly-used timber harvest practices exert adverse impacts on the retention of old-growth forests. Forest management planning prescribes harvest levels based on the planning policy and models, but the impact of the management strategies on the retention of old-growth forests has not been well studied. The objectives of this study were to examine: a) the impact of implementing three different harvest policies on the retention of oldgrowth forest and b) the impact of implementing a policy of maintaining a targeted minimum of 20% old-growth area on the harvest revenue that would be generated over a long planning horizon. To simulate the implementation of these policies, we developed three strategic timber harvest-scheduling models. The first model (Model 1) maximizes harvest timber volume; Model 2 maximizes the net present value (NPV) of the timber harvested; and Model 3 maximizes the NPV of value-added products at the primary processing mills. The valueadded products we considered were lumber, chips and sawdust. The models were solved for three forest management units with different fire regimes. Solutions to models that did not include a strict constraint on oldgrowth forest area retention did not retain the targeted level of old-growth forest over a 150-year planning horizon. When an old-growth constraint was implemented, Model 3 produced the greatest revenue with the least variation by 5-year period over the planning horizon. The probability of finding a feasible solution to our optimization Model 3 with an old-growth forest constraint increased to 0.87–1.0 compared with 0.71–0.83 using Model 1, and 0.78–0.87 using Model 2. We conclude that the value-added policy model increases the probability of sustaining the bioeconomy while preserving forest ecosystems initiated by disturbance.

1. Introduction

objectives. The harvest plans are periodically revised at specified time intervals (e.g. 5 or 10 years; Savage et al., 2010) to account for unpredicted changes in forest structure and production or to accommodate the effects of disturbance events on timber supply (Jensen and Bard, 2003). Periodic replanning over a rolling planning horizon in which only the planned activities for the first period are implemented (e.g. BFEC, 2013) ensures a long-term flow of harvests. Traditional forest management planning is largely based on sustained-yield harvest policies that maximize harvest volumes which favour an even flow of harvest volume by period over a planning horizon (Davis et al., 2001; Gunn, 2007). In addition, the classical Faustmann model (Faustmann, 1849) that maximizes stand-level net present value (NPV) of the harvest is also used in forest level management planning

The production of high-value timber is an important aspect of commercial forest management that aims to sustain a forest-based bioeconomy and wood products industry in the face of changing forest production and world markets (Toppinen et al., 2010). The timber supply available at any time depends upon past management activities (e.g. silviculture treatments and harvest schedules), the disturbance regime that was experienced during the preceding periods, and longterm forest site productivity. Long-term timber supplies are routinely projected using linear programming models that produce optimal solutions that specify harvest plans and silviculture schedules in interaction with forest structure, growth dynamics and forest management

⁎

Corresponding author at: Faculté de foresterie, de géographie et de géomatique, Université Laval, 2405 rue de la Terrase, Québec, QC G1V 0A6, Canada. E-mail addresses: [email protected] (B. Rijal), [email protected] (L. LeBel), [email protected] (D.L. Martell), [email protected] (S. Gauthier), [email protected] (J.-M. Lussier), [email protected] (F. Raulier). https://doi.org/10.1016/j.foreco.2018.06.045 Received 30 March 2018; Received in revised form 23 June 2018; Accepted 28 June 2018 0378-1127/ © 2018 Elsevier B.V. All rights reserved.

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production, as dictated by classical volume-maximizing models. The objectives of this study were to; (a) examine the impacts of implementing three different harvest planning policies on the preservation of old-growth forest area, and (b) evaluate the effects of those policies on the revenues from timber harvest to the sawmill, while meeting the old-growth forest level strict requirements. The first policy maximizes the harvest volume subject to constraints on the long-term even-flow of harvest volume over the planning horizon. The second policy maximizes the NPV from the sale of the harvest log volume subject to the same constraints. The third policy maximizes the NPV for the first two periods from the sale of value-added products subject to the even-flow of high-value products over the planning horizon. We treated processed products at the primary processing mill, namely, lumber, wood chips and sawdust, as value-added products. We used data for three commercially-managed boreal forests in the province of Quebec, Canada and developed three harvest scheduling optimization models, one for each policy that accounts for the potential impacts of fire on supply.

(Davis et al., 2001). Such harvest policies account for dynamic growth processes, but they do not account for ecosystem conservation or industrial sustainability over long planning horizons. Alternative forest harvest policies and modelling frameworks based upon explicit economic principles in an integrated framework within the wood processing industry (e.g. Barros and Weintraub, 1982; Gunn and Rai, 1987) have also been suggested, but there remain conflicts between the production of commodities and the provision of ecological services (Mönkkönen et al., 2014). Conservation of the ecological integrity of managed forests is an important aspect of sustainable forest management for which the maintenance of mature and old-growth forest stages is important (Esseen et al., 1997). The rotation age in eastern Canada ranges from 70 to 100 years (Bouchard and Garet, 2014), which poses threats to oldgrowth forest stands. Ecosystem-based forest management practices have been developed to maintain natural ecosystem integrity by narrowing the gap between the natural processes of stand development dynamics (viz., initiation, stem exclusion, re-initiation and old-growth (Oliver, 1980)) and commercial forest management (Gauthier et al., 2009). From an ecological stand point, old-growth stands have higher structural and functional diversity than younger stands (Chambers and Beckley, 2003). Consequently, the total area of old-growth stands on the landscape scale is a key indicator of structural diversity (Powelson and Martin, 2001; Fall et al., 2004). When the effects of disturbances such as stand replacing fire are accounted for in a volume-maximizing model, both the rotation cycle and the old-growth forest area decrease (Martell, 1980; Savage et al., 2011). Moreover, when economic parameters are included in such models, rotation ages decrease further, depending upon the discount rate (Clark, 2005), which also reduces the proportion of old-growth forests. Harvest activities and the disturbance regime affect forest age structure (e.g. Fall et al., 2004; Barclay et al., 2006; Didion et al., 2007; Bergeron et al., 2017) and, not surprisingly they have economic consequences (Binkley et al., 1994). Management solutions can restore or maintain the targeted proportions of old-growth forest area by retaining a portion of the old-growth stands (Seymour and Hunter, 1999), by lengthening the rotation cycle (Burton et al., 1999; Koskela et al., 2007), or by the use of silviculture treatments that retain or support the creation of some structural characteristics that are similar to old-forests (Bergeron et al., 1999), or triad management (Messier et al., 2009; Tittler et al., 2012). However, the economic impact of using such alternative solutions to retain old-growth stands has not been well studied. Although, old-growth forests have been defined in many ways (Wirth et al., 2009), in this paper, we consider a stand to be an oldgrowth stage when it enters its old-growth phase as defined by Oliver (1980) or when post-disturbance cohorts start dying (Franklin et al., 2002; Kneeshaw and Gauthier, 2003). This consideration matches forest-harvesting activities that result in gap creation that may be similar to the gap (shape, size and frequency) dynamics of natural disturbance in terms of canopy openness, which is a key attribute of ecosystem-based forest management (Hunter, 1993). It is consistent with the definition used by the Ministère des Forêts, de la Faune et des Parcs du Québec (MFFPQ). Forest management policies that ensure the preservation of at least some specified proportion of old-growth forest areas are often recommended in order to conserve forest ecosystems (e.g. in Quebec, Jetté et al., 2013; Bouchard et al., 2015) but the adoption of such policies may reduce harvest volumes. In some cases, the formulated optimization problems do not have feasible solutions, which results in zero (no) harvest volume during some planning periods (Conrod, 2010; Savage et al., 2011). Such fluctuations or zero-harvest situations jeopardize economic opportunities. Managers should aim to minimize such potential adverse impacts on economic opportunities when the old-growth forest area constraint is strictly implemented. One possible option may be to employ alternative harvest policies that increase efficiency in revenue production (Rijal and Lussier, 2017), which implies high-value harvest prescriptions rather than timber volume

2. Methods 2.1. Study area The boreal forest region is the most fire-prone in the province of Quebec. It has been subjected to increased anthropogenic disturbance as timber-harvesting activities have been gradually extended northward (Powers et al., 2013). We selected three forest management units (FMUs) from the fire-prone boreal region (Fig. 1). These FMUs have distinct initial age structures (which are dominated by immature and old-growth stands), an indicator of varying harvest and fire regime histories. These three management units are in the black spruce-feather moss bioclimatic domain within the continuous boreal forest subzone (Robitaille and Saucier, 1998). Black spruce (Picea mariana (Mill.) BSP) dominates the region. Jack pine (Pinus banksiana Lamb.), a species that is well adapted to fire, is present in the central part of the study area (FMU 026-65). This FMU represents the most flammable forest in the boreal region (mean annual burn rate: 0.48% year−1; details follow) of Quebec and has a relatively longer history of harvesting activities. The forest is dominated by immature (≤ 50-years-old) stands (43% of total area) and a lower proportion (21%) of old-growth (≥ 100-years-old; Jetté et al., 2013) compared with the historical proportion of oldgrowth forest area (Bouchard et al., 2015; Annex C). The eastern forest management unit (094-52) is dominated by old-growth forest (73%; Table 1). This condition may be due to the relatively recent introduction of harvesting activities (< 30 years; Bouchard and Pothier, 2011) and a low annual burn rate (0.06% year−1) compared with the other two FMUs. It has substantial proportion of balsam fir (Abies balsamea (L.) Mill.) followed by black spruce. The western forest management unit (085–51) has been intensively harvested since the 1970s (Belleau and Légaré, 2009) and is characterized by a dominance of immature (51%) stands. This FMU has an intermediate mean annual burn rate of 0.13% year−1. 2.2. Data We used (a) forest inventory, (b) financial, (c) fire and (d) spatial data. The forest inventory (2002–2004) data were obtained from the MFFPQ. We constructed strata-based yield tables by dividing each FMU into aspatial strata based upon landscape unit and cover type to represent biogeographically specific growth potentials. A landscape unit is defined as “a portion of landscape characterized by a recurrence of environmental attributes (type of relief, average altitude, nature and proportion of the main surficial deposits, hydrography) and vegetation factors” (Robitaille and Saucier, 1998, page 3). The landscape unit allows for a specialization of forest composition and growth variability based on soil and bioclimatic parameters. The forest management units 45

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52° N

50° N

48° N

46° N

44° N -75° W

-70° W

-65° W

-60° W

Fig. 1. Study area showing the three forest management units 085-51 (west), 026-65 (centre) and 094-52 (east) in dark grey together with the boundary of the fireprone black spruce-feather moss forest (bold continuous line). Light gray polygons are other commercially-managed forests in the Province of Quebec, Canada.

period for a 150-year planning horizon. The log and transformed product yield tables for all species groups were summed for each stratum and subjected to non-parametric smoothing using the R loess function (R Development Core Team, 2014) to construct a stratum-wise single yield table. We used data that were provided by Tembec Inc. (a forest products company) to estimate the costs of forest management, harvesting and transportation from harvest site to mill gate for the western forest (FMU 085-51) (Pasturel, 2013). To estimate transportation costs from the forest to the mill, we first identified the softwood sawmill that was closest to the FMU using a publicly available list of mills active in 2009 (MRNFQ, 2009). We assumed all harvested timber from each FMU would be transported to the sawmill that would convert the timber into lumber, chips and sawdust as the primary-processed wood products. We then used an ArcGIS 10.2 (ESRI, Redlands, CA, USA) network analysis tool to estimate the driving distance between each landscape unit centroid and the assigned mill using forest road network data (Adresses Québec, 2015). We estimated the transportation cost using a linear relationship between cost and distance using Pasturel (2013: Fig. H-1) assuming constant road and driving conditions. The same procedure was used to estimate transportation costs for central and eastern forests. For the sake of simplicity, the selling price of timber at the harvest site was kept constant for all three forests by using the average for the western forest (Pasturel, 2013). We further assumed that transformed products were delivered from the sawmills to product-specific sites for secondary processing or marketing, i.e. lumber to the Montreal market, chips to the closest paper

that we selected encompass 18 landscape units, ranging in area from 3150 to 21,160 km2 in size, with a median of 7000 km2. Cover types were obtained from forest stand maps prepared by the MFFPQ. We then aggregated the forest stands into strata as a function of landscape unit and species composition based upon the dominance of species (i.e. balsam fir, black spruce, pine) in each stand. Each stratum was therefore, a collection of stands with a mixture of species and age classes (Table 1). In this study, we considered only three softwood species groups (spruce, pine and fir) because of their dominance in the area (Table 1). The NATURA-2009 growth and yield model (Pothier and Auger, 2011) was used to generate merchantable volume (log diameter ≥9 cm) yield tables for each stratum. NATURA-2009 is a stand-level dynamic model that consists of three sets of five equations. They predict the 5-year periodic progression of dominant height, quadratic mean diameter, stem density, basal area and timber volume per species group (viz., balsam fir, shade intolerant softwood other than balsam fir and shade tolerant softwoods) as a function of age and other stand variables iteratively over a 150-year time horizon. NATURA assumes that stand growth conditions and log volume remain constant after 150 years of age. We considered lumber, chips and sawdust as primary-processed forest products as value-added products and lumber had the highest selling price (Table 2). The product yield tables were derived from the empirical models that were developed by Liu and Zhang (2005), Zhang and Tong (2005), and Liu et al. (2009) for black spruce, jack pine and balsam fir respectively, using the inputs (diameter, height and stem density) that were obtained from the NATURA simulations by 5-year

Table 1 Summary statistics of the forest data for the three forest management units (FMUs) that were studied. FMU

Western (085–51) Central (026–65) Eastern (094–52)

Productive (% of terrestrial) area (km2)1

SPF2 spatial abundance (%)

Area of strata, mean (min – max), ha

Driving distance, mean (min – max), km

Initial state of old-growth forest (% of productive area)

Mean annual burn rate (% year−1; 1971–2014)

5734 (59%) 3188 (70%) 6954 (76%)

80

14,335 (39 – 138,552) 11,384 (5–72,960) 10,399 (8–247,645)

65 (31–120) 162 (131–230) 196 (140–255)

24

0.13

21

0.48

73

0.06

92 96

1 Forest area that produces at least 50 m3 ha−1 of merchantable timber (diameter at breast height ≥ 9 cm) over a 150 year planning horizon, with a mean stem volume greater than 50 dm3 stem−1 (Raulier et al., 2013). 2 SPF denotes species group; spruce, pine and fir combined (a trade name). Spatial coverage percent was estimated using the forest inventory data.

46

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Table 2 Model parameters used in the three harvest planning models. The terms that are used in the table are described in the text. A portion of the table has been reproduced with permission from Rijal and Lussier, 2017, Table 2, © 2017 Elsevier B.V. Parameter (Eqs. (2)–(7), (10) and (11))

vsa vpsa amin . s

Merchantable volume of stratum s, in age class a (m3 ha−1) Product volume (m3 ha−1)

rtimber . sm rp . m

Constant merchantable timber volume selling price to mill Transformed product selling price at their product (p) wise destinations (m) ($ m−3)

cf cpr.m

Constant forest management cost ($ m−3 merchantable volume) Product processing cost at primary processing mill ($ m−3 merchantable volume) Transportation cost for harvest volume between the harvest site (hs) and the mill (m) Sum of forest management and harvest and transportation costs (cf + ctr.hs.m) Transportation cost for processed wood between the mill and the delivery site Discount factor for 5-year periods Distance between the harvested stratum and the closest mill (m)

ctr.hs.m ctimber.sm ctr.pm γt ds . m 1

Minimum harvest age (periods), it varies by stratum

Parameter value

Source

Stand volume ≥ 50 m−3 ha−1 and individual tree volume ≥ 50 dcm−3 tree−1. $58.7 m−3 Lumber $155.0 m−3 Chips $52.0 m−3 Sawdust $9.0 m−3 $39.7 m−3 $24.0 m−3

Raulier et al. (2013)

$9.0–25.0 m−3

Tembec Inc. (Pasturel, 2013) QFIC1, Groupe DDM (2012) Pasturel (2012) Pasturel (2013) Groupe DDM (2010) Pasturel (2013: Fig. H-1)

$48.7–64.7 m−3 In m−3 km−1 lumber $0.02; chips $0.02; sawdust: $0.02 (truck) or $0.002 (train) Rate = 4% year−1 31–255 km

CPCS (2013) and Laurent et al. (2013) BFEC (2013, page 228) –

Quebec Forest Industry Council.

experiment. The first policy maximized the harvest volume. The second maximized the net present value (NPV) of the sustained yield of timber harvest volume. This model considers costs of forest management, harvesting, loading and transportation from harvest site to mill, and revenue from the sale of harvest timber with a discount rate. The third policy was sustained yield of high-value primary-processed products as well as timber volume throughout the planning horizon with NPV maximization for the first two periods only. We used our simulation framework to generate an array of possible solutions (outcomes) with stochastic burn rates. We used these simulated outcomes to construct frequency (and empirical probability) distributions, together with central tendencies (the median) and 90th percentile ( ± 5%) confidence intervals. Although we obtained stratum-wise 5-yearly periodic simulated outcomes (harvest volumes, harvest rates, and revenues), we compared the annualized outcomes on a per hectare basis dividing by 5 (a period) and area of the respective stratum. The following three subsections (Sections 2.3.1-2.3.3) describe our optimization and simulation processes in more detail. We used the MFFPQ’s definition of stand development stages, which correspond with following age classes: average age below 50 years (young), 50–74 years (immature), 75–99 years (mature) and 100 years and above (old-growth) (Jetté et al., 2013; Bouchard et al., 2015). The MFFPQ recommends that the three forest management units in our study area be managed so as to maintain at least 20% old-growth forests by the rule described by Jetté et al. (2013) and Bouchard et al. (2015). Preservation of the mature stage is also important to ecosystem function. Bouchard and Garet (2014) used 28% retention of mature and oldgrowth combined. Some proportion of mature area is maintained once the specified old-growth forest area constraint is employed by period over the planning horizon. Based on these recommendations, we added an old-growth area constraint to all our planning models. Consequently, we had six scenarios overall. We then compared the simulated outcomes with and without the old-growth forest area constraint in order to examine their impact on revenue. We further compared the constrained three models to examine the performance on the sustained revenue through the planning horizon.

mill, and sawdust to the panel mill. We used the 10-year (2004–2013) average lumber and chips selling price delivered to their delivery site. A constant price for sawdust was derived from Pasturel (2013). All prices were standardized to constant 2010 Canadian dollars ($) using the inflation calculator of the Bank of Canada (2015). Transportation costs from the sawmill to product destinations varied as a function of transportation modes for truck or train (CPCS, 2013; Laurent et al., 2013) to the product-specific delivery sites. Mill capacities for processing timber were assumed to be non-limiting because these are considered as tactical level parameters (D’Amours and Rönnqvist, 2008; Bouchard et al., 2016). Details of the parameter values are provided in Table 2. Because forest management units were deemed to be too small to estimate an FMU-specific fire burn rate (Boulanger et al., 2012, 2013), we used the homogenous fire region (HFR), i.e. a contiguous area of similar fire fuel environment (weather, topography, soil and fuel combustibility), delimited by Chabot et al. (2009). The annual burn rate for each FMU was estimated empirically (annual area burned as a fraction of total terrestrial area) at the spatial scale of HFR that encompasses the FMU of study using data that described past fire events (1971–2014). The Société de protection des forêts contre le feu (SOPFEU), the agency responsible for fire management in the province of Quebec, provided us with the burned area data by individual fire with spatiotemporal details. 2.3. Simulation framework Our simulation framework has two primary components: (a) a deterministic timber harvest scheduling optimization model, and (b) a stochastic landscape simulation model (Fig. 2). The deterministic component uses a constant annual burn rate over the entire planning horizon. The linear programming (LP) model solution prescribes a harvesting plan and produces a set of planned harvest attributes (area harvested, harvest volume and revenue) and standing volume. The landscape simulation model generates the stochastic annual burn rate with random draws from a pool of empirically calculated values for each period. The simulation model actualizes the planned harvest by accounting for potential impacts of stochastic fires and produces simulated (which we describe as “realized”) outcomes. We then analyze these outcomes and use them as the initial conditions for the next replanning cycle (Fig. 2). We considered three management policies in our simulation

2.3.1. Timber harvest scheduling optimization models All three models were constructed using a Model III network structure linear programming framework with age class movement by 5-year period while accounting for growth, fire disturbances and harvesting (García, 1984; Reed and Errico, 1986; Gunn and Rai, 1987). The 47

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B. Rijal et al. S

Z = max ∑

30

30

∑ ∑ vsa hsat

(1)

s = 1 a = amin . s t = 1

which is constrained as follows: Even-flow of harvest volume: 30

S

∑s=1 ∑a=amin.s

vsa hsa (t − 1) =

30

S

∑s=1 ∑a=amin.s

vsa hsat , ∀ t ∈ 2..30}

(2)

We assumed stand replacing fire, so entire forest burns when a fire occurs regardless of species and age composition. The planned harvest area is limited to be less than or equal to the area that is available for harvest (xsat) in each stratum, age class and period, after accounting for fire in any given period:

hsat ≤ (1−bf ) x sat , ∀ s, a

and

t

(3)

where bf is a constant periodic burn rate (fraction of the forest that is burned during each period) and used over the planning horizon and repeated simulations. We followed the supposition made by Reed and Errico (1986), who assumed that stands burn independently of their age and dominant species. Therefore, bf does not vary by age, stratum or period in our optimization models for the selected FMU. Following common practice in Quebec forest management, we assumed clear cut harvesting. We assumed that stand would follow the same growth trajectory of species as it was before harvested and have no lagging period for regeneration as in the previous studies in timber supply planning (e.g. Reed and Errico, 1986; Savage et al., 2010; 2011). The area accounting constraints are as follows. For the youngest age class (a = 1)

xs1t =

30

30

∑a=1 hsa (t−1) + bf ∑a=1 xsa (t−1) , ∀ s,

a

and

t ∈ {2...30} (4)

We assumed any forest stratum that exceeded the age of 150 years (or the 30th period) remained in the same class as a sink that implied any stand growing beyond this age would have a constant yield as NATURA assumes. Therefore, for the oldest age class (sink, a = 30):

xs30t = (1−bf )

30

30

∑a=29 xsa(t−1) − ∑a=29 hsa(t−1) ,

∀s

and

t ∈ {2...30} (5)

For intermediate age classes (a = 2…29) Fig. 2. A process flow diagram of the simulation experiment of linear programming (LP) and landscape simulation (LS) models. The LP model (step 2) solutions with (w/) or without (w/o) specified constraints are implemented using LS model (step 7). Notations are defined in Table 2 and relevant text.

xsat = (1−bf ) xs (a − 1)(t − 1)−hs (a − 1)(t − 1) ,

∀ s, a ∈ {2...29}

∈ {2...30}

and

t (6)

By our definition and modelling framework, old growth stands are those lying in age classes between the 20th and 30th (i.e. 100–150 years). Therefore, the old-growth forest area constraint at the forest level:

main justification for using this model was to simplify the inclusion of fire disturbances (Savage et al., 2010). We used the AMPL modelling language (Fourer et al., 2003) to model the optimization problems and Gurobi 5.6.0 (Gurobi Optimization Inc., Houston, TX) to solve them on the AMPL platform. The descriptions of the three model objective functions and constraints are presented below. The notations and parameters used in the mathematical models below are defined in Table 2. These models were solved separately for each FMU.

S

30

∑s=1 ∑a=20 (xsat−hsat ) ≥ 0.20∗Af

∀ t ∈ {1...30}

(7)

We set the harvest volume equal to zero for the period when the LP model indicated there were no feasible solutions due to the old-growth constraint. To evaluate the timber prescribed by Model 1 to the sawmill, we assumed that all the prescribed harvests were brought to the mill and processed regardless of economic loss.

Model 1: Harvest planning model that maximizes harvest volume over the planning horizon

Model 2: Harvest planning model designed to maximize the NPV of the harvest over a planning horizon from the sale of the harvest timber volume.

Let decision variable hsat be the area that is planned to be harvested (ha) in stratum s (s = 1, 2…S; where number of strata S = 52, 39 and 70 in FMUs 085–51, 026–65 and 094–52, respectively), in age class a (a = 1, 2…30, by 5-year period). The objective function is to maximize the harvest timber volume as:

By construction, Model 1 does not consider the economic value of harvests and that may produce overestimates of the harvest area by including wood volumes that are not economically profitable. An alternative solution to this problem would be to change the model with the maximization of the NPV of the harvest timber by accounting for revenue from log sales to mills and all types of forest management, 48

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forest age structure over the planning horizon by accounting for the cumulative effects of harvesting and stochastic fire. It employs the same equations as those used for the area accounting constraints to model the effects of fire (Eqs. (4)–(6)). However, the constant periodic burn rate, bt, varies from period to period and is generated from random draws of annual burn rates. The annual burn rates were calculated empirically based on the fire data for the years 1971 through 2014 in the three HFRs that correspond with each forest management unit. Assuming the annual burn rates are independently distributed through time and are equivalent to annual fire probabilities (van Wagner, 1978), the burn rate that is observed during a specific 5-year time period is equal to one minus the product of annual probabilities of observing no fire (the complementary probability). Thus, the 5-year periodic burn rate is:

harvesting and transportation costs. Our second model (Model 2) therefore, maximizes the NPV to the forest owner. The mathematical form of the model is: 30

⎡ NPVtimber = max ∑ ⎢γt t=1 ⎣

30

S

∑ ⎡⎢ (rtimber .sm−ctimber .sm ) ∑ s=1

⎣

a = min.s

⎤⎤ vsa hsat ⎥ ⎥ ⎦⎦

(8)

which is constrained to an even-flow of harvest volume (Eq. (2)), availability (Eq. (3)) and area accounting or balancing (Eqs. (4)–(6)), with or without the old-growth forest area constraint (Eq. (7)). Model 3: Harvest planning model designed to maximize the NPV from the sale of processed wood over the first two periods - an integrated model

5

Maximizing the NPV (Model 2) is a greedy approach because it favours the most profitable action in the short term and defers the least profitable harvesting to later. Typically, all decisions taken more than 50 years from now have little effect on forest value (revenue), with a typical 4% compound interest rate that is commonly used for long-term forest management planning including in Quebec (BFEC, 2013, p. 228). It tends to leave fewer economic opportunities for future generations and it may therefore, jeopardize the sustainability of the forest for industrial wood production. Further consideration is required to ensure even flow of primary-processed products over the planning horizon to address this problem. Model 3 was designed to maximize the NPV of the primary-processed products produced. The model accounts for the product-processing costs in addition to all forest management, harvesting, transportation and processing costs during the first two periods. Considering only the first two periods can be viewed as being consistent with the strategic planning horizon of the primary-processing softwood sawmill (Gunn, 2007). Because lumber has the highest value (price) among the three products (lumber, chips and sawdust), maximizing the NPV of primary-processed wood products will deplete the high-value timber during the early periods. Similarly, transportation costs may result in the harvest being prescribed for the stands that are located near the processing mills. This problem was addressed by considering: a) longterm even flow of lumber volume to ensure the maintenance of forest quality in terms of high-value recovery potential, and b) distanceweighted lumber volume by period over the entire planning horizon, in addition to even flow of timber harvest volume, as: 2

⎡ NPVProducts = max ∑ ⎢γt t=1 ⎢ ⎣

3

(12) ∼ The realized harvest (hsat ), which corresponds to the minimum of the planned harvest hsat that is obtained from optimization model and the area that is available for harvest in the same age class (a ) in the xsat ), is: same stratum (s ) during period (t ) (∼ i=1

∼ hsat = min(∼ xsat , hsat )

∼ xsa1 = (1−bt ) xsa1, ∀s and a ∼ xs1t =

∑ a = amin . s

S

30

vpsa hsa (t − 1) =

∼ xsat

30

S

(10)

Even-flow of the distance-weighted lumber volume: S

∑s=1

1 dsm

30

∑a=amin.s

vpsa hsa (t − 1) =

S

∑s=1

1 dsm

30

∑amin.s

= lumber, ∀ t ∈ {2...30}

∼ xsa(t − 1) −

30

∑ a = 29

∼ hsa(t − 1) , ∀ s and t ∈ {2. ..30}

(16)

∼ xs (a − 1)(t − 1)−hs (a − 1)(t − 1) , ∀ s, a ∈ {2. ..29} and t ∈ {2. ..30} = (1−bt )∼

2.3.3. Repeated simulation in a periodic replanning framework We solved the optimization model within a periodic replanning framework (Fig. 2). When the optimization model was solved, a set of planned harvest attributes, i.e. timber harvest areas (ha), harvest volumes (m3), the age structure of forest area (ha by age class), the standing timber volumes (m3) and the (net) revenues ($), were obtained by 5-year age class and 5-year period for each stratum over a 30-period planning horizon. We implemented the optimization model in a periodic replanning framework and used only the first period planned harvest level in our analyses. The planned harvest volume and standing volume in the first period served as inputs to the landscape simulation model, which in turn provided the simulated realized harvest by period with respect to the stochastic periodic burn rate (Fig. 2). Of the realized attributes that were obtained from the simulated implementation of landscape model solutions, the harvest area was taken as an output to be implemented for harvesting (prescribed harvest). It was used to readjust the available forest area for replanning at the start of the next period and thus served as an input for the next period. The replanning simulation continued through the 30th period. The realized harvest attributes and forest area in each age class that were obtained for the first period of each repeated optimization were retained for further analyses. The stochastic burn rate was incorporated in the simulation process through the landscape simulation model (Eqs. (12)–(17)). Given such stochastic fire inputs, we constructed frequency and empirical probability distributions of the expected outcomes using 100 repetitions of the 5 yearly 30-periodic replanning processes (Eq. (12)) (Fig. 2). It produced an array of 3000 (100 repeated simulations over a 30-period

vpsa hsat , p

= lumber, ∀ t ∈ {2...30}

30

∑

(15)

(17)

(9)

∑s=1 ∑a=amin.s

a=1

a = 29

which is constrained by an even-flow of volume (Eq. (2)), the availability of harvestable area (Eq. (3)) and area accounting constraints (Eqs. (4)–(6)), with or without the old-growth forest area constraint (Eq. (7)). Model 3 also has two additional constraints. Even-flow of the lumber volume produced by the mills:

∑s=1 ∑a=amin.s

30

∼

∼ xs30t = (1−bt )

⎣

⎤⎤ vpsa hsat ⎥ ⎥ ⎦⎥ ⎦

30

(14)

∑ hsa (t−1) + b(t−1) ∑ ∼xsa (t−1) , ∀ s, a and t ∈ {2. ..30} a=1

S

p=1 s=1

(13)

Harvesting occurs after accounting for fire in each 5-year period. These changes lead to the following stochastic simulation model:

∑ ∑ ⎡⎢ (rp .m−ctimber .sm−cpr.m

30

−ctr . pm )

bt = 1− ∏ (1−βi )

vpsa hsat ,p (11)

2.3.2. Landscape simulation model The landscape simulation model simulates the dynamics of the 49

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planning horizon) outputs. Our descriptive and inferential analyses were based upon these outputs. The inferential analyses produced estimates of the probability of obtaining values greater than or equal to specified volumes and revenues (the complementary cumulative probability distribution function, 1-CDF = P(x) ≥ X) over the planning horizon. This probabilistic expression was used to categorize risk into four classes as: (a) 0.33 is unlikely to occur; (b) 0.33–0.66, equally likely or unlikely to occur; (c) 0.66–0.90, likely to occur; and (d) > 0.90, very likely to occur (Mastrandrea et al., 2010).

went to zero in the western forest, approached zero in the eastern forest, and fluctuated out after the 15th period in the central forest (Fig. 3). The median proportions of old-growth forest using this model ranged from 6 to 25%. These values are substantially higher than those obtained using Model 1 (Table 3). Unlike Model 2, Model 3 led to harvesting activity in all strata by deferring harvest age and obtaining a better lumber recovery value.

3. Results

3.1. Old-growth forest area without an old-growth area constraint

The inclusion of an old-growth constraint was expected to affect harvesting activities and their impact on both the bioeconomy and the ecosystem over the planning horizon. We evaluated three harvest attributes: (a) harvest volume flow; (b) revenue generated by the harvest prescriptions; and (c) harvest rate (harvest area, expressed in percentage of forest area). These attributes were obtained by simulated implementations of the three policy models. They were compared with respect to their median values, fluctuations and the probability of obtaining values equal to or greater than volume and revenue (complementary cumulative probability distribution function, P(x) ≥ X) over a planning horizon. The following three Sections 3.2.1–3.2.3 present results regarding effects of adding the old-growth constraint.

When the volume-maximizing planning policy model (Model 1) was simulated without an old-growth area constraint, the proportion of oldgrowth forest area declined rapidly reaching zero by the start of the 15th period of the planning horizon, even in the case where the forest was initially dominated by old-growth stands, as was the case in the eastern forest (Fig. 3). Consequently, the median proportion of the old growth forest area that was retained using this model was almost zero in all three FMUs (Table 3). When harvest policy models were changed to maximize the NPV of harvested timber (Model 2) and the NPV of primary-processed products (Model 3), the proportions of retained old-growth forest area varied, depending upon model and forest (initial forest age structure and fire regimes). With Model 2, the proportions of old-growth forest varied considerably for all three forests (Fig. 3). The proportion gradually declined in the western forest and reached zero at the 14th period. In the central forest, it did not systematically decline to zero, but fluctuated by period, with the values ranging from 0.10 to 0.30. In the eastern forest, it declined from 0.73 to 0.05. Model 2 did not schedule harvests in 4% and 25% of forest areas that were located farther than 200 km from the mills for the eastern and central forests, respectively. In contrast, Model 1 prescribed harvesting across all strata in all three FMUs because costs were not considered in the harvest planning. In the western forest, all the strata are located within 200 km of the mill (Table 1). Model 3 maximized the NPV from the sale of primary-processed products. With this model, the proportion of old-growth forest gradually decreased, but the gradient of reduction was smaller than that of Model 1. Over the 30 simulation periods using Model 3, proportions

3.2.1. Harvest volume The effects on the quantity and variability of the harvest volume that resulted from imposing the old-growth forest area constraint differed by forest age structure, fire regime, and planning model used. When we used Model 1 with the old-growth forest area constraints, the annual medians of prescribed harvest volumes were 0.82 m3 year−1, 0.81 m3 year−1 and 0.68 m3 year−1 in the western, central and eastern forests, respectively, resulting in reductions of 12%, 20% and 10% in each of the respective forests when compared with the unconstrained results (Table 3). More importantly, when we included the old-growth constraints and accounted for the possible effects of fire, there were many cases in which there were no feasible solutions due to insufficient (at least 20%) old-growth forest area. We assumed that no harvesting took place if the model optimization process encountered such infeasibility. This infeasibility resulted in no (zero) harvesting in many periods, with repeated iterations giving rise to wide variation in harvest volumes and consequently on revenue for both within- and betweenperiods over a planning horizon (Fig. 4). The number of (in)feasible solutions can be expressed in terms of empirical probabilities. The probabilities of finding a feasible solution using Model 1 were 0.83, 0.71 and 0.80 in the western central and eastern forests, respectively (Fig. 5). Similarly, the probability of achieving a value greater than or equal to a specified volume harvested (e.g., 0.75 m3 ha−1 year−1) with constrained Model 1 varied in all three forests (Fig. 5). The inclusion of an old-growth constraint in Model 2 reduced the harvest volume substantially and increased its variability in a manner similar to the realized harvest volume using constrained Model 1. The median proportions of the reductions in the harvest volumes were

3.2. The effects of retaining at least 20% old-growth forests

0.10 10 15 20 25 30

0.00

5

5

10

15

20

Period

25

30

0.00 0.20 0.40 0.60 0.80

0.30

Central FMU (026-65)

0.20

0.20

0.30

Western FMU (085-51)

0.10 0.00

Proportion of area

Old-growth forest covered 24%, 21% and 73% of the total area of the western, central and eastern forests, respectively at the beginning of the planning horizon. All results that are presented here are the “realized” harvest attributes that were obtained from the simulated implementation of the landscape simulation models. The simulation results consist of 100 repetitions of the 5 yearly periodic replanning loop over a 30- period planning horizon (Fig. 2) for each policy model and forest management unit.

50

Eastern FMU (094-52) Model 1 Model 2 Model 3

5

10

15

20

25

30

Fig. 3. Boxplots showing the distribution of the proportion of old-growth forest area that was retained by period over the planning horizon without the imposition of a 20% old-growth forest area constraint in three forest management units (FMUs). Note that the Y-axis has a different scale for the eastern FMU. Please note that zero, very small values or values of small variation could not be visualized as boxplots that are depicted as dash-like lines.

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Table 3 Medians of the performance measures of the three policies with and without employing a hard constraint to preserve at least 20% old-growth forest area by period over the planning horizon in three forest management units (FMUs). The numbers in the parentheses are the 90% ( ± 5%) percentile confidence intervals. Forest (FMU)

Measurement attributes

Without old-growth constraint

Harvest volume (m3 ha−1year−1)

Western (085-51)

Revenue ($ ha−1 year−1) Harvest rate (% year−1) Proportion of old-growth area Harvest volume (m3 ha−1 year−1)

Central (026-65)

Revenue ($ ha

−1

year

−1

)

Harvest rate (% year−1) Proportion of old-growth area Harvest volume (m3 ha−1 year−1)

Eastern (094-52)

Revenue ($ ha

−1

year

−1

)

Harvest rate (% year−1) Proportion of old-growth area

Model 1

Model 2

Model 3

0.94 (0.92–0.96) 16.73 (13.04–27.26) 0.81 (0.67–1.26) 0.00 (0.00–0.28)

0.93 (0.90–0.94) 15.99 (12.02–23.39) 0.83 (0.72–1.27) 0.02 (0.00–0.27)

0.81 (0.75–0.89) 18.06 (16.89–19.00) 0.75 (0.60–0.90) 0.06 (0.00–0.32)

1.01 (0.94–1.03) 5.31 (-1.89–36.77) 1.03 (0.82–1.26) 0.00 (0.00–0.14)

0.70 (0.65–0.81) 4.63 (1.2–19.53) 0.73 (0.63–0.88) 0.19 (0.13–0.25)

0.80 (0.79–0.8) 8.57 (5.11–22.78) 1.23 (0.98–1.46) 0.01 (0.00–0.70)

0.70 (0.68–0.77) 7.24 (4.30–21.26) 1.17 (0.77–1.47) 0.09 (0.07–0.71)

Western FMU (085-51)

Model 2

Model 3

0.82 (0.00–0.89) 15.85 (0.00–21.47) 0.64 (0.00–0.76) 0.21 (0.20–0.43)

0.79 (0.00–0.86) 14.57 (0.00–19.49) 0.66 (0.00–0.79) 0.22 (0.20–0.42)

0.73 (0.00–0.78) 14.53 (0.00–17.5) 0.60 (0.00–0.72) 0.21 (0.20–0.44)

0.61 (0.54–0.71) 14.35 (12.86–15.39) 0.57 (0.49–0.76) 0.06 (0.01–0.24)

0.81 (0.00–0.85) 6.4 (0.00–21.57) 0.68 (0.00–0.84) 0.21 (0.19–0.28)

0.70 (0.00–0.76) 6.35 (0.00–19.55) 0.68 (0.00–0.84) 0.22 (0.19–0.32)

0.45 (0–0.53) 11.67 (0.00–12.84) 0.41 (0.00–0.50) 0.23 (0.20–0.36)

0.54 (0.47–0.65) 12.24 (11.83–13.29) 0.92 (0.77–1.09) 0.25 (0.03–0.73)

0.68 (0.00–0.72) 14.3 (0.00–19.06) 0.83 (0.00–1.17) 0.26 (0.20–0.73)

0.63 (0.00–0.66) 9.53 (0.00–17.87) 0.88 (0.00–1.17) 0.24 (0.20–0.73)

0.45 (0.41–0.56) 10.75 (9.85–11.70) 0.72 (0.63–0.87) 0.35 (0.21–0.73)

0.8

0.8

0.8

1.0

Eastern FMU (094-52)

1.0

1.0

Central FMU (026-65)

0.6 0.4 2

3

2

3

1

2

3

30 0

10

20

30 -10

0

10

20

30 20 10

1

40

3

1

Model

-10

3

2

0.0

0.2 2

0.0

1

1

40

3

0.2

0.4

0.4 0.2 0.0

2

40

1

0 -10

−1

−1

Revenue ($ ha year )

3

0.6

0.6

−1

−1

Model 1

harvesting in order to meet the 20% old-growth requirement. The reduced harvest volume due to the old-growth constraint helped increase the availability of wood for harvest during successive periods. As a result, Model 2 solutions resulted in a higher probability of obtaining feasible solutions compared with Model 1 in successive periods with the respective probabilities of 0.78 (vs. 0.71), 0.87 (vs. 0.83) and 0.82 (vs.

respectively 15% and 10% in the western and eastern forests, but almost the same in the central forest (0%) compared with the unconstrained Model 2 (Table 3). This result can be explained by the fact that Model 2 without the old-growth constraint did not prescribe harvesting the stands that would produce negative revenues. Model 2 with the constraint protected against further losses due to a lack of

Volume (m ha year )

With old-growth constraint

Fig. 4. Violin plots showing the effect of imposing at least a 20% old-growth area constraint on the harvest volume and revenue for the entire planning horizon and repeated simulations (30 periods × 100 repetitions) by applying three models to three forest management units (FMUs). Light grey violins correspond to “without old-growth constraint” models and the dark grey to “with old-growth constraint” models. The horizontal lines are included to help identify when there are zero, positive and negative revenues. 51

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Eastern FMU (094-52)

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

Central FMU (026-65)

0.0 0.2 0.4 0.6 0.8 1.0

1 - CDF

Western FMU (085-51)

0.0 0.2

0.4 0.6 0.8

1.0

0.0

0.2 0.4

0.6 0.8 3

1.0 −1

0.0

0.2 0.4 0.6

0.8 1.0

−1

-10

0

10

20

30

40

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

1 - CDF

Harvest volume (m ha year )

-10

0

10

20

30 −1

40

-10

0

10

20

30

Fig. 5. Complementary cumulative density function (1 - CDF) plots of the prescribed harvest volume and corresponding revenue using three planning models (Model 1, red; Model 2, blue; and Model 3, green) without (continuous line) and with (dotted line) imposing old-growth forest area constraint over a 30-period planning horizon for 100 time repetitions in three forest management units (FMUs). The horizontal dotted lines are probability levels that qualify as risk category: very likely (greater than0.90), likely (0.67–0.90), likely or not (0.33–0.66) and not likely (< 0.33) (Mastrandrea et al., 2010). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

40

−1

Revenue ($ ha year )

lower than that without that constraint (p = 0.30), as seen in the central forest (Fig. 5). With the inclusion of the old-growth constraint, Model 2 generated revenue similar to that obtained using Model 1, but the former (Model 2) avoided potential losses (negative revenue for timber) that would have been incurred due to high transportation costs. The median revenue decreased by 9% in the western forest, but increased by 37% and 32% in the central and eastern forests, respectively, despite reductions in the harvest volume (Table 3). Besides exhibiting a shorter “tail” towards the lower values (i.e. reduced left-hand skew), the probability distributions of revenue using Models 1 and 2 are similar in their shape and spread for the three FMUs (Fig. 5). Model 3 outperformed the two other models because of its higher and more consistent revenues to wood mill (Fig. 4), both with and without the imposition of the old-growth constraint. Unlike Models 1 and 2 which increased or decreased the revenues depending upon the FMU, the old-growth constraint that was incorporated in Model 3 reduced the median revenue in all FMUs (20% in western, 19% in central and 12% in central forests). The decreased revenues that resulted when we implemented the old-growth forest area constraint in Model 3 in the central and eastern forests were due to increased revenue because of the age-related value of the forest even without imposing the constraint. This result is unlike Models 1 and 2, where constraints substantially helped increase value-added harvest in the succeeding periods. The probability of obtaining revenue greater than or equal to a specified value, e.g. $10 ha−1 year−1, varied with forests and models over a planning horizon (Fig. 5). When we implemented the old-growth forest area constraint, the probability of obtaining positive (> $0) revenue increased (0.78–1.00) in Model 3 compared with Models 1 and 2 in all three forests (Fig. 5).

0.80) that were observed for the western, central and eastern forests, respectively. Fluctuations in the harvest volume however, varied widely from no harvesting (when model encountered infeasibility) and different levels of harvest by gradual accumulation of timber supplies through successive periods over the planning horizon. Model 3 led to results that differed from the previous two models because it prescribed harvesting only timber that would yield high value for the sawmill. It caused substantial reductions in the harvest level over the planning horizon, regardless of whether the old-growth constraint was employed or not. Constrained Model 3 reduced the harvest volume by 10–26% relative to the unconstrained model (Table 3). The probability of obtaining a feasible solution was greater with constrained Model 3 than with constrained Models 1 and 2, as evidenced by estimates of 0.92, 0.87 and 1.0 for the western, central and eastern forests, respectively. Implementation of constrained Model 3 also resulted in lower harvest variability in all forests (Figs. 4 and 5).

3.2.2. Revenue The effects of including the old-growth forest area constraint on revenue varied depending upon the harvest planning policy model (Table 3). Model 3 produced higher median revenue together with lower volume harvested than those obtained using Models 1 and 2, especially in the central and eastern forests (Fig. 4). Revenues were frequently increased by the imposition of constrained Models 1 and 2, compared with unconstrained models. When we implemented Model 1, the constrained model reduced median revenue by 5.3% in the western forest. In contrast, the median revenue increased by 20% and 66% in the central and eastern forests, respectively when the old-growth constraint was implemented (Table 3). This increase in the revenue likely arose because the constraint excluded the harvesting and transportation to sawmill of timber from unprofitable stands that were composed of young and small trees from being harvested due to low lumber recovery rates (Fig. 4). In turn, it created an opportunity to accumulate forest value in terms of the recovery of a greater proportion of lumber for successive periods. Such protections could be realized most notably in later periods. As a result, the probability of generating negative revenue by Model 1 with the old-growth constraint in place (p = 0.20) was

3.2.3. Harvest rate The constrained models reduced the harvest rate but increased its variability depending upon the forests and models used. The constrained Model 1 reduced the harvest rate by 20%, 35% and 26% in the western, central and eastern forests, respectively (Table 3). As described in Section 3.2.1 for harvest volume, wide variation in harvest rates was observed, due to infeasibility of constrained model solutions 52

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10 14 18 22 26 30

1.5 1.0 0.5 6

1.0 2

6

10 14 18 22 26 30

1.0

Eastern FMU (094-52)

0.0

0.5

1.0 10 14 18 22 26 30

Central FMU (026-65)

0.0 10 14 18 22 26 30

0.0 6

10 14 18 22 26 30

1.5

6

1.5

2

0.5

1.0 0.5 0.0 2

6

0.5

1.0 0.0 10 14 18 22 26 30

2

10 14 18 22 26 30 1.5

2

0.5

1.0 0.5 0.0

6

1.5

2

Western FMU (085-51)

0.0

0.5

1.0

1.5

Model 3

1.5

6

1.5

2

Harvest rate (% year-1)

Model 2

0.0

0.0

0.5

1.0

1.5

Model 1

2

6

10 14 18 22 26 30

2

6

10 14 18 22 26 30

Period Fig. 6. Violin plots showing the simulated harvest rate (%year−1) for three models without (dark grey) and with (light grey) the imposition of old-growth forest area constraints in the three forest-management units (FMUs).

studies were confined), given that we also encountered the infeasibility situation in all our forests, including one that was initially dominated by old-growth stands (Fig. 4). We extended our analyses to estimate the likelihood of events of other outcomes, but focused primarily on the revenue that was generated by the sale of primary-processed products. Other studies (e.g. Attiwill, 1994; Didion et al., 2007; Bergeron et al., 2017) have further reinforced the notion that sustained yieldbased (i.e. log volume) forest management practices should be modified to maintain a specified amount of old-growth forest, which is considered to be an important element of sustainable forest management. We explored alternative harvest policy models that would minimize economic losses while ensuring the retention of a specified proportion of old-growth forest area. Our models also addressed the potential effects of fire that resulted in within- and among-periods variation in outcomes (especially net undiscounted revenue), while interacting with the potential effects of stochastic fires. Model 3 produced the highest probability of success in terms of meeting the objective of retaining a specified amount of old-growth forest area while lowering adverse effects on revenue over the planning horizon (Fig. 5). When considering stochastic fire, public forest managers usually select decision rules that are less risky, i.e. likely to result in a high probability of success (Savage et al., 2010, 2011), together with minimizing losses (potent value or effect: Schmoldt, 2001). The probabilities of finding feasible solutions to the optimization models when we employed an old-growth constraint depended upon the forest conditions (age structure), fire regimes and models that we used. Age structure has only a short-term effect on maintaining the proportion of old-growth forest over time. The age of the stands may quickly decline, as was observed in the eastern forest initially dominated by old-growth (Fig. 3) when no old-growth constraints are used. Model 2 produced revenue similar to Model 1 but reduced economic losses by not harvesting timber that would generate negative revenue.

in the three forests (Fig. 6). Model 2 exhibited no substantial differences in the median and variability within- and among-periods when compared with Model 1, except for the inclusion of a few more cases of feasible or infeasible solutions (Fig. 6). The distributions of harvest rates when the old-growth constraint was applied were frequently higher than rates that were obtained in the absence of the constraint. This was due to lower or no harvesting during preceding periods. When Model 3 was implemented, harvest rate reductions were 18%, 29% and 19% in the western, central and eastern forests, respectively (Table 3). More importantly, we see that the reduced harvest rate in Model 3 produced greater revenues, regardless of whether the old growth constraint was used or not (Table 3).

4. Discussion When a harvest planning model that maximizes sustained-yield volume is implemented it can deplete the old-growth area of a forest because harvesting is scheduled at a specified rotation age (van Wagner, 1983) that is much earlier than the old-growth stage or commences harvesting when the specified minimum age to harvest is attained (Savage et al., 2010; 2011; Rijal and Lussier, 2017). If we treat the existence of a specified proportion of old-growth forest as an indicator of natural ecosystem functioning (Seymour and Hunter, 1999; Koskela et al., 2007), such a model, when implemented, will have an adverse impact on the ecosystem. Our analyses indicate, as has been shown in previous studies (e.g. Fall et al., 2004; Didion et al., 2007), that the age structure of the forest depends upon the harvesting activities as prescribed by the harvest planning models. Savage et al. (2011) and Conrod (2010) demonstrated that LP harvest planning models can encounter infeasibility when old-growth constraints are employed. Our results are consistent with previous studies in terms of the magnitude of the harvest attributes (particularly, harvest volume, to which most 53

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incurred by fire (Johnson and Gutsell, 1994). There are a number of ways of retaining old-growth stands as the literature suggests, especially with respect to Canadian forest management practices (e.g. Bergeron et al., 1999; Burton et al., 1999; Messier et al., 2009; Tittler et al., 2012). Our Model 3 results are somewhat consistent with Burton et al. (1999) and Koskela et al. (2007) that suggest extending (average stand) rotation age. Silviculture treatments suggested by Bergeron et al. (1999) may provide another option but it will increase cost which may not be financially viable for the expensive northern forests and such practice is not common in our study area. Messier et al. (2009) and Tittler et al., (2012) suggested a triad approach. Our economic evaluation approach can help locate areas where permanent reserves are warranted to conserve core wildlife habitats and specific ecologically vulnerable sites. In the disturbance-borne commercially-managed forest, our solution of developing a mosaic of stand structure across the area dynamically through time may be better than fixing one block for commercial intervention and another for ecosystem function wherever it is most economically and ecologically viable to harvest for at least three reasons as we note: (1) mimic disturbance-borne ecosystem-based forest management, (2) minimize the risk of collapsing entire concentrated area of old-growth by stand replacing fire, and (3) make the entire forest area financially profitable. From a management perspective, the latter is very important as large forest areas located in the commercially viable zones will always face harvest pressure, which is not consistence with ecosystem-based forest management, a mainstream of forest management in Canada. The reduced harvest rate in Model 3 can allow for greater flexibility in absorbing natural disturbances (Boychuk and Perera, 1997; Peterson et al., 1998). The lower harvest rate (area) implies a lower realized impact of fire on the harvest volume (van Wagner, 1983; Fig. 2). As a result, Model 3 solutions are more robust than that of Models 1 and 2 when the timber supply is impacted by potentially increased disturbance rates. We therefore confirmed our hypothesis regarding an improved modelling framework that considered a primary-processed product value that could help reduce adverse effects on revenue when the strict requirement of old-growth forest retention is implemented. The improved model strikes a balance between forest bioeconomy and the ecosystem. We acknowledge that reductions in harvest area and volume may have economic impacts on forest-based employment (Patriquin et al., 2008). In addition, reduced harvesting may not fulfil current demand that could result in mill closures as was observed in Canada during the 2000–2005 period, or increases in production costs, thereby reducing profit margins. Our study used forest financial data for the highly fragile 2004–2013 period, which included the year (2009) when the price was at its lowest level during the past 20 years (Natural Resources Canada, 2013). Nevertheless, this study presents a specific case of managing a value-added supply chain with specified product recovery at the mill as a method of valuing forest products. We have demonstrated that an industrial product value-added model is compatible with sustainable forest management that aims at reducing the adverse impacts of fire on supply economics while maintaining a specified proportion of old-growth forests area. Although the existence of all stand stages and corresponding age-classes are important for sustaining forest ecosystem functions, our study was limited to the old-growth stage, a widely recognized indicator of biodiversity and ecosystem health. Our modelling scheme, which considered lumber as a value-added product, may not be a universal solution appropriate for a wider array of products. Nevertheless, this study has introduced an approach that does account for specific industrial products in the strategic forest planning process.

Remote stands associated with higher transportation costs were left untouched (Fig. 4, Table 3). There were no substantial differences in the revenues from primary-processed wood by the harvest plan generated using Models 1 and 2, despite varying levels of harvest volumes. We see a “paradox” in that an old-growth constraint reduced the median revenue in the western forest, but increased it in the central and eastern forests while simulated the experiment using Models 1 and 2. Closer examination of the results showed that when we employed the oldgrowth constraint, uncut stands, which otherwise would have been harvested, had opportunities to add age-related product recovery value for successive periods. In other words, imposing a constraint to maintain old-growth area helped accumulate value (potential of higher recovery proportion of lumber) by postponing harvesting to later periods because of larger tree size. The use of an old-growth forest area constraint (e.g. Models 1 and 2) can therefore, often be economically beneficial in the long run by an effect of no-harvest of unprofitable stands. Ensuring economic benefit to the mill is important for the success of commercial forest management (Lehoux et al., 2012). The objective of our study was to explore alternative models that diminish adverse economic impacts on the wood processing industry. Model 3 can act as an alternative to more commonly used planning models (e.g. Models 1 and 2) by reducing impacts on revenue because of its old-growth forest constraint. Long-term median revenues generated using Model 3 with an old-growth constraint were greater, with lower variation, than the revenue generated using Models 1 and 2 with (and without) the oldgrowth constraint in central and eastern forests; it was almost the same in the western forest (Fig. 4, Table 3). Compared with Models 1 and 2, Model 3 can be regarded as a “no-regret” risk mitigation strategy: even if the old-growth constraint is relaxed, the probability of obtaining positive revenues is greater than that associated with the other models (Fig. 5). In addition, Model 3 has a higher probability of identifying feasible solutions with the optimization model, implying the model is more protective against periodic infeasibility. In our study, variations in the revenue were functions of lumber recovery that was associated with stand age at harvest, together with distance between harvest sites and the sawmill. The mean distance between the selected sawmill and western forest is 65 km (31–120 km), whereas the average distance to the sawmill that is closest to eastern forest sites is 196 km (140–255 km) (Table 1). Compared with Model 1, Model 2 increased the profit by reducing distance-related expenditures. We observed that 25% and 4% of the areas were not harvested during any period throughout the planning horizon in the central and eastern forests, respectively resulting in a greater proportion of old-growth forest area at the forest level (Fig. 3). All strata were within profitable distances in the western forest; thus, there were no substantial differences in the old-growth area retained, regardless of whether Model 1 or 2 was implemented. As an integrated model framework, Model 3 takes into consideration the entire forest management process: harvesting and transportation costs and revenues from the processed products. Within this model framework, harvests that would lead to lower revenue during the current period, are postponed and produce higher revenues in later periods as a result of larger tree sizes that generate greater processing values. Such a mechanism of value-selective harvest prescriptions ensures that forest resources which do not generate a positive financial return at the mill will not be harvested despite the fact that it may produce profit from the sale of timber as in Model 2 (Rijal and Lussier, 2017). This deferral provides two types of benefits: increased opportunities for a sustained bioeconomy and increased ecosystem conservation. Model 3 prescribed harvests in stands that have an older mean age at harvest (≈100 years; 75–150 years) compared with models 1 and 2 (≈70 years; 45–100 years). A simple calculation shows that increased economic values due to age deferral from 70 to 100 years surpass the time–cost values that could be attributed to the discount rate (4% year−1) and which could be due to lower survival probabilities that are

5. Conclusion Our results clearly show that none of the three models we present, without an old-growth forest area constraint, could secure a targeted 54

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20% area of old-growth forest over the entire planning horizon. When the old-growth forest area constraint was employed, adverse effects on revenue using constrained Model 3 were the smallest. Due to value-base harvesting over the planning horizon, Model 3 apparently eliminates harvest flows that exert negative effects on profits, especially during the first few periods. Over the long-term, Model 3 compensates for shortterm reductions and may serve as an alternatively improved model that helps reduce long-term effects on revenue when there is a mandatory policy for retaining a targeted proportion of old-growth forest area. The use of Model 3 has significant implications when transportation costs of harvesting timber are substantially higher and age-related value recovery is substantially different. Age-deferral in harvesting using Model 3 can provide greater opportunities for harvesting value-added timber and retaining old-growth forest.

Boulanger, Y., Gauthier, S., Gray, D.R., Le Goff, H., Lefort, P., Morissette, J., 2013. Fire regime zonation under current and future climate over eastern Canada. Ecol. Appl. 23, 904–923. http://dx.doi.org/10.1890/12-0698.1. Boychuk, D., Perera, A.H., 1997. Modeling temporal variability of boreal landscape ageclasses under different fire disturbance regimes and spatial scales. Can. J. For. Res. 27, 1083–1094. https://doi.org/10.1139/x97-063. Burton, P.J., Kneeshaw, D.D., Coates, K.D., 1999. Managing forest harvesting to maintain old growth in boreal and sub-boreal forests. For. Chron. 75, 623–631. http://dx.doi. org/10.5558/tfc75623-4. Chabot, M., Blanchet, P., Drapeau, P., Fortin, F., Gauthier, S., Imbeau, L., Lacasse G., Lemaire G., Nappi A., Quenneville, R., Thiffault, E., 2009. Le feu en milieu forestier. In: Ordre des ingénieurs forestiers du Québec. Manuel de foresterie, 2e édition, ouvrage collectif, Québec, Éditions MultiMondes. pp. 1037–1090. Chambers, F.H., Beckley, T., 2003. Public involvement in sustainable boreal forest management. In: Burton, P.J., Messier, C., Smith, D.W., Adamowicz, W.L. (Eds.), Towards Sustainable Management of the Boreal Forest. NRC Research Press, pp. 113–154. Clark, C., 2005. Mathematical Bioeconomics: The Optimal Management of Renewable Resources, second ed. John Wiley & Sons, pp. 386. Conrod, M.D., 2010. A simulation/optimization system for modelling timber and old forest under stochastic fire disturbance. Master’s thesis. Department of Renewable Resources, University of Alberta, Edmonton, AB. pp. 139. CPCS (Canadian Pacific Consulting Services), 2013. Transportation costs and competitiveness of eastern Canada lumber in GCC markets. http://canadawood.org/pdf/ report_transportation_costs_competitiveness.pdf (accessed 12.02.15). D’Amours, S., Rönnqvist, M., Weintraub, A., 2008. Using operational research for supply chain planning in the forest products industry. INFOR 46, 265–281. http://dx.doi. org/10.3138/infor.46.4.265. Davis, L.S., Johnson, K.N., Bettinger, P., Howard, T.E., 2001. Forest Management: To Sustain Ecological, Economic, and Social Values. McGraw-Hill, New York. Didion, M., Fortin, M.J., Fall, A., 2007. Forest age structure as indicator of boreal forest sustainability under alternative management and fire regimes: a landscape level sensitivity analysis. Ecol. Model. 200, 45–58. http://dx.doi.org/10.1016/j. ecolmodel.2006.07.011. Esseen, P.-A., Ehnström, B., Ericson, L., Sjöberg, K., 1997. Boreal forests. Ecol. Bull. 46, 16–47. Fall, A., Fortin, M.-J., Kneeshaw, D.D., Yamasaki, S.H., Messier, C., Bouthillier, L., Smyth, C., 2004. Consequences of various landscape-scale ecosystem management strategies and fire cycles on age-class structure and harvest in boreal forests. Can. J. For. Res. 34, 310–322 https://doi.org/10.1139/x03-143. Faustmann, M., 1849. Berechnung des Werthes welchen Waldboden sowie noch nicht haubare Holzbestände für die Waldwirtschaft besitzen. Allgemeine Forst und Jagdzeitung, 25, 441–455. [English translation by W. Linnard, W., M. Gane. in M. Gane, M., E.F. von Gehren, M. Faustmann (Eds.), 1968. Martin Faustmann and the evolution of discounted cash flow. Commonwealth Forestry Institute Paper 42. Oxford, UK. Fourer, R., Gay, D.M., Kernighan, B.W., 2003. AMPL: A modeling language for mathematical programming, second ed. Duxbury Press, Belmont, CA. http://ampl.com/ resources/the-ampl-book/chapter-downloads/ (accessed 10.01.14). Franklin, J.F., Spies, T.A., Pelt, R.V., Carey, A.B., Thornburgh, D.A., Berg, D.R., Lindenmayer, D.B., Harmon, M.E., Keeton, W.S., Shaw, D.C., Bible, K., Chen, J., 2002. Disturbances and structural development of natural forest ecosystems with silvicultural implications, using Douglas-fir forests as an example. For. Ecol. Manage. 155 (1–3), 399–423. http://dx.doi.org/10.1016/S0378-1127(01)00575-8. García, O., 1984. FOLPI, a forestry-oriented linear programming interpreter. In: Proceedings IUFRO Symposium on Forest Management Planning and Managerial Economics. University of Tokyo, Tokyo. pp. 293–305. Gauthier, S., Vaillancourt, M.-A., Kneeshaw, D.D., Drapeau, P., De Grandpre, L., Claveau, Y., Pare, D., 2009. Forest ecosystem management: Origins and foundations. In: Gauthier, S., Vaillancourt, M.-A., Leduc, A., De Grandpré, L., Kneeshaw, D., Morin, H., Drapeau, P., Bergeron, Y. (Eds.), Ecosystem Management in the Boreal Forest. Presses de l’Université du Québec, Quebec, QC. pp. 13–38. Groupe DDM (Del Degan, Massé et Associés), 2010. Impact des coûts d’operation sur la valeur de la redevance et les coûts d’approvisionnment en bois. Prepared for the Ministère des Resources naturelles et Faune Québec, Québec. http://www.mffp.gouv. qc.ca/publications/forets/gestion/ impact-couts-operation.pdf (accessed 15.03.15). Groupe DDM (Del Degan, Massé et Associés), 2012. Structure de l’industrie de la récuperation du bois provenant de la construction, la rénovation et la démolition au Québec. Recyc-Québec, QC. http://www.recyc-quebec.gouv.qc.ca/Upload/Rapportfinal-bois.pdf (accessed 15.03.15). Gunn, E., 2007. Models for strategic forest management. In: Weintraub, A.J., Miranda, J.P., Romero, C., Bjørndal, T., Epstein, R. (Eds.), Handbook of operations research in natural resources. Springer, Heidelberg Berlin New York, pp. 317–341. Gunn, E.A., Rai, A.K., 1987. Modelling and decomposition for planning long-term forest harvesting in an integrated industry structure. Can. J. For. Res. 17, 1507–1518. http://dx.doi.org/10.1139/x87-233. Hunter, M.L., 1993. Natural fire regimes as spatial models for managing boreal forests. Biol. Conserv. 65, 115–120. http://dx.doi.org/10.1016/0006-3207(93)90440-C. Jensen, P.A., Bard, J.F., 2003. Operations Research Models and Methods Vol. 1 John Wiley & Sons Inc, New York. Jetté, J.-P., Leblanc, M., Bouchard M., Villeneuve, N., 2013. Intégration des enjeux écologiques dans les plans d’aménagement forestier intégré, Partie I – Analyse des enjeux, Québec, gouvernement du Québec, ministère des Ressources naturelles, Direction de l’aménagement et de l’environnement forestiers, pp. 150. Johnson, E.A., Gutsell, S.L., 1994. Fire frequency models, methods and interpretations. Adv. Ecol. Res. 25, 239–283. http://dx.doi.org/10.1016/S0065-2504(08)60216-0.

Acknowledgements We thank the Ministère des Forêts, de la Faune et des Parcs du Québec (MFFPQ) for providing data from their third Forest Inventory Program 2002–2004 and the Société de protection des forêts contre le feu (SOPFEU) for fire data that were collected between 1971 and 2014. We also thank Julien Beguin for providing us with a map of mill locations, and Phyllis Daly and William F.J. Parsons for thoroughly editing the English of this manuscript. This study was supported by the NSERC Value Chain Optimization (VCO) Network under its research theme 1 “Integrated Forest and Industry Strategies for the Modern Bioeconomy” and an NSERC Discovery grant to LeBel. References Adresses Québec, 2015. AQ réseau (data base) http://adressesquebec.gouv.qc.ca/ aqreseau.asp (accessed 16.09.15). Attiwill, P.M., 1994. The disturbance of forest ecosystems: the ecological basis for conservative management. For. Ecol. Manage. 63, 247–300. http://dx.doi.org/10.1016/ 0378-1127(94)90114-7. Bank of Canada, 2015. Inflation calculator. Bank of Canada. http://www.bankofcanada. ca/rates/related/inflation-calculator/?__utma=1.1835431595.1440610285. 1440610285.1440610285.1&__utmb=1.1.10.1440610285&__utmc=1&__utmx=(accessed 20.03.15). Barclay, H.J., Li, C., Hawkes, B., Benson, L., 2006. Effects of fire size and frequency and habitat heterogeneity on forest age distribution. Ecol. Model. 197, 207–220. http:// dx.doi.org/10.1016/j.ecolmodel.2006.03.007. Barros, O., Weintraub, A., 1982. Planning for a vertically integrated forest industry. Oper. Res. 30, 1168–1182. http://dx.doi.org/10.1287/opre.30.6.1168. Belleau, A., Légaré, S., 2009. Project Tembec: towards the implementation of a forest management strategy based on the natural disturbance dynamics of the northern Abitibi region. In: Gauthier, S., Vaillancourt, M.-A., Leduc, A., De Grandpré, L., Kneeshaw, D., Morin, H., Drapeau, P., Bergeron, Y. (Eds.), Ecosystem Management in the Boreal Forest. Presses de l’Université du Québec, Quebec, QC. pp. 479–499. Bergeron, Y., Harvey, B., Leduc, A., Gauthier, S., 1999. Forest management guidelines based on natural disturbance dynamics: stand-and forest-level considerations. For. Chron. 75, 49–54. http://dx.doi.org/10.5558/tfc75049-1. Bergeron, Y., Irulappa Pillai, D.B., Ouzennou, H., Raulier, F., Leduc, A., Gauthier, S., 2017. Projections of future forest age class structure under the influence of fire and harvesting: implications for forest management in the boreal forest of eastern Canada. Forestry 90, 85–495. http://dx.doi.org/10.1093/forestry/cpx022. BFEC (Bureau du forestier en chef), 2013. Manuel de détermination des possibilités forestières 2013–2018. Gouvernement du Québec, Roberval, QC. pp. 247. http:// forestierenchef.gouv.qc.ca/wp-content/uploads/2013/01/MDPF_VF.pdf (accessed 08.08.2014). Binkley, C.S., Percy, M., Thompson, W.A., Vertinsky, I.B., 1994. A general equilibrium analysis of the economic impact of a reduction in harvest levels in British Columbia. For. Chron. 70, 449–454. http://dx.doi.org/10.5558/tfc70449-4. Bouchard, M., Boucher, Y., Belleau, A., Boulanger, Y., 2015. Modélisation de la variabilité naturelle de la structure d'âge des forêts du Québec. Gouvernement du Québec. Direction de la recherche forestière, Ministère des Forêts, de la Faune et des Parcs, Direction de la recherche forestière. Mémoire de recherche forestiére-175. pp. 32. Bouchard, M., Pothier, D., 2011. Long-term influence of fire and harvesting on boreal forest age structure and forest composition in eastern Québec. For. Ecol. Manage. 261, 811–820. http://dx.doi.org/10.1016/j.foreco.2010.11.020. Bouchard, M., Garet, J., 2014. A framework to optimize the restoration and retention of large mature forest tracts in managed boreal landscapes. Ecol. Appl. 24 (7), 1689–1704. http://dx.doi.org/10.1890/13-1893.1. Boulanger, Y., Gauthier, S., Burton, P.J., Vaillancourt, M.A., 2012. An alternative fire regime zonation for Canada. Int. J. Wildland Fire 21, 1052–1064. http://dx.doi.org/ 10.1071/WF11073.

55

Forest Ecology and Management 429 (2018) 44–56

B. Rijal et al.

l’échelle du peuplement pour les forêts du Québec. Mémoire de recherche forestière 163. Ministère des Ressources naturelles et de la Faune du Québec. http://www.mffp. gouv.qc.ca/publications/forets/connaissances/recherche/Auger-Isabelle/ Memoire163.pdf (accessed 15.10.13). Powelson A, Martin P., 2001. Spacing to increase diversity within stands. Stand density management diagrams. http://www.for.gov.bc.ca/hfp/pubs/standman/Sp_Div.pdf (access 10.08.2016). Powers, R.P., Coops, N.C., Morgan, J.L., Wulder, M.A., Nelson, T.A., Drever, C.R., Cumming, S.G., 2013. A remote sensing approach to biodiversity assessment and regionalization of the Canadian boreal forest. Prog. Phys. Geogr. 37, 36–62. R Development Core Team, 2014. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.Rproject.org/ (accessed 15.02.14). Raulier, F., Le Goff, H., Gauthier, S., Rapanoela, R., Bergeron, Y., 2013. Introducing two indicators for fire risk consideration in the management of boreal forests. Ecol. Indic. 24, 451–461. http://dx.doi.org/10.1016/j.ecolind.2012.07.023. Reed, W.J., Errico, D., 1986. Optimal harvest scheduling at the forest level in the presence of the risk of fire. Can. J. For. Res. 16, 266–278. http://dx.doi.org/10.1139/x86-047. Rijal, B., Lussier, J.-M., 2017. Improving sustainability of value-added forest supply chain through coordinated production planning policy between forests and mills. For. Policy. Econ. 83, 45–57. http://dx.doi.org/10.1016/j.forpol.2017.06.003. Robitaille, A., Saucier, J.-P., 1998. Paysages régionaux du Québec méridional. Les Publications du Québec, Quebec. Savage, D.W., Martell, D.L., Wotton, B.M., 2010. Evaluation of two risk mitigation strategies for dealing with fire-related uncertainty in timber supply modelling. Can. J. For. Res. 40, 1136–1154. http://dx.doi.org/10.1139/X10-065. Savage, D.W., Martell, D.L., Wotton, B.M., 2011. Forest management strategies for dealing with fire-related uncertainty when managing two forest seral stages. Can. J. For. Res. 41, 309–320. http://dx.doi.org/10.1139/X10-212. Schmoldt, D.L., 2001. Application of artificial intelligence to risk analysis for forested ecosystems. In: von Gadow, K. (Ed.), Risk Analysis in Forest Management. Kluwer Academic Publishers. Seymour, R., Hunter, M.L., 1999. Principles of ecological forestry. In: Hunter, M.L. (Ed.), Maintaining Biodiversity in Forest Ecosystems. Cambridge. University Press, Cambridge, UK. Tittler, R., Messier, C., Fall, A., 2012. Concentrating anthropogenic disturbance to balance ecological and economic values: applications to forest management. Ecol. Appl. 22 (4), 1268–1277. http://dx.doi.org/10.1890/11-1680.1. Toppinen, A., Zhang, Y.Q., Geng, W., Laaksonen-Craig, S., Lähtinen, K., Li, N., Liu C., Majumdar, I., Shen, Y., 2010. Changes in Global Markets for Forest Products and Timberlands. IUFRO (International Union of Forestry Research Organizations) Secretariat. IUFRO World Series 2010, vol. 25, pp.137–156. van Wagner, C.E., 1978. Age-class distribution and the forest fire cycle. Can. J. For. Res. 8, 220–227. http://dx.doi.org/10.1139/x78-034. van Wagner, C.E., 1983. Simulating the effect of forest fire on long-term annual timber supply. Can. J. For. Res. 13, 451–457. http://dx.doi.org/10.1139/x83-068. Wirth, C., Messier, C. Bergeron Y. Frank, D., Fankhaenel A., 2009. Old-growth forest definitions: a pragmatic View. In: Wirth, C., Gleixner, G., Heimnann, M. (Eds.). Old‐Growth Forests: Function, Fate and Value. Ecological Studies 207. Springer‐Verlag Berlin Heidelberg. pp. 11–33. Zhang, S.-Y., Tong, Q.-J., 2005. Modeling lumber recovery in relation to selected tree characteristics in jack pine using sawing simulator Optitek. Ann. For. Sci. 62, 219–228. http://dx.doi.org/10.1051/forest: 2005013.

Kneeshaw, D., Gauthier, S., 2003. Old growth in the boreal forest: a dynamic perspective at the stand and landscape level. Enviro. Rev. 11 (S1), S99–S114. http://dx.doi.org/ 10.1139/a03-010. Koskela, E., Ollikainen, M., Pukkala, T., 2007. Biodiversity conservation in commercial boreal forestry: the optimal rotation age and retention tree volume. For. Sci. 53, 443–452. http://dx.doi.org/10.1093/forestscience/53.3.443. Laurent, A.B., Vallerant, S., Bouchard, M., Carle, M.A., D’Amours, S., 2013. Outil d’aide à la décision intégrant les critères environnementaux pour le transport des produits du bois. In: Proceedings of the 10ème Congrès international de génie industriel, La Rochelle, France. Lehoux, N., Amours, S.D., Beaulieu, J., Marier, P., Ouellet, D., 2012. The Value Creation Network of Canadian Wood Fibre. Centre interuniversitaire de recherche sur les reseaux d’entreprise, la logistique et le transport, FORAC Research Consortium, Université Laval, Québec. CIRRELT-2012-34. Liu, C., Ruel, J.-C., Groot, A., Zhang, S.Y., 2009. Model development for lumber volume recovery of natural balsam fir trees in Quebec, Canada. For. Chron. 85, 870–877. http://dx.doi.org/10.5558/tfc85870-6. Liu, C., Zhang, S.Y., 2005. Models for predicting product recovery using selected tree characteristics of black spruce. Can. J. For. Res. 35, 930–937. http://dx.doi.org/10. 1139/X05-025. Martell, D.L., 1980. The optimal rotation of a flammable forest stand. Can. J. For. Res. 10, 30–34. https://doi.org/10.1139/x80-006. Mastrandrea, M.D., Field, C.B., Stocker, T.F., Edenhofer, O., Ebi, K.L., Frame, D.J., Held, H., Kriegler, E., Mach, K.J., Matchoss, P.R., Plattner, G-K, Yohe, G.W., Zwiers F.W., 2010. Guidance note for lead authors of the IPCC fifth assessment report on consistent treatment of uncertainties. Intergovernmental Panel on Climate Change (IPCC). http://www.ipcc.ch/pdf/supporting-material/uncertainty-guidance-note.pdf (accessed 10.09.16). Messier, C., Tittler, R., Kneeshaw, D.D., Gélinas, N., Paquette, A., Berninger, K., Paquette, A., Rheault, H., Meek, P., Beaulieu, N., 2009. TRIAD zoning in Quebec: experiences and results after 5 years. For. Chron. 85, 885–896. http://dx.doi.org/10.5558/ tfc85885-6. MRNFQ (Ministère des Ressources Naturelles et de la Faune du Québec), 2009. Répertoire des usines de transformation primaire du bois. Édition juillet 2009. http://www.mrn. gouv.qc.ca/forets/entreprises/entreprises-transformation-publications-industrietable.jsp (accessed 05.1209). Mönkkönen, M., Juutinen, A., Mazziotta, A., Miettinen, K., Podkopaev, D., Reunanen, P., Salminen, H., Tikkanen, O.-P., 2014. Spatially dynamic forest management to sustain biodiversity and economic returns. J. Environ. Manage. 134, 80–89. http://dx.doi. org/10.1016/j.jenvman.2013.12.021. Natural Resources Canada, 2013. The state of Canada’s forest. Annual report. http://cfs. nrcan.gc.ca/pubwarehouse/pdfs/35191.pdf (accessed 22.11.16). Oliver, C.D., 1980. Forest development in North America following major disturbances. For. Ecol. Manage. 3, 153–168. http://dx.doi.org/10.1016/0378-1127(80)90013-4. Pasturel, T., 2013. Étude de la rentabilité de différentes stratégies d’aménagement forestier en forêt boréale du nord de l'Abitibi. Thesis. Maîtrise en Sciences de l’Environment, Université du Québec à Montréal, Montréal, QC. pp. 150. Patriquin, M.N., Lantz, V.A., Stedman, R.C., White, W.A., 2008. Working together: a reciprocal wood flow arrangement to mitigate the economic impacts of natural disturbance. Forestry 81, 227–242. http://dx.doi.org/10.1093/forestry/cpn017. Peterson, G., Allen, C.R., Holling, C.S., 1998. Ecological resilience, biodiversity and scale. Ecosystems 1, 6–18. Pothier, D., Auger, I., 2011. NATURA-2009: un modèle de prévision de la croissance à

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