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Picea rubens growth at high versus low elevationsin the Great Smoky Mountains National Park:evaluation by systems modeling
Kyung-Ah Koo, Bernard C. Patten, and Irena F. Creed
Abstract: For half a century, red spruce (Picea rubens Sarg.), a commercially and ecologically important boreal tree spe-cies, has experienced growth decline and high mortality in eastern North America. A tree growth systems model, ARIM(annual radial increment model), was developed to evaluate responsible factors for red spruce growth in the Great SmokyMountains National Park. The dominant cause at higher elevations (1800–2000 m) was found to be air pollution involvinghigh-frequency acidic rain and cloud immersion. The identified causes at lower elevations (1450–1700 m) were insufficientsolar absorption due to photoinhibition, drought stress resulting from reduced precipitation and high evapotranspiration dueto warmer temperatures, and minor effects of air pollution. The ARIM exemplifies a complex systems concept and method-ology for evaluating multivariable factors in tree growth systems. ARIM provides a general model structure that incorporatescomplex direct and indirect interactions for tree system studies and quantitatively integrates knowledge and data from differ-ent disciplines by developing a new set of indices, the relative basis index values. The ARIM results implicate comprehen-sive habitat-dependent directions for long-term conservation policies and management of red spruce with environmentalchanges, climate change, and air pollution in the Great Smoky Mountains National Park.
Résumé : Depuis un demi-siècle, l’épinette rouge (Picea rubens Sarg.), une essence boréale importante du point de vuecommercial et écologique, connaît une baisse de croissance et une forte mortalité dans l’est de l’Amérique du Nord. Un mo-dèle de croissance, MARA (modèle d’accroissement radial annuel), a été développé pour évaluer les facteurs responsablesde la croissance de l’épinette rouge dans le parc national des Great Smokey Mountains. À haute altitude (1 800 à 2 000 m),nous avons identifié la pollution de l’air, impliquant la fréquence élevée de pluie acide et d’immersion nuageuse, commecause dominante. Les causes identifiées à basse altitude (1 450 à 1 700 m) étaient l’absorption insuffisante de rayonnementsolaire due à la photo-inhibition, le stress causé par la sécheresse due à la diminution des précipitations et à une forte évapo-transpiration associée à des températures plus chaudes, ainsi que des effets mineurs de la pollution de l’air. Le MARA illus-tre le concept de systèmes complexes et de méthodologie pour évaluer les facteurs multivariés dans les systèmes decroissance des arbres. Le MARA fournit une structure de modèle générale qui incorpore des interactions complexes directeset indirectes pour les études du système arbre et intègre de façon quantitative la connaissance et les données provenant dedifférentes disciplines en développant un nouvel ensemble d’indices, les valeurs de l’indice de base relatif. Des directivesdétaillées, dépendantes de l’habitat, découlent des résultats du MARA pour l’aménagement et les politiques de conservationà long terme de l’épinette rouge en fonction des changements environnementaux, du changement climatique et de la pollu-tion de l’air dans le parc national des Great Smokey Mountains.
[Traduit par la Rédaction]
Introduction
For half a century, red spruce (Picea rubens Sarg.), a com-mercially and ecologically important boreal tree species, hasexperienced growth decline and high mortality in easternNorth America (McLaughlin et al. 1987; Deusen 1988; Web-ster et al. 2004; Dumais and Prévost 2007). This has raisedconcern, as these changes are indicative of an ecosystemunder stress. Air pollution and climate change are frequentlycited as possible causes, and some research has found corre-lations with physiological processes (Johnson et al. 1992; De-Hayes et al. 1999; Dumais and Prévost 2007; Schaberg and
Hawley 2010). However, few- or single-factor results cannotcomprehensively address the full spectrum of complex factorsinvolved (McLaughlin et al. 1987; Schuler et al. 2002; Bus-ing 2004; Webster et al. 2004).Red spruce is long lived (>300 years) and shade tolerant
with a low reproductive rate and low genetic diversity (Whiteand Cogbill 1992). It is dominant or codominant in high-ele-vation coniferous forests in the Great Smoky Mountains(Busing 2004). In the eastern United States, it has been ex-posed to increasing anthropogenic emissions of acidic pollu-tants and greenhouse gases over the past century, among thehighest in the country (EPA 2000). Climate change has also
Received 15 June 2010. Accepted 12 December 2010. Published at www.nrcresearchpress.com/cjfr on 19 April 2011.
K.-A. Koo. Georgia Sea Grant, University of Georgia, 220 Marine Science Bldg., Athens, GA 30602, USA.B.C. Patten. Odum School of Ecology, 140 E. Green Street, University of Georgia, Athens, GA 30602-2202, USA.I.F. Creed. Department of Biology, The University of Western Ontario, London, ON N6A 5B7, Canada.
Corresponding author: K.-A. Koo (e-mail: [email protected] and [email protected]).
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Can. J. For. Res. 41: 945–962 (2011) doi:10.1139/X10-243 Published by NRC Research Press
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stressed populations near the southern edge of their range(Nicholas et al. 1999). Some pollutants, particularly SO2,have been partly alleviated by implementation of the CleanAir Act (1970, with amendments in 1977 and 1990; EPA2000). In contrast, the stress of climate change remains aconcern.Previous dendrochronological studies showed regional de-
clines from the 1960s to the 1980s in some southern Appala-chian areas (McLaughlin et al. 1987; Deusen 1988; Websteret al. 2004) but not others (LeBlanc 1993; Schuler et al.2002). The variable results may reflect methodological limi-tations in addressing the organized complexity of forest eco-systems. System theory methods, focusing on systemelements and their interrelationships, may be more appropri-ate (Odum 1962; von Bertalanffy 1969, 1975; Patten 1997).Open system theory, in particular, may enable researchers toevaluate the operation of large numbers of direct and indirectinteractions and factors (von Bertalanffy 1975; White et al.1992; Patten 1997; Lambers et al. 1998).The current study uses systems modeling based on open
system theory to examine how hierarchically organized bioticand abiotic complexity contribute to red spruce growth in theGreat Smoky Mountains National Park. The study objectivesare to (i) develop a tree growth systems model, ARIM (an-nual radial increment model), representing complex interac-tions between growth and environmental factors, such asradiation, water availability, and temperature, and (ii) usethis model to evaluate causes and processes of red sprucegrowth at higher versus lower elevations.
Materials and methods
Study areaThe study area is the Great Smoky Mountains National
Park (GSMNP) located in the southern Appalachian Moun-tains of the southeastern United States (Fig. 1). The GSMNPhas a cool, temperate, rainforest climate with a mean annualair temperature of 8.5 °C and mean annual precipitation of222 cm (Webster et al. 2004). These conditions result inshort growing seasons (100–150 days), frequent cloud im-mersion, and strong winds (Johnson et al. 1992). TheGSMNP is part of the mature Appalachian range character-ized by rounded summits and ridges that drain into ruggedslopes uniformly eroded by fluvial and colluvial processes.Relief ranges from about 250 to 2025 m at Clingman’sDome (Welch et al. 2002; Madden et al. 2004). The underly-ing bedrock is metamorphosed sedimentary material (Whit-taker 1956). Soils are inceptisols with abundant surfaceorganic matter and silt to sandy loam textures (Madden et al.2004). A red spruce – Fraser fir (Abies fraseri (Pursh) Poir.)forest follows the elevation gradient, with spruce dominatingat lower elevations (1370–1675 m), fir at higher elevations(>1890 m), and both codominating at midlevels (1675–1890 m) (Nicholas et al. 1992).
Tree growth responseAnnual red spruce growth was estimated from mean stand-
ardized ring width chronologies (Webster et al. 2004). In thisstudy, trees from permanent GSMNP plots of the NationalAcid Precipitation Assessment Program were cored (Nicholaset al. 1992) (Fig. 2). A minimum of 30 trees were selected
from higher (1800‒2000 m, n = 35) and lower (1450‒1700 m, n = 37) elevations. While sample size often de-pended on site conditions, 20 is generally accepted for char-acterization of a population (Fritts 1976; Cook andKairiukstis 1990; http://www.ncdc.noaa.gov/paleo/treeinfo.html#references). The sampling criteria were (i) live trees,(ii) >5 cm diameter at breast height, (iii) dominant or codo-minant in the canopy, and (iv) age >100 years. These criteriawere used to maximize the length of record and minimize theeffects of competition or other growth suppression withinstands. Two cores per tree were collected to facilitate accu-rate ring dating and cross-correlation. Individual chronologieswere standardized to remove systematic aging changes inring width by fitting a growth curve (negative exponential,negative line, or constant rate function) to the chronologyand dividing each measured ring width by the expectedgrowth curve value (Fritts 1976; Cook and Kairiukstis1990). Standardized ring width chronologies of subsampleswere combined to obtain a mean chronology for each tree,
Fig. 1. (a) Location of Great Smoky Mountains National Park in theeastern United States and (b) the boundaries elevation of the summitarea, Clingmans Dome (maps from Welch et al. 2002).
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and similarly, standardized ring width chronologies of treeswere combined to obtain a mean chronology for the plot andthen the elevation range. The length of mean chronology is271 years (1729–1999) at high elevations and 356 years(1644–1999) at low elevations.An expressed population signal (EPS) (Wigley et al. 1984)
was used to show the significance of mean chronology de-picting growth for the plot and elevation range. EPS relatesthe uncertainty of mean chronology correlations to the frac-tional common variance occurring as a parameter in an AN-OVA. EPS is a function of the number of cores and varianceamong cores and is estimated by
½1� ESP � ðRNÞ2 � Nr
1þðN � 1ÞrHere, ðRNÞ2 is the correlation between an N-series averageand the population, N is the total number of chronologies,and r is the average value of riI, i ≠ I, where riI is the corre-lation between chronologies i and I. EPS was applied to de-termine the number of tree cores required to significantlyrepresent a population-level growth signal where 0.85 ofEPS is generally accepted as a threshold (Wigley et al. 1984;Webster et al. 2004). Thus, mean standardized ring widthchronologies with EPS ≥ 0.85 were used for the present ana-lyses.
Environmental and ecosystem factorsTemperature, precipitation, air pollutants (nitrogen oxides
(NOx), sulphur oxides (SOx), and ozone (O3)), and standar-dized ring width data were compiled for ARIM. Temperatureand precipitation data were obtained from the airport mete-orological recording station (1939–1998) in Knoxville, Ten-nessee. Temperature was obtained by averaging dailytemperature records for each year. Extreme winter tempera-ture events were calculated by averaging the lowest dailytemperatures (cool events) and highest daily temperatures(warm events) during the winter months from November toFebruary. Extreme summer temperature events were calcu-lated by averaging the highest daily temperatures from Juneto August. Precipitation was obtained by totaling daily pre-cipitation records for each year. Climatic parameters were ad-justed by local factors in submodels, e.g., temperature wasadjusted by interactions with elevation, aspect, and slope inARIM submodels (Fig. 3; Appendix A (Tables A1–A4)). Airpollution data, national total values of NOx, SOx, and volatileorganic compound (VOC) emissions, were obtained from theUS Environmental Protection Agency (EPA 2000). The localair pollution data were not available for the entire study pe-riod. Specifically, O3 data were not available for the study pe-riod, so O3 data were estimated using the following equation(after http://www.epa.gov/air/ozonepollution/basic.html):
½2� O3 ¼ NOx þ VOCþ sunlight
where O3 is ground-level O3. Sunlight was excluded due to alack of long-term monitoring data, and theoretically, thereshould be no or little annual variation during a relativelyshort period of 59 years (Geiger et al. 2003; Aguado andBurt 2004).
ARIM structureARIM predicts tree growth (mean standardized ring width)
of red spruce populations. The model system boundary is de-fined by the annual tree growth of the red spruce populationinstead of the individual tree. Annual growth is divided bythe corresponding long-term average to highlight year-to-year changes. ARIM assumes that the relative annual growthof the red spruce population behaves as an open system (i.e.,increasing biomass more or less than the long-term average)in response to annual variations in photosynthesis and respi-ration in association with environmental interactions.ARIM consists of two parts: ARIMhigh for elevations
≥1700 m and ARIMlow for elevations <1700 m. The partshave the same conceptual design (one main model and eightsubmodels) but each uses different combinations of parame-ter values. The main model accounts for direct interactions(i.e., radiation, CO2, water availability, nutrient availability,herbivory, weather disturbance, soil-mediated disturbance,and air pollution disturbance (APD) (Fig. 2)). Data for all di-rect factors were simulated in the corresponding submodels.For example, the data for radiation in the main model weresimulated in the radiation submodel. The submodels accountfor the hierarchically organized indirect interactions (Fig. 3).The first step in developing ARIM was acquiring the rele-
vant data through a combination of published literature andexisting data on influential environmental factors and physio-logical responses of red spruce in GSMNP (see online sup-plementary data SD11; Koo 2009; Koo et al. 2011). Next, aconceptual model was constructed to organize the interac-tions between red spruce growth and the environment (Ap-pendix A (Tables A1–A4)). This conceptual model was thenused to construct conceptual diagrams in STELLA (Fig. 2)(http://www.iseesystems.com/softwares/Education/StellaSoft-ware.aspx). Finally, simulations were performed by (i) quan-tifying parameters, (ii) developing mathematical models, rule-based models, and graph functions of processes for each in-teraction, (iii) calibrating the parameters through sensitivityanalysis, and (iv) validating the models by comparing modeloutputs with observed data (Jørgensen and Bendoricchio2001). Details about equations and parameterizations ofARIMhigh and ARIMlow are shown in online supplementarydata SD2 and SD3.1
ARIM parameterizationParameter quantification can be difficult in systems model-
ing because different methods, measurements, and units areused. Dimensionless units were obtained by dividing eachyearly average value by the corresponding long-term mean,creating a relative basis index value (RBIV):
½3� RBIVij ¼cij
mi
where RBIVij is the RBIV of parameter i in year j, cij is themonitored value of parameter i in year j, and mi is the meanvalue of parameter i. RBIVs for environmental factors arepresented in online supplementary data SD2 and SD3.1
ARIM factor interactionsRandomness of data, the lack of correlation among obser-
1Supplementary data are available with the article through the journal Web site (http://www.nrcresearchpress.com/cjfr).
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vations in statistics, is a fundamental assumption for usingstatistical models. The randomness of the simulated data forthe eight direct factors in the main model was tested prior toapplication in the classification and regression tree (CART)
models and generalized linear models (GLMs). All data inthis study are time-series data, so an autocorrelation functionwas used to test autocorrelations among the data (Venablesand Ripley 2002). The randomness tests also showed whether
Fig. 2. Tree core sampling locations in the National Acid Precipitation Assessment Program plots within GSMNP (maps from Webster et al. 2004).
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the ARIM simulation process created autocorrelations amongdata in the submodel systems, which would mean that appli-cations of the CART models and GLMs should be used withcaution.Annual standardized ring width was computed as
½4� ARIRSj ¼X
i¼k
ai � RBIVij þ b
where ARIRSj is the standardized ring width of red spruce inyear j, RBIVij is the index value of parameter i in year j, ai is
Fig. 3. Structure of the ARIMs. The model was constructed based on the annual radial increment of red spruce (ARIRS) envirogram (Koo2009). (a) The main model consisted of ARIRS and factors contributing to the centrum. (b) Each submodel was constructed based on theinteractions between the centrum and webs. Circles represent the parameters and are linked with other factors using arrows based on equa-tions. Factors pointed at by an arrow represent dependent variables or controlled factors, and factors at the other side of an arrow representindependent variables or controlling factors. Circles with solid lines represent original parameters. Circles with broken lines represent copiedparameters of original parameters with the same name, so circles with the same names always represent the same hierarchically organizedinteractions and parameter values. For example, radiation in the main model includes all of the interactions and parameter values in the ra-diation submodel. This figure is from Koo (2009).
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the coefficient value of parameter i, b is the intercept value,and k is the total number of independent parameters of themain model.ARIM’s main model used a combination of CART models
and GLMs to determine the influential submodels (direct fac-tors in the main model) and coefficients. CART models wereused to identify influential direct factors; once identified,these direct factors were then used in GLMs fitted with aGaussian distribution to determine the coefficient of each di-rect factor. For the CART models, cross-validation was usedto obtain realistic estimates of prediction error (Crouse et al.1987). For the GLMs, Akaike’s information criterion (AIC)and dispersion parameters (DPs) obtained from analysis ofthe deviations were used to determine the models with thebest fits (Venables and Ripley 2002).The equations and coefficients for factor interactions in
submodels are summarized in Appendix A (Tables A3 andA4) (also see online supplementary data SD2 and SD31;Koo 2009). Linear deterministic equations were generallyused for simulating factor interactions in the submodels; oneexception was that a nonlinear relation was used for express-ing interactions between temperature and red spruce growth,the logistic map. “IF–THEN” rule-based models were used toquantify the interactions between spatial factors, such as ele-vation, slope, aspect, and other environmental factors. For ex-ample, the interaction between temperature and aspect wasexpressed by Temperature × (IF Aspect = east THEN 0.5else (IF Aspect = south THEN 1 else (IF Aspect = westTHEN 0.65 else 0.3))). The brief documentations of equa-tions and coefficients and raw data are described in onlinesupplementary data SD2 and SD3.1
ARIM validationThe generality and parameter estimation errors of the
GLM results for ARIMhigh and ARIMlow were checked by anonparametric bootstrapping test (Venables and Ripley 2002;Gelman et al. 2004; Tan et al. 2006). The bootstrapping testassumes that the observed data set is the entire data set thatwe wish to generalize and a bootstrap resample is a subset ofthe entire data set (Tan et al. 2006). The bootstrapping test isimplemented by randomly taking m (the number of resam-ples) from the observed data set with replacement and calcu-lating t* (the parameter estimates) for these resamples(Venables and Ripley 2002). The bootstrapping tests show(i) the probability distribution function that the parameter es-timates for resamples follow, (ii) the representativeness of theselected parameter estimate as showing the relative likelihoodof parameter estimates, and (iii) the standard error range andbias range of the original parameter estimates (Gelman et al.2004; Tan et al. 2006). For this study, the bootstrap resam-ples were implemented 10 000 times.ARIM was simulated using STELLA 9.0.0 and 9.0.3. A
particular advantage of STELLA modeling is that many fac-tors influencing a system can be considered at once. Also,different types of formulations, including linear, nonlinear,and rule based, can be applied to the interactions. All statisti-cal analyses, including the CART models, GLMs, and boot-strapping analysis, were carried out in R.2.6.1 (Venables andRipley 2002). A significance level of P < 0.05 was used forstatistical tests.
Results
ARIM factorsThe autocorrelation tests showed that the majority of the
parameters were random. The exception was parameters re-lated to the air pollution factors in the submodels, includingsoil-mediated disturbance, APD, and nutrients (Fig. 3). How-ever, the lack of randomness could not be avoided because itoriginated from the observed air pollution data such as ob-served air pollutants and ozone. On the other hand, the first-year autocorrelation of the water availability parameter wascaused by the system modeling process (i.e., Precipitation Ef-fect 2 in the Water Availability submodel (Fig. 3; AppendixA (Tables A3 and A4))). This first-year autocorrelation wascreated on purpose to emulate the 1-year-delayed interactionbetween precipitation and the production of buds on thetrees. Precipitation from one year influences the number ofbuds in the next year, which in turn impacts growth condi-tions (Meier and Leuschner 2008). The randomness tests re-vealed that the parameters generally met the assumptions ofthe model, and where they did not, the lack of randomnesswas explained by the observed data or by model designrather than unknown consequences of the model structure.
ARIM model performanceCART modeling identified APD as the only influential ex-
planatory variable for ARIMhigh and radiation (RA), APD,and water availability (WA) as the influential explanatoryvariables for ARIMlow (Table 1; Fig. 4). APD was a signifi-cant explanatory variable for ARIMhigh, showing the lowestcross-validation relative error, but RA, APD, and WA forARIMlow were not because the cross-validation relative errorsincreased with increasing tree size (the number of splits).However, even though their predictions were not significant,they were still more influential than other variables for ex-plaining annual variations of red spruce growth at low eleva-tions. Therefore, the CART modeling results for ARIMlowwere still useful for selecting influential variables to apply inthe GLMs. The selected parameters have been mentioned asimportant factors in red spruce growth in other research(Webster et al. 2004; Hawley et al. 2006; Dumais and Prévost2007; Schaberg and Hawley 2010). The GLM for ARIMhighis detailed in eq. 5 and the GLM for ARIMlow is detailed ineq. 6:
½5� ARIMhighi ¼ �0:6796APDi þ 1:5577
½6� ARIMlowi ¼ 5:3397RAi þ 11:3237WAi
� 0:2697APDi � 11:4031
where ARIMhighi is growth of the high-elevation red sprucepopulation in year i, ARIMlowi is growth of the low-elevationred spruce population in year i, RAi is radiation in year i,WAi is water availability in year i, and APDi is air pollutiondisturbance in year i.The GLM for ARIMhigh indicated that APD explained the
variation in the mean standardized tree ring width of thehigh-elevation red spruce population (DP = 0.28, AIC = –39.91) (Table 2). The GLM for ARIMlow indicated that WA,APD, and RA explained the variation in the mean standar-dized tree ring width of the low-elevation red spruce popula-
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tion. The first GLM for ARIMlow had the lowest DP (0.036)and AIC (–23.22), indicating the best fit with the data, andtherefore was selected for inclusion in the STELLA model.The P values and significance tests based on complete prob-ability models in Table 2 were not used for model selection.The fundamental assumptions for complete probability mod-els are easily violated in ecological studies due to small sam-ple size, autocorrelations frequently found in observationsand data (Appendix A (Fig. A1)), and nonlinearity of ecolog-ical phenomena (Bhattacharyya and Johnson 1977; Hilbornand Mangel 1997; Johnson 1999). STELLA simulated meanstandardized tree ring widths, which were compared with ob-served data (Fig. 5). STELLA simulations for ARIMhighshowed good correspondence to the tree growth of the high-elevation red spruce population up to 1995, after whichARIMhigh underestimated tree growth (Fig. 5a). STELLAsimulations for ARIMlow showed fair correspondence to thetree growth of the low-elevation red spruce population, miss-ing most of the extremes in tree growth (Fig. 5b).The bootstrapping statistics for the ARIMhigh and ARIMlow
GLMs showed that the original parameter estimations signifi-cantly represented the observed mean standardized tree ringwidth data with the highest relative likelihoods (Fig. 6). Thebootstrapping statistics explained the bias ranges and thestandard error ranges of the original parameter estimations(Table 3). The probability distribution functions of parameterestimations for both GLMs followed the Gaussian probabilitydistribution (Fig. 6). These standard error (SE) ranges, there-fore, significantly explain the confidence intervals, SE × 1.96for a 95% confidence interval, of the original parameter esti-mations (Altman and Bland 2005).
Habitat-dependent causes determining red spruce growthThe ARIMhigh simulations together with the CART models
and GLMs showed a negative relationship between APD andtree growth of the red spruce population at high elevations(Table 2; Figs. 4a and 5a). In contrast, ARIMlow simulationstogether with the CART models and GLMs showed that treegrowth of the low-elevation red spruce population was posi-tively related to WA and RA and negatively related to APD(Table 2; Fig.s 4b and 5b). The factors selected for ARIMhighand ARIMlow represent all interactions within the correspond-
Table 1. CART model results for ARIMhigh and ARIMlow.
Number ofsplits
Complexity parameter(CP) Relative misclassification error
Cross-validation relative error(SD)
ARIMhigh
0 0.4506 1 1.0235 (0.1422)1 0.0626 0.5494 0.7988 (0.1927)2 0.0432 0.4868 0.7245 (0.1623)3 0.0100 0.4436 0.7119 (0.1547)ARIMlow
0 0.0860 1 1.0345 (0.1478)2 0.0381 0.8280 1.3207 (0.2180)3 0.0277 0.7900 1.3519 (0.2170)4 0.0100 0.7632 1.3519 (0.2170)
Note: ARIMhigh is a function of air pollution disturbance (APD). ARIMlow is a function of water availability (WA),APD, and radiation (RA). The number of nodes for both models is 59. The root node error for ARIMhigh is 0.05179 andfor ARIMlow is 0.043735. CP = a/R0, where R0 is the mean square error of the predictions for the root tree. As increasinga, the optimal size of tree can be found by a sequence of cutting processes. CP with the lowest cross-validation relativeerror presents the optimal tree size (the number of splits) for the current data. This table is from Koo (2009).
Fig. 4. CART model trees for (a) ARIMhigh and (b) ARIMlow. Eachtree shows the parameters with criterion values (at the nodes) usedto split the node and a predicted mean standardized radial incrementvalue at the terminal node of each branch. The length of thebranches indicates the relative strength of the parameter used forsplitting in classification. APD, air pollution disturbance; WA, wateravailability; RA, radiation. This figure is from Koo (2009).
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ing submodels, e.g., interactions among temperature, precipi-tation, local spatial factors, and fir mortality in the RA sub-model. Based on all interactions in the submodels,temperature and precipitation played dominant roles in deter-mining red spruce growth in high- and low-elevation habitatsby controlling main factors, WA, RA, and APD (Fig. 3).
DiscussionSystems modeling based on open system theory can be
used to study hierarchically organized complexity. In thisstudy, we developed ARIM, a tree growth systems model, toexplain the hierarchically organized complex interactions be-tween red spruce growth and its environment in the GreatSmoky Mountains. The ARIM results explained habitat-de-pendent environmental factors that influenced growth in highand low elevations.
ARIM: indirect effects dominanceARIM simulations indicated that APD was the most im-
portant responsible factor for red spruce growth at high ele-vations (1800–2000 m). APD included frequent interactionsamong air pollutants, rain, and clouds (Fig. 3) (McLaughlinand Kohut 1992; Webster et al. 2004). These interactionscause acidic rain and clouds, accounting for crown diebackas well as growth and population declines by increasing tis-sue injury and leaching of foliar constituents (Johnson et al.1992; Dumais and Prévost 2007; Schaberg and Hawley2010). Ozone also reduces photosynthetic pigments, carbohy-drate contents, and frost hardiness by inducing the erosion ofepistomatal and epicuticular layers of foliage, increasing two-fold by acidic rain clouds (McLaughlin and Kohut 1992; Du-
Table 2. GLM results for ARIMhigh, and ARIMlow.
Variable Estimate SE t Pr > |t| DP AIC
ARIMhighIntercept 1.5577 0.0886 17.575 <2 × 10–16*** 0.028 –39.91APD –0.6796 0.0935 –7.265 1.15 × 10–9***
ARIMlowIntercept –11.4031 3.2042 –3.559 0.0008*** 0.036 –23.22WA 11.3237 2.7470 4.122 0.0001***APD –0.2697 0.1774 –1.52 0.1342RA 5.3397 1.8696 2.856 0.0060**Intercept –3.3103 1.5885 –2.084 0.0418* 0.040 –17.06WA 5.6473 2.0138 2.804 0.0069**APD –0.2648 0.1884 –1.406 0.1654Intercept –10.6040 3.1980 –3.316 0.0016** 0.037 –22.79WA 10.1540 2.6680 3.806 0.0004***RA 5.3120 1.8910 2.809 0.0068**Intercept 1.2945 1.0004 1.294 0.2010 0.046 –9.33APD –0.0649 0.1931 –0.336 0.7380RA –0.2366 1.4633 –0.162 0.8720Intercept –2.5660 1.5100 –1.699 0.0948 0.041 –17.02WA 4.5270 1.8650 2.427 0.0184*Intercept 1.1339 0.1157 9.799 7.87 × 10–14*** 0.045 –11.31APD –0.0558 0.1832 –0.304 0.7620Intercept 1.1609 0.9108 1.275 0.2080 0.045 –11.22RA –0.0934 1.3889 –0.067 0.9470
Note: Asterisks indicate significance level based on the P value (Pr > |t|): ***P = 0.001, **P = 0.01, and *P = 0.1. DP, dispersion parameter;AIC, Akaike’s information criterion; APD, air polution disturbance; WA, water availability; RA, radiation. The minimum value for DP and AIC (inbold) indicates the model that best fits the observed data, standardized ring width chronologies of red spruce. This table is from Koo (2009).
Fig. 5. Comparison of simulated and observed standardized mean ringwidths for (a) ARIMhigh and (b) ARIMlow. This figure is from Koo (2009).
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mais and Prévost 2007). Acidic rain and clouds increased soilacidity related to nutrient leaching in soil (Dumais and Pré-vost 2007; Huggett et al. 2007; Schaberg and Hawley 2010).SO4
2– concentrations increased with SO42– loading and cation
leaching increased with increasing SO42– in the order Mg >
Al > Ca > K > Na (Fernandez and Rustad 1990). Soil solu-tion Al increased by soil acidification increment prevents Cauptake, Ca deficiency decreases cambial growth, reducedcambial growth causes sapwood function to decrease, andthis finally causes a reduction in leaf area.
In contrast, ARIM simulations indicated that interactionsaffecting the low-elevation (1450–1700 m) red spruce popu-lation are more complex. Warmer temperatures and less pre-cipitation at low elevations accounted for the positiverelationships between red spruce growth and water availabil-ity and radiation. Higher temperatures cause a decrease inboth radiation absorption by photoinhibition and water avail-able for photosynthesis due to increased evapotranspiration(Lambers et al. 1998; Pandey et al. 2003; Koo 2009; detailsabout physiological processes given in online supplementary
Fig. 6. Bootstrapping test results of the GLMs of (a) ARIMhigh and (b) ARIMlow. In the graphs, t* indicates the bootstrap resamples and thebroken line on the histogram shows the original estimated parameter value from the GLMs. t* is the estimated parameter values of interceptsin the GLMs of ARIMhigh and ARIMlow (Table 3). This figure is from Koo (2009).
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data SD1).1 Less precipitation directly decreases water avail-able for photosynthesis and indirectly enhances photoinhibi-tion by increased leaf temperature due to reduced waterresources for evapotranspiration (Koo 2009; details aboutphysiological processes given in online supplementary dataSD1).1 Less precipitation in one year negatively influencesthe number of buds in the next year, which in turn decreasesred spruce growth (Meier and Leuschner 2008). APDs hadminor effects on red spruce growth at low elevations due toless exposure to acid rain and cloud immersion. However,dry air pollutants, especially O3, caused negative effects onthe low-elevation system by direct foliar damage by enteringduring normal gas exchanges (Fig. 3) (McLaughlin and Ko-hut 1992; McLaughlin and Percy 1999; Borer et al. 2005; de-tails given in supplementary data SD1).1The results of ARIMhigh and ARIMlow were consistent with
several findings from previous studies, including negativecorrelations between red spruce growth and both air pollution(McLaughlin and Kohut 1992; Dumais and Prévost 2007;Schaberg and Hawley 2010) and high temperature (Deusen1988; Webster et al. 2004; Dumais and Prévost 2007) and apositive correlation with precipitation (Deusen 1988; Websteret al. 2004; Dumais and Prévost 2007).On the other hand, the findings of ARIM also differed
from those of previous studies. Most suggested the potentialof air pollution to affect red spruce growth based on labora-tory or plot-based experiments and field observations butcould not statistically demonstrate the significant negative ef-fects in field studies (e.g., McLaughlin and Kohut 1992;Webster et al. 2004; Dumais and Prévost 2007). ARIM wasable to demonstrate that air pollution was the major cause ofred spruce growth decline at high elevation and a minorcause at low elevation using confronting simulation resultswith tree-ring width data collected at field sites. While den-drochronological studies could not always find significant di-rect correlations between red spruce growth and bothtemperature and precipitation (Deusen 1988; Cook and Ze-daker 1992), ARIM showed the importance of temperatureand precipitation as indirect controlling factors that regulateall direct factors (Fig. 3). The positive relationship betweenred spruce growth and radiation at low elevation was incon-sistent with previous research, which found negative effectsof intensive radiation with lower seedling and sapling sur-vival rate (White and Cogbill 1992; Day et al. 2001; Men-cuccini et al. 2007). Radiation considered in ARIM was not
raw data collected in the field. It was the simulated valuesmediated by all factor interactions in the radiation submodel(Fig. 3). This accounts for the inconsistent results at low ele-vations when comparing the current and previous studies us-ing raw data.The unique feature of ARIM is its attention to indirect and
direct causes of growth. Most previous research has not con-sidered indirect causes and failed to obtain significant corre-lations in the field. ARIM demonstrated that the indirectinteractions were dominant, explaining the inconsistent re-sults found in other studies. Figure 3 shows the many indirectinteractions in the submodels and only eight direct interac-tions in the main model. Incorporating these indirect interac-tions helped account for the complicated habitat conditionsthat are necessary to understand red spruce growth inGSMNP. For example, radiation in the ARIM main modelrepresents the amount absorbed by red spruce as mediatedby many indirect factors influencing real radiation conditionsshown in the radiation submodel (Fig. 3; Appendix A (TablesA1–A4)). As a result, the values for radiation as modeled inthe main model more accurately described the true conditionsfor red spruce growth than those directly derived from rawdata collected in the field.
ARIM: a general model for tree growth systemsProcess-based models and ecosystem models are often ap-
plied to ecosystem studies (Kerr et al. 2007). These modelsconsider reality and the complexity of nature and incorporatemany factors, comprehensively synthesizing data and knowl-edge. However, they are often too case and species specific,hampering broad application to other studies. In this study, asystems modeling approach was applied to achieve both real-ity and generality.The ARIM modeling process can be classified into two
parts, structural and functional. The structural part of ARIMexplains its generality and the functional part reality. TheARIM structure was constructed based on general metabolicprocesses, including photosynthesis and respiration, of alltree species (Table 1; Fig. 3). The disturbance factors inARIM also reflect general disturbances known from long-term tree growth studies, and therefore, the ARIM modelstructure can be applied to studies on other tree species,with a few modifications. For example, the weather disturb-ance submodel may need to include fire disturbance for fire-sensitive species. The functional part of ARIM was explainedby various models used for factor interactions and location-and species-specific data for parameters and parameter esti-mations (Appendix A (Tables A3 and A4)); online supple-mentary data SD3 and SD41; Koo 2009). Some models forfactor interactions were gained from general functional rela-tionships due to lack of literature. Most models and data,however, were obtained from the red-spruce-specific researchresults (online supplementary data SD3 and SD41; Koo2009). For example, rule-based models for interactions be-tween air pollution, precipitation, and elevation were selectedfrom the red spruce research in GSMNP. Temperature andprecipitation data were gained from a local meteorologicalstation, the Knoxville, Tennessee, airport meteorological re-cording station. The red spruce tree-ring data used for param-eter estimations were collected in GSMNP by Webster et al.(2004). Therefore, in spite of some limitations, ARIM pro-
Table 3. Bootstrapping statistics for each parameter of the ARIM-
high and ARIMlow GLMs.
VariableOriginal estimatedparameter Bias SE
ARIMhigh
Intercept 1.5577 6.6348 × 10–5 0.0878APD –0.6796 1.2508 × 10–5 0.0925
ARIMlowIntercept –11.4031 7.3056 × 10–3 3.0728WA 11.3237 –1.9963 × 10–3 2.6305APD –0.2697 6.4119 × 10–4 0.1717RA 5.3397 –8.4959 × 10–3 1.8015
Note: APD, air pollution disturbance; WA, water availability; RA, ra-diation. This table is from Koo (2009).
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vides a general model framework for tree growth studies aswell as the red-spruce-specific research.
ARIM: confronting complexityARIM, as a systems model, provides a general framework
for interdisciplinary synthesis in studying tree growth.ARIM’s structure incorporates all possible direct and indirectinteractions among factors studied in several disciplines, in-cluding climatology, soil ecology, disturbance ecology, andtree physiology (Fig. 3). Also, a variety of models, includinglinear deterministic models, nonlinear deterministic models,and rule-based models, were used to account for each func-tional relationship between submodel factors. In particular,statistical models, CART models and GLMs, were used forthe ARIM main models to estimate coefficients of direct fac-tors and determine the influential submodels and factors inthe ARIM submodels. By using statistical models for themain models, ARIM possesses the flexibility of a systemsmodel in incorporating a variety of model approaches andshows that a systems model can quantitatively explain theconfidence level and generality of modeling results. The factthat ARIM maintains the features of observed data, such asrandomness and the lack of correlations among data, in spiteof the complicated model structure, enables these statisticalmodels to be linked to the ARIM modeling without violatingthe randomness assumption.The dimensionless index value RBIV developed for ARIM
enabled data from different disciplines and monitoring sys-tems to be quantitatively integrated (eq. 3). Some modelingapproaches, such as process-based models and ecosystemmodels, have tried to synthesize interdisciplinary data tounderstand complex multiscale phenomena (Kerr et al.2007). However, such models still have problems in quantita-tively dealing with the hierarchically organized complexity ofnature because different units are used for each kind of dataand information. RBIV in ARIM solves this problem. RBIVcan be applied to other interdisciplinary studies due to its di-mensionless feature.
ARIM: limitations and future researchARIM provides innovative progress in modeling a tree
growth system as adapting systems concept and methodol-ogy. The ARIM results significantly explained habitat-de-pendent mechanisms at high versus low elevations todetermine red spruce growth in GSMNP. The predictive ca-pability of ARIM, however, depends on the monitored data,which were lacking in some cases. This study used nationaltotal data for air pollution due to insufficient local monitoreddata in GSMNP. This may cause ARIM to underestimate redspruce growth after 1995 in high elevations. Also, the lengthof air pollution data, 59 years, may influence the significanceof the CART model results (Table 1) and the P value for theAPD parameter in the GLM for ARIMlow (Table 2). In addi-tion, there is little research explaining the acclimation abilityof red spruce to environmental changes, effects from insectsand parasites, interactions between red spruce and coexistingtree species, and interactions among red spruce individuals(e.g., density-dependent self-thinning or outgrowing, growinglarger than a long-term average) in GSMNP. These could ex-plain why the ARIMlow simulations missed most of the ex-tremes in red spruce growth (Fig. 5b). The lack of
acclimation studies could also partly account for the underes-timated tree growth after 1995 at high elevation (Fig. 5a).
ConclusionARIM discriminated habitat-dependent causes of red
spruce growth declines in GSMNP. ARIM identified air pol-lution, in interaction with precipitation, as the dominant causeof red spruce growth decline at high-elevation habitats andthe lack of water availability and radiation, in interactionswith temperature and precipitation, as the dominant causeswith a minor negative effect of air pollution at low-elevationhabitats. It implicates comprehensive habitat-dependent direc-tions for long-term conservation policies and management ofred spruce with environmental changes, climate change, andair pollution in GSMNP. ARIM provides a general modelstructure that incorporates complex direct and indirect inter-actions for tree system studies and quantitatively integratesknowledge and data from different disciplines by developingRBIVs. ARIM demonstrates the flexibility of systems modelsin incorporating modeling methods by applying statisticalmodels such as CART models and GLMs to the ARIM mainmodels.
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Appendix AFigure A1 and Tables A1–A4 appear on the following pages.
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Fig. A1. Randomness tests (autocorrelation tests) for the observed data and the simulated data. In the plots, ACF is the autocorrelation coef-ficients. The broken lines in the plot show the 95% confidence interval. The autocorrelations within the lines are not significant, so they arerejected. High, high elevation; Low, low elevation; Water, water availability; WD, weather disturbances; SMD, soil-mediated disturbances;APD, air pollution disturbances.
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Table A1. Input environments of the annual radial increment of red spruce (Picea rubens) (ARIRS) envirogram.
...Input environments →
...Web 3 Web 2 Web 1 Centrum Focal system
Elevation (9) Temperature Annual radial increment of redspruce growth (ARIRS)Aspect
SlopeGreenhouse gasesElevation (10) PrecipitationSlopeAspectElevation (11) Cloud immersion (1) Radiation
SlopeAspectElevation
Temperature® Balsam woolly adelgid (12) Fir mortalityPopulation density(13) Phenotypic plasticityTemperature® (2) Water availabilityPrecipitation®Radiation®SlopeAspectElevationDistance to streamFir mortality®Population densityPhenotypic plasticityTemperature® (3) Carbon dioxideWater Availability®Radiation®Phenotypic plasticityTemperature® (4) NutrientsRadiation®Fir mortality®Phenotypic plasticityWater availability®
Precipitation® Air-loaded nutrients (SO42–, NO3
–)Cloud immersion®Phenotypic plasticity
Population density
Note: The ARIRS envirogram is based on annual variation of relative energy and matter flow among ARIRS and environmental factors in the context of relations existing amongthem. Centrum refers to direct environmental factors and webs refer to indirect environmental factors. Centrum factors are directly controlled by Web 1 and indirectly by Web 2, Web3, .... A factor in a web is directly controlled by the factors in the next web and indirectly by the factors in webs beyond the next web. The notation ® is used for avoiding iterativewriting of the same interactions, exhibited in the first part, for the later parts. The factors not bolded account for nonwebs followed (adapted from chapter 2 in Koo 2009). Numbers inparentheses are for the corresponding documentations for factor interactions involved in online supplementary data SD11 and Koo (2009).
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Table A2. Output environments of the annual radial increment of red spruce (Picea rubens) (ARIRS) envirogram.
Output environments
Focal system → Centrum Web 1 Web 2 Web 3...Annual radial increment of redspruce growth (ARIRS)
(5) HerbivoryHerbivory Temperature®
Precipitation®(6) Weather disturbanceWinter cold temperature Elevation
SlopeAspectGreenhouse gasesAir pollution®Phenotypic plasticity
Winter warm temperature ElevationSlopeAspectGreenhouse gasesWater availability®Phenotypic plasticity
Summer hot temperature ElevationSlopeAspectGreenhouse gasesWater availability®Phenotypic plasticity
(7) Soil-mediated disturbanceSoil acidity Air pollution®
Phenotypic plasticitySoil solution Al (soil toxicity) Soil acidity®
Phenotypic plasticity(8) Air pollution disturbanceAir pollution (SO4
2–, NO3–) Precipitation®
Cloud immersion®Phenotypic plasticity
Ozone Air pollution®Phenotypic plasticity
Note: The ARIRS envirogram is based on annual variation of relative energy and matter flow among ARIRS and environmental factors inthe context of relations existing among them. Centrum refers to direct environmental factors and webs refer to indirect environmental factors.Centrum factors are directly controlled by Web 1 and indirectly by Web 2, Web 3, .... A factor in a web is directly controlled by the factorsin the next web and indirectly by the factors in webs beyond the next web. The notation ® is used for avoiding iterative writing of the sameinteractions, exhibited in the first part, for the later parts. The factors not bolded account for nonwebs followed (adapted from chapter 2 inKoo 2009). Numbers in parentheses are for the corresponding documentations for factor interactions involved in online supplementary dataSD11 and Koo (2009).
960 Can. J. For. Res. Vol. 41, 2011
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Table A3. Model equations used for ARIMhigh based on published literature.
Parameter EquationARIM (ARIRS)high 0 × Radiation + 0 × Nutrients + 0 × Carbon dioxide + 0 × Water availability –0.67955 × Air pollution dis-
turbance – 0 × Herbivory + 0 × Soil-mediated disturbance – 0 × Weather disturbance + 1.55774Radiation (If Aspect = 2 then 2 else (if Aspect = 3 then 3 else (if Aspect = 4 then 2.5 else 1))) + Fir mortality + (if
Slope = 5 then 1 else (if Slope = 4 then 2 else (if Slope = 3 then 3 else (if Slope = 2 then 4 else 5)))) –Cloud immersion – Precipitation effect 1 + ((1.276949 – Temperature) × Temperature))/6
Water availability ((3 × Precipitation effect 2 + (if Distance to stream = 1 then 3 else (if Distance to Stream = 2 then 2 else 1))– Fir mortality – Temperature + (if Aspect = 2 then 2.5 else (if Aspect = 3 then 1 else (if Aspect = 4 then 2else 3))) + (if Slope = 1 then 1 else (if Slope = 2 then 2 else (if Slope = 3 then 3 else (if Slope = 4 then 4else 5)))) + ((1.276949 – Temperature) × Temperature) + Radiation)/10)
Carbon dioxide (((1.276949 – Temperature) × Temperature) + Radiation + Water availability)/3Nutrients (Fir mortality + Radiation + Water availability + Atmospheric deposition of nutrients + ((1.276949 – Tem-
perature) × Temperature))/5Herbivory Annual mean temperatureWeather disturbance (0 × Summer hot temperature + 2 × Winter cold temperature + 1 × Winter warm temperature)/3)Soil-mediated disturbance (Soil acidity + Soil solution Al)/2Air pollution disturbance (Air pollution + Ozone)/2Temperature Average temperature × ((2 + 0 × Observed CO2 + 0 × Observed ozone + 1 × (if Aspect = 2 then 0.65 else (if
Aspect = 3 then 1 else (if Aspect = 4 then 0.65 else 0.3))) + 1 × (if Elevation = 1000 then 1 else (if Eleva-tion = 1100 then 0.9 else (if Elevation = 1200 then 0.8 else (if Elevation = 1300 then 0.7 else (if Elevation= 1400 then 0.6 else (if Elevation = 1500 then 0.5 else (if Elevation = 1600 then 0.4 else (if Elevation =1700 then 0.3 else (if Elevation = 1800 then 0.2 else 0.1))))))))) + 1 × (if Slope = 5 then 0.2 else (if Slope =4 then 0.4 else (if Slope = 3 then 0.6 else (if Slope = 2 then 0.8 else 1)))))/5)
Summer hot temperature Observed summer temperature × ((2+1 × (if Aspect = 2 then 0.5 else (if Aspect = 3 then 1 else (if Aspect = 4then 0.65 else 0.3))) – 1 × Water availability + 0 × Observed CO2 + 0 × Observed ozone + 1 × (if Elevation= 1000 then 1 else (if Elevation = 1100 then 0.9 else (if Elevation = 1200 then 0.8 else (if Elevation = 1300then 0.7 else (if Elevation = 1400 then 0.6 else (if Elevation = 1500 then 0.5 else (if Elevation = 1600 then0.4 else (if Elevation = 1700 then 0.3 else (if Elevation = 1800 then 0.2 else 0.1))))))))) + 1 × (if Slope = 5then 0.2 else (if Slope = 4 then 0.4 else (if Slope = 3 then 0.6 else (if Slope = 2 then 0.8 else 1)))))/6)
Winter cold temperature Observed winter cold temperature × ((2 + 4 × Air pollution – 0 × Observed CO2 – 0 × Observed ozone + 1 ×(if Elevation = 1000 then 0.1 else (if Elevation = 1100 then 0.2 else (if Elevation = 1200 then 0.3 else (ifElevation = 1300 then 0.4 else (if Elevation = 1400 then 0.5 else (if Elevation = 1500 then 0.6 else (if Ele-vation = 1600 then 0.7 else (if Elevation = 1700 then 0.8 else (if Elevation = 1800 then 0.9 else 1))))))))) +1 × (if Slope = 5 then 0.2 else (if Slope = 4 then 0.4 else (if Slope = 3 then 0.6 else (if Slope = 2 then 0.8else 1)))) + 1 × (if Aspect = 2 then 0.5 else (if Aspect = 3 then 1 else (if Aspect = 4 then 0.65 else 0.3))))/9)
Winter warm temperature Observed winter warm temperature × ((2 + 0 × Observed CO2 + 0 × Observed ozone + 1 × (if Aspect = 2then 0.5 else (if Aspect = 3 then 1 else (if Aspect = 4 then 0.65 else 0.3))) + 1 × (if Elevation = 1000 then0.1 else (if Elevation = 1100 then 0.2 else (if Elevation = 1200 then 0.3 else (if Elevation = 1300 then 0.4else (if Elevation = 1400 then 0.5 else (if Elevation = 1500 then 0.6 else (if Elevation = 1600 then 0.7 else(if Elevation = 1700 then 0.8 else (if Elevation = 1800 then 0.9 else 1))))))))) + 1 × (if Slope = 5 then 0.2else (if Slope = 4 then 0.4 else (if Slope = 3 then 0.6 else (if Slope = 2 then 0.8 else 1)))))/5)
Precipitation effect 1 Precipitation effect 1 × ((If Elevation < 1700 then 1 else 2)/3)Precipitation effect 2 ((Precipitation effect 1 + Precipitation effect 2)/2) × ((if Elevation < 1700 then 1 else 2)/3)Cloud immersion (If (Elevation < 1400) then (0) else (if (Elevation ≥ 1400 and Elevation < 1800) then (1) else (2)))/2Air pollution Observed air pollution × ((1 + 3 × Cloud immersion + 2 × Precipitation effect 1)/6)Ozone Observed ozone × ((1 + 2 × Air pollution)/3)Soil acidity Observed air pollution × ((1 + 2 × Precipitation effect 1 + 3 × Cloud immersion)/6)Soil solution Al (1+ 2 × Soil acidity)/3Fir mortality Balsam woolly adelgid × ((if (Elevation ≥ 1700) then (2) else (1))/3)Balsam woolly adelgid Observed winter cold temperature
Note: See online supplementary data SD31 for more details.
Koo et al. 961
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ReferenceKoo, K. 2009. Distribution of Picea rubens and global warming — a systems approach. Ph.D. dissertation, University of Georgia, Athens, Ga.
Table A4. Model equations used for ARIMlow based on published literature.
Parameter EquationARIM (ARIRS)low 5.3397 × Radiation + 0 × Nutrients + 0 × CO2 + 11.3237 × Water availability – 0.2697 × Air pollution dis-
turbance – 0 × Herbivory + 0 × Soil-mediated disturbance – 0 × Weather disturbance – 11.4031Radiation ((If Aspect = 2 then 2 else (if Aspect = 3 then 3 else (if Aspect = 4 then 2.5 else 1))) + Fir mortality + (if
Slope = 5 then 1 else (if Slope = 4 then 2 else (if Slope = 3 then 3 else (if Slope = 2 then 4 else 5)))) –Cloud immersion – Precipitation effect + ((1.317288136 – Temperature) × Temperature))/6
Water availability (3 × Precipitation effect 2 + (if Distance to stream = 1 then 3 else (if Distance to stream = 2 then 2 else 1)) –Fir mortality – Temperature + (if Aspect = 2 then 2.5 else (if Aspect = 3 then 1 else (if Aspect = 4 then 2else 3))) + (if Slope = 1 then 1 else (if Slope = 2 then 2 else (if Slope = 3 then 3 else (if Slope = 4 then 4else 5)))) + ((1.317288136 – Temperature) × Temperature) + Radiation)/10
Carbon dioxide (((1.317288136 – Temperature) × Temperature) + Radiation + Water availability)/3Nutrients (Fir mortality + Radiation + Water availability + Atmospheric deposition of nutrients + ((1.317288136 –
Temperature) × Temperature))/5Herbivory Annual mean temperatureWeather disturbance (2 × Summer hot temperature + 0 × Winter cold temperature + 2 × Winter warm temperature)/4Soil-mediated disturbance (Soil acidity + Soil solution Al)/2Air pollution disturbance (Air pollution + Ozone)/2Temperature Average temperature × ((2 + 0 × Observed CO2 + 0 × Observed ozone + 1 × (if Aspect = 2 then 0.5 else (if
Aspect = 3 then 1 else (if Aspect = 4 then 0.65 else 0.3))) + 1 × (if Elevation = 1000 then 1 else (if Eleva-tion = 1100 then 0.9 else (if Elevation = 1200 then 0.8 else (if Elevation = 1300 then 0.7 else (if Elevation= 1400 then 0.6 else (if Elevation = 1500 then 0.5 else (if Elevation = 1600 then 0.4 else (if Elevation =1700 then 0.3 else (if Elevation = 1800 then 0.2 else 0.1))))))))) + 1 × (if Slope = 5 then 0.2 else (if Slope =4 then 0.4 else (if Slope = 3 then 0.6 else (if Slope = 2 then 0.8 else 1)))))/5)
Summer hot temperature Observed summer hot temperature × ((2 + 1 × (if Aspect = 2 then 0.5 else (if Aspect = 3 then 1 else (ifAspect = 4 then 0.65 else 0.3))) – 1 × Water availability + 0 × Observed CO2 + 0 × Observed ozone + 1 ×(if Elevation = 1000 then 1 else (if Elevation = 1100 then 0.9 else (if Elevation = 1200 then 0.8 else (ifElevation = 1300 then 0.7 else (if Elevation = 1400 then 0.6 else (if Elevation = 1500 then 0.5 else (ifElevation = 1600 then 0.4 else (if Elevation = 1700 then 0.3 else (if Elevation = 1800 then 0.2 else0.1))))))))) + 1 × (if Slope = 5 then 0.2 else (if Slope = 4 then 0.4 else (if Slope = 3 then 0.6 else (if Slope= 2 then 0.8 else 1)))))/6)
Winter cold temperature Observed winter cold temperature × ((2 + 4 × Air pollution – 0 × Observed CO2 – 0 × Observed ozone + 1 ×(if Elevation = 1000 then 0.1 else (if Elevation = 1100 then 0.2 else (if Elevation = 1200 then 0.3 else (ifElevation = 1300 then 0.4 else (if Elevation = 1400 then 0.5 else (if Elevation = 1500 then 0.6 else (ifElevation = 1600 then 0.7 else (if Elevation = 1700 then 0.8 else (if Elevation = 1800 then 0.9 else1))))))))) + 1 × (if Slope = 5 then 0.2 else (if Slope = 4 then 0.4 else (if Slope = 3 then 0.6 else (if Slope =2 then 0.8 else 1)))) + 1 × (if Aspect = 2 then 0.5 else (if Aspect = 3 then 1 else (if Aspect = 4 then 0.65else 0.3))))/9)
Winter warm temperature Observed winter warm temperature × ((2 + 0 × Observed CO2 + 0 × Observed ozone + 1 × (if Aspect = 2then 0.5 else (if Aspect = 3 then 1 else (if Aspect = 4 then 0.65 else 0.3))) + 1 × (if Elevation = 1000 then0.1 else (if Elevation = 1100 then 0.2 else (if Elevation = 1200 then 0.3 else (if Elevation = 1300 then 0.4else (if Elevation = 1400 then 0.5 else (if Elevation = 1500 then 0.6 else (if Elevation = 1600 then 0.7 else(if Elevation = 1700 then 0.8 else (if Elevation = 1800 then 0.9 else 1))))))))) + 1 × (if Slope = 5 then 0.2else (if Slope = 4 then 0.4 else (if Slope = 3 then 0.6 else (if Slope = 2 then 0.8 else 1)))))/5)
Precipitation effect 1 Precipitation1 × ((if Elevation < 1700 then 1 else 2)/3)Precipitation effect 2 ((Precipitation effect 1 + precipitation effect 2)/2) × ((if Elevation < 1700 then 1 else 2)/3)Cloud immersion (If(Elevation < 1400) then (0) else (if (Elevation < 1800 and Elevation ≥ 1400) then (1) else (2)))/2Air pollution Observed air pollution × ((1 + 3 × Cloud immersion + 2 × Precipitation effect 1)/6)Ozone Observed ozone × ((1 + 2 × Air pollution)/3)Soil acidity Observed air pollution × ((1 + 2 × Precipitation effect 1 + 3 × Cloud immersion)/6)Soil solution Al (1 + 2 × Soil acidity)/3Fir mortality Balsam woolly adelgid × ((if (Elevation ≥ 1700) then (2) else (1))/3)Balsam woolly adelgid Observed winter cold temperature
Note: See online supplementary data SD21 for details.
962 Can. J. For. Res. Vol. 41, 2011
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