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Supplementary Materials for Environmental Management submission:
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Technical Appendix
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Stand Growth and Yield
Incorporating Carbon Storage into the Optimal Management of Forest Insect Pests: A Case Study of the Southern
Pine Beetle (Dendroctonus Frontalis Zimmermann) in the New Jersey Pinelands
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We model a fully stocked pitch pine stand which grows 120 years based on data collected by Illick and
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Aughanbaugh (1930) on pitch pine in Pennsylvania. Initial stand ages between 0 and 60 were modeled, and the
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forest was assumed to remain at a steady state after 120 years of age. The stand modeled grows at low elevations in
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sandy loam soils with moderate moisture (Illick and Aughanbaugh 1930). Diameter at breast height, trees per acre,
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and volume grow as a function of stand age:
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𝐷𝐵𝐻 = 4.923 ln(𝑥) − 10.251 (R2= .978)
𝑆 = 1407.8𝑒 −.026𝑥 (R2= .974)
𝑉 = 𝑆 × .0248 𝐷𝐵𝐻 2.9142 (R2= .998)
Where:
x= stand age (years)
DBH= Average DBH (in.)
S= Number of stems per acre
V= Total Stand Volume (ft3/acre)
For the thinning scenarios, one thin from a basal area of 120ft2/ac to 80 ft2/ac is modeled, which is the
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typical recommended thinning levels for reducing risk of SPB (Fettig et al. 2007). The number of thinned trees was
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determined from basal area and DBH, using the definition of basal area:
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(𝐵𝐴𝑝𝑟𝑒𝑡ℎ𝑖𝑛 −𝐵𝐴𝑝𝑜𝑠𝑡𝑡ℎ𝑖𝑛)
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𝑇𝑅 =
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Where:
BA= Basal area (square feet/acre)
DBH= Average Diameter at Breast Height (in.)
TR= Number of Trees Removed per acre
(.00545 × 𝐷𝐵𝐻 2 )
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The biomass of thinned wood was calculated using allometric relationships derived from pitch pine in New York
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(Whittaker and Woodwell 1968):
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𝑂𝐷𝐵 = ( .1040𝐷𝐵𝐻 2.3373 ) × 𝑇𝑅
Where:
ODB= Oven Dry Above-ground Biomass (kg/acre)
DBH= Diameter at breast height (cm)
TR= Number of Trees removed per Acre
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Basal area and thus the weighted incidence probabilities are recalculated after thinning using growth and
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yield relationships. Because the effects of thinning on growth rates of remaining trees in pitch pine stands in New
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Jersey has not been studied, DBH growth rates of trees are adjusted to increase .01 in. per year after thinning. This
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estimate was based on the range of increased growth rates from data of shortleaf and loblolly stands in the South
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(Feduccia et al. 1979; Mann 1952).
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Southern Pine Beetle Infestations and Ecological Data
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This study considers a weighted incidence probability used in previous literature, as well as regional SPB
population levels and climate to stochastically generate SPB infestations through Monte Carlo simulations.
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Weighted Incidence Probability: We consider a model in which the risk of a Southern Pine Beetle attack increases
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as a function of basal area of a stand, according to the Daniel’s (1979) incidence probability function:
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1
𝑃𝐷𝐾 =
1 + 𝐸𝑋𝑃(4.829 − (. 0519 ∗ (
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65
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(
𝐵𝐴
)) − (4.062 ∗ (%𝑃𝑆𝐶))
4.356
)
Where:
PDK= Daniels Incidence Probability for stand
BA= Basal area (m2/ac)
%PSC= Percent pine composition of stand
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This incidence probability has been used in previous models of SPB pestilence (Costanza et al. 2012; Burkhart et al.
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1986). Percent pine composition of the stand is assumed to be a constant 80% as in Reed et al. (1982).
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The Daniels function estimate is “unweighted,” or it assumes that there are an equal number of infested and
un-infested stands in a region. Thus, it must be adjusted for region-wide infestation risk or the average number of
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infested stands of host type across the region during an outbreak year. In order to weight this function, we use a
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similar weighting system as Naumann (2012) to adjust the Daniels et al. (1979) probability function by the New
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Jersey regional risk:
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𝑃𝑠
𝑃̅𝐷
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𝑃𝑘 = 𝑃𝐷𝑘 ∗
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Where:
Pk = probability of mortality from SPB
Ps= regional SPB risk
PDk= Daniels probability
𝑃̅𝐷 = average Daniels probability for stand
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New Jersey regional SPB risk was determined through an ArcGIS analysis of New Jersey Department of
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Environmental Protection SPB spot data between 2002 and 2011 over outbreak years and New Jersey Department of
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Environmental Protection Land Use Land Cover (LULC) 2007 data on forest types. Stands were assumed to have
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similar species composition between 2002-2011 as they had when they were surveyed in 2007. The regional SPB
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risk, measured in median infested acres/ acre of host type for outbreak years, was calculated assuming that any
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stands with greater than 50% conifer composition were host stands.
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Regional SPB Populations: In this model, each year was stochastically determined to be an “outbreak year,” in
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which the weighted incidence probability was invoked, or an “endemic year,” in which SPB populations were
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assumed to be so low that no forest damage occurred. In endemic years, the weighted incidence probability was
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assumed to be 0. We modeled high, medium, and low SPB population levels, in which 80%, 50%, and 20% of years
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modeled, respectively, were outbreak years.
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Climate: Climate, another factor that is not typically incorporated into economic analyses of SPB infestations, is
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also incorporated into this model for greater biological accuracy. Studies have projected that future climate change
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may increase SPB infestation risk in certain areas by 2.5-5 times (Gan, 2004). Minimum winter temperature (MWT)
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was modeled in this study because it is the most well-known regulating factor of SPB outbreak, since notable winter
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mortality occurs when temperatures drop below -12°C and beetles freeze (Lombardero et al. 2000a). Tran et al.
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(2007) found that if the coldest winter night dropped below -16°C, the probability of a decrease in SPB population
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was 65%. If temperatures dropped below -20°C, then there was an 80% likelihood that populations significantly
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declined. This study thus assumed the same criteria as Tran et al. (2007).
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Volumetric Losses and Severity: If a stand is determined to be infested based on the incidence probability, climate,
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and regional outbreak, we assume that a “spot” or growing infestation will develop that affects a proportion of the
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stand. We assume that suppression will stop spot growth after 45 days (Burkhart et al. 1986) while no management
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will allow spot growth to continue throughout the summer (Fettig et al. 2007), which we modeled as being 120 days.
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Many studies of SPB in the South have documented that spot growth and thus volumetric losses from SPB vary with
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basal area, DBH and other stand parameters (Lorio et al. 1982; Nebeker et al. 1985). Thus, we used the Reed et al.
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(1981) severity function derived from data in Texas to model spot growth over the 45 or 120 day period of spot
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growth:
𝑇𝐵𝐴
𝑙𝑛(𝑇𝐾𝐷) = 3.43 + .965𝑙𝑛(𝐴𝑇) − 2.85𝑙𝑛(𝐷𝐵𝐻) − 22.13(
) + .074𝑇𝐵𝐴 + .5576𝑃𝑂𝑃
𝐷𝐵𝐻 2
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As in Burkhart et al. (1986) we assume the initial spot size is .05 acres so the number of initial attacked trees is
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derived from stand density at the time of infestation. Volumetric losses are then calculated using the following
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formula, based on Burkhart et al. (1986) and pitch pine growth and yield from Illick and Aughenbaugh (1930):
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Where:
TKD= Trees killed per day
AT=Number of initial attacked trees
DBH= Diameter at breast height (cm)
TBA= Total Basal Area (m2/ha)
POP= annual number of spots/405 ha of host trees for entire region/year
𝑉𝐿 = (𝐴𝑇 + (𝑇𝐾𝐷 ∗ 𝐷)) ∗ .0248 ∗ (𝐷𝐵𝐻 2.9143 )
Where:
TKD= Trees killed per day
AT=Number of initial attacked trees
DBH= Diameter at breast height (cm)
D= Days of spot growth
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Once volumetric losses are calculated, the proportion of the stand infested, or the “sub-stand” is reset to stand age of
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zero while the remaining proportion of the stand continues growing unharmed. Basal areas and thus infestation
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probabilities are then weighted based on the proportion of the stand each “sub-stand” represents. We assume our
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stand is infested a maximum of seven times in the 120 year modeling period.
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Incorporating and Valuing Carbon Sequestration
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Following Gutrich and Howarth’s (2007) model, carbon storage is determined from four main components:
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live above ground biomass, root biomass, soil, and dead and downed wood. Carbon is then valued assuming a future
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global carbon emissions and offsets trading market, as in Gutrich and Howarth (2007), and incorporated into
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economic analyses using social net present value calculations.
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Live Biomass: Carbon in live biomass is calculated from total above and below ground biomass of trees using the
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50% rule, which is the default used in IPCC reports. This rule states that standing live carbon content of a stand is
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approximately 50% of oven-dry biomass ( Brown and Lugo 1982). As was followed in Lathrop et al.’s (2011)
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analysis of carbon sequestration in New Jersey, below ground, or root biomass, was assumed to be directly related to
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above ground biomass, using relationships developed by Cairns et al. (1997):
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𝑅𝐵 = 𝐸𝑋𝑃(−1.085 + .926𝐿𝑛(𝐴𝐺𝐵))
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where:
RB= Root Biomass (tons/acre)
AGB= Above ground Biomass (tons/acre)
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Soil Carbon: Soil carbon was assumed to be independent of management as in Gutrich and Howarth (2007) and thus
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assumed to be a constant value of 20 tons/acre in this study. This figure was derived from Lathrop et al. (2011), who
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found from USDA Soil Survey Geographic (SSURGO) database and Forest Inventory and Analysis data that soil
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carbon density in the Pinelands ranged from between 20 and 75 tons/ acre. The highest soil carbon densities were
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found in poorly drained soils of coastal wetland areas, while the lowest soil carbon densities were found in the drier
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soils of the Uplands, which most closely resembled the soil conditions of the stands modeled in Illick and
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Aughanbaugh (1930).
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Dead and Downed Wood: Carbon in dead and downed wood was determined from an equation developed by
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Gutrich and Howarth (2007), which allows dead and downed wood to decay at a certain rate each year and new dead
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biomass to be added each year to the dead and downed wood stock:
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𝐶𝑑𝑒𝑎𝑑 = (1 − 𝜕0 )[𝐶𝑑𝑒𝑎𝑑 (𝑡 − 1) + 𝜕1 𝐶𝑙𝑖𝑣𝑒 (𝑡 − 1)𝜕2 ]
where:
𝐶𝑑𝑒𝑎𝑑 = Carbon in dead/ downed wood (tons)
𝜕0 = Decay rate of dead/downed wood (%/year)
𝜕1 , 𝜕2 =Formation coefficients for dead/ downed wood
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Formation and decay rates of dead and downed wood determined by Gutrich and Howarth from Forest Inventory
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and Analysis data for red/white/jack pine in the Northeast were used, as no data existed for pitch pine in New Jersey.
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It was assumed that carbon converted into mulch from thinning or cut and remove suppression was completely
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released within a year after mulching, and trees left from cut and leave suppression were added as dead and downed
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wood and decayed at the same rate as other dead and downed wood.
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Carbon Valuation: As discussed in the manuscript, increasingly, the social costs of carbon- and thus the value of
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carbon sequestration- are increasingly being considered in forest management. The value of carbon, or the marginal
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benefit of a ton of carbon sequestered, can be determined from the social costs of carbon over time using an
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Integrated Assessment Model, which uses an aggregate damage function to determine prices of carbon under future
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emissions scenarios. We used the 2007 version of the DICE integrated assessment model (Nordhaus, 2008) to
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determine marginal benefits over time in two potential future policy scenarios. In the first policy scenario, or the
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“low marginal benefits of carbon scenario,” we assume climate mitigation aims to maximize net benefits and
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marginal benefits of carbon increase over time according to the following equation:
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𝑀𝐵𝑙𝑜𝑤 = 39.874 ∗ 𝐸𝑋𝑃(. 0167𝑡)
where:
MBlow= Marginal benefits of Carbon ($/ton)
t= time (years)
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In the second policy scenario, or the “high marginal benefits of carbon” scenario, we assume emissions
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abatement programs prevent more than a 2 degree F increase in global mean temperatures over the next century;
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thus, marginal benefits of carbon increase over time according to the following equations:
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For t<80,
For t>80,
𝑀𝐵ℎ𝑖𝑔ℎ = 72.987 ∗ 𝐸𝑋𝑃(.0336𝑡)
𝑀𝐵ℎ𝑖𝑔ℎ = .23267𝑡 2 − 50.217𝑡 + 3451.1
Where:
MBhigh= Marginal benefits of Carbon ($/ton)
t= time (years)
Private and Social Net Present Value Calculations:
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Without considering carbon sequestration or other ecosystem services, a rational forest manager would
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choose to follow the SPB management scenario that would maximize net benefits from chips and mulch, or the
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private net present value:
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𝑡
𝑁𝑃𝑉𝑝𝑟𝑖𝑣𝑎𝑡𝑒 = ∑(𝑅𝑡ℎ𝑖𝑛 − 𝐶𝑡ℎ𝑖𝑛 + 𝑅𝑠𝑢𝑝𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 − 𝐶𝑠𝑢𝑝𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 ) ∏
𝑡=0
𝑖=1
1
(1 + 𝑟(𝑖))
Where:
𝑅𝑡ℎ𝑖𝑛 = Revenue from 1 acre of thinning
𝐶𝑡ℎ𝑖𝑛 = Costs/acre of thinning
𝑅𝑠𝑢𝑝𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 = Revenue/ acre of suppression
𝐶𝑠𝑢𝑝𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 = Costs/acre of suppression
r(i) = discount rate
t= time (years)
The Private NPV is calculated as zero unless the basal area of the stand exceeds 120 square feet per acre
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and the stand is thinned or if the stand is stochastically determined to be infested that year. Marginal benefits derived
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from chips and mulch were determined from an internet search of mulch and chip prices; the majority of the
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contractors interviewed conducting SPB management were in the business as developers and land clearers, so the
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marginal benefits from mulch and chips derived from costs avoided from having to buy mulch and chips for
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developments. Costs of thinning and suppression per acre were also determined from interviews with contractors in
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NJ. Because cost estimates per acre were provided and the majority of infestations modeled were less than an acre,
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we modeled scenarios in which costs of suppressing an infestation were 75% and 50% of costs/per acre.
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When carbon sequestration is considered, net benefits derived from carbon, or the carbon net present value,
can be calculated from the marginal benefits of carbon from global emissions and abatement schemes:
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𝑁𝑃𝑉𝑐𝑎𝑟𝑏𝑜𝑛 = ∑ 𝑀𝐵(𝑡) ∗ ∆𝐶(𝑡) ∏
t=0
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𝑡
i=1
1
(1 + 𝑟(𝑖))
Where:
MB(t)= marginal benefit of a ton of carbon sequestered
∆𝐶(𝑡)=change in carbon stored (tons) from t to t+1
r(i)= discount rate
t= time (years)
In the case of a carbon emissions and offsets market, a rational forest manager would want to maximize the
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social net present value, or the addition of the private and carbon net present values when managing for SPB
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pestilence:
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𝑁𝑃𝑉𝑠𝑜𝑐𝑖𝑎𝑙 = 𝑁𝑃𝑉𝑝𝑟𝑖𝑣𝑎𝑡𝑒 + 𝑁𝑃𝑉𝑐𝑎𝑟𝑏𝑜𝑛
Sensitivity and Scenario Analyses:
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Sensitivity analyses were conducted by varying inputs parameters by 25%. In addition, sensitivity analyses
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were conducted for 2%, 4%, 8%, and 12% discount rates and assuming that costs of suppression for each infestation
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(which were under an acre) were 100%, 75%, and 50% the costs of suppression per acre. Formation and decay
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coefficients of dead and downed wood as well as regional SPB risk had the greatest effect on mean Social NPV, as
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well as regional SPB risk. Thus, scenario analyses were conducted with dead and downed wood formation and
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decay coefficients from the literature derived from oak/pine and white/red pine. In addition, scenarios were
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conducted by increasing regional SPB risk two, three, and six fold to assess under what conditions thinning would
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be favored when both carbon and timber are considered.
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At 100% the costs of suppression, the strategy that maximized Private NPV varied based on SPB
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population levels and initial stand age. At 50% and 75% the costs of suppression per acre, thinning maximized
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Private NPV at all stand ages in medium population levels. However, no management strategies still maximized
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Social NPV. Formation coefficients for oak/pine did not affect optimal management results.
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For every discount rate modeled, no management strategies maximized social NPV. However, for the
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highest discount rate scenario (12%), social NPV for thinning scenarios exceeded that of suppression cut and leave
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scenarios (Table S-1).
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Social net present value of thinning scenarios also exceeded that of suppression only scenarios when
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regional SPB population risk increased to six times that of current population levels or thinning completely
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eradicated risk of SPB and regional SPB population risk increased to two times that of current levels.
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Table S-1: For all discount rates, social net present value (NPV) ($/acre) is maximized for no management
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scenarios.
Discount rate
No management
(%/year)
Suppression cut and
Thinning and cut and
leave
leave suppression
2
1244
1181
892
4
924
886
791
8
510
486
479
2
339
315
322
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References
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