Climate-diameter growth relationships of black spruceand jack pine trees in boreal Ontario, CanadaNIRMAL SUBED I and MAHADEV SHARMA

Ontario Forest Research Institute, Ministry of Natural Resources, 1235 Queen St. East, Sault Ste Marie, ON P6A 2E5, Canada

Abstract

To predict the long-term effects of climate change – global warming and changes in precipitation – on the diameter

(radial) growth of jack pine (Pinus banksiana Lamb.) and black spruce (Picea mariana [Mill.] B.S.P.) trees in boreal

Ontario, we modified an existing diameter growth model to include climate variables. Diameter chronologies of 927

jack pine and 1173 black spruce trees, growing in the area from 47°N to 50°N and 80°W to 92°W, were used to

develop diameter growth models in a nonlinear mixed-effects approach. Our results showed that the variables long-

term average of mean growing season temperature, precipitation during wettest quarter, and total precipitation dur-

ing growing season were significant (alpha = 0.05) in explaining variation in diameter growth of the sample trees.

Model results indicated that higher temperatures during the growing season would increase the diameter growth of

jack pine trees, but decrease that of black spruce trees. More precipitation during the wettest quarter would favor the

diameter growth of both species. On the other hand, a wetter growing season, which may decrease radiation inputs,

increase nutrient leaching, and reduce the decomposition rate, would reduce the diameter growth of both species.

Moreover, our results indicated that future (2041–2070) diameter growth rate may differ from current (1971–2000)growth rates for both species, with conditions being more favorable for jack pine than black spruce trees. Expected

future changes in the growth rate of boreal trees need to be considered in forest management decisions. We recom-

mend that knowledge of climate–growth relationships, as represented by models, be combined with learning from

adaptive management to reduce the risks and uncertainties associated with forest management decisions.

Keywords: boreal forest, climate–growth relationship, diameter growth model, forest management, growing season tempera-

ture, precipitation

Received 29 February 2012; revised version received 4 September 2012 and accepted 5 September 2012

Introduction

The boreal forest, which includes jack pine (Pinus bank-

siana Lamb.)- and black spruce (Picea mariana [Mill.]

B.S.P.)-dominated stands, supplies about two-thirds of

harvested roundwood in Ontario [National Forest

Database (NFD), 2012] and is important for the eco-

nomic well-being of northern rural populations (Burton

et al., 2003). Boreal forest composition is the result of

complex interactions among climate, solar radiation,

topography, geology, nutrient availability, soil mois-

ture, soil temperature, permafrost, depth of forest floor

organic layer, species ecology, forest fire, and insect

and pest infestations (Sojo et al., 2007). Climate change

– global warming and changes in precipitation – may

affect seedling establishment (Daniels & Veblen, 2004)

and mortality (McDowell et al., 2011), tree growth

(Peterson & Peterson, 2001), tree species distribution,

and competition among species (Hamann & Wang,

2006). Therefore, it is important to increase our

knowledge of climate–growth relationships, in particu-

lar, the factors affecting forest growth and their sensi-

tivity to climatic variables (Aber et al., 2001; Deslauriers

et al., 2003; Crookston et al., 2008, 2010). Climate–growth relationship information can provide valuable

insight to forest managers formulating forest manage-

ment strategies to achieve sustainable use (Worbes,

1999) or to adapt to climate change (Littell et al., 2011).

Projections made using climate change models have

indicated that global surface air temperature will

increase between 1.4 and 5.8 °C by 2100 relative to

2000 (Intergovernmental Panel on Climate Change

(IPPC), 2001). Based on Environment Canada’s cli-

mate model, version 2 of Canadian Coupled Global

Circulation Model (CGCM) using the A2 scenario

(Intergovernmental Panel on Climate Change (IPPC),

2001), in Ontario, Canada, average summer tempera-

tures are expected to rise by 3–6 °C by the end of

21st century, with more pronounced differences in

the north (Colombo et al., 2007). Rising temperatures

increase the availability of soil nitrogen, which

Correspondence: Present address: Nirmal Subedi, Forest

Economics and Tenure Branch, Forest Industry Division, Ministry

of Natural Resources, 70 Foster Drive, Suite 210, Sault Ste. Marie,

ON, P6A 6V5, Canada, tel. 705 945 5843, fax 705 541 5111,

e-mail: nirmal.subedi@ontario.ca

© 2012 Blackwell Publishing Ltd 505

Global Change Biology (2013) 19, 505–516, doi: 10.1111/gcb.12033

combined with a longer growing season is expected

to increase overall tree growth/biomass production

(Parker et al., 2000; Stromgren & Linder, 2002). How-

ever, on some sites increased temperature may result

in temperature-induced drought stress and reduced

tree growth (Wilmking et al., 2004; Wilmking &

Juday, 2005).

The effects of climate on radial growth of trees has

been studied at diurnal (Tardif et al., 2001; Duchesne &

Houle, 2011), seasonal (Belyea et al., 1951; Fraser, 1956;

Clark & Gibbs, 1957), annual (Fritts, 1958; Pokharel &

Froese, 2009), and multiannual (D’Arrigo et al., 1992;

Brooks et al., 1998; Hofgaard et al., 1999) intervals.

These studies have broadened our understanding of cli-

mate–growth relationships. For example, Fraser (1956)

indicated that late winter and early spring tempera-

tures might control when growth resumes, as soil mois-

ture was not a limiting factor at the study site (i.e.,

Chalk River, Ontario, Canada) at that time of year.

However, on wet sites, a thick organic horizon delays

the spring warming of the soil, which slows the onset

of tree growth. Fritts (1958) reported that more than

half of the growth rate changes due to concurrent envi-

ronmental variation in American beech (Fagus grandifo-

lia Ehrh.) trees from a central Ohio forest could be

attributed to maximum temperature and soil moisture.

Furthermore, he reported that during the early part of

the growing season, maximum temperature was more

influential than soil moisture, but later in the season

soil moisture became more important. Similarly, Pokha-

rel & Froese (2009) found that the mean annual temper-

ature was important in describing basal area growths

of four tree species including jack pine and black

spruce trees grown in natural stands in eastern Canada.

Overall, temperature and moisture seem to be the most

limiting factors for radial growth of trees in the eastern

boreal region of North America.

Recently, Subedi & Sharma (2011) and Lacerte et al.

(2006) developed diameter growth models for jack pine

and black spruce plantations in boreal Ontario, but

their models did not account for climate–growth rela-

tionships. When climate variables are not included in

growth models, the implicit assumption is that the rate

of tree growth observed when the data used to cali-

brate the model were collected will remain constant in

the future (Crookston et al., 2008). As a result, predic-

tions from such models are insensitive to changes in

climate. Therefore, the objectives of this study were to

incorporate climate variables in the diameter growth

models developed by Subedi & Sharma (2011) for jack

pine and black spruce trees and to assess the effects of

future climate scenarios on the diameter growth rate of

these tree species using a mixed-effects modeling

approach.

Materials and methods

Tree-ring data

Tree-ring width (diameter) measurements of jack pine and

black spruce trees from plantations throughout boreal Ontario,

Canada (47° 27′ 36″ N to 50° 11′ 24″ N; 80° 6′ 0″ W to 92° 47′ 24″W; 214–539 m a.s.l.) formed the basis for this study. For each

species, 25 even-aged monospecific plantations were selected

to represent the species’ geographical range, as well as stand

density and stand structure variations (Fig. 1). From each plan-

tation site, three stands were selected fromwhich 15–16 trees in

each, spanning the range of tree basal area, were randomly

selected for destructive sampling. Thus, for both species 45–48

trees were sampled from each plantation. From each selected

tree, stem sections were sampled at approximately 0.15, 0.5,

and 0.9 m, at breast height (1.3 m), and above breast height at

certain (i.e., either 10 or 5) percentages of relative height above

breast height. A unique code was assigned to each stem section

to identify the site, plot, and tree from which it was sampled.

These stem sections were placed in a large breathable bag,

transported, and stored at –10 °C until 24 h before preparation.

For this study, only the stem sections from breast height were

used. These stem sections were sanded and geometric mean

radius was calculated frommajor and minor radii on each stem

section [i.e., r = (r1 9 r2)0.5]. Two radii that were equal to the

geometric mean radius in length and at least 90° apart were

located, and trajectories were drawn along these radii using a

sharp pencil in each section. These sections were then scanned

to at least 720 dpi resolution and the images were saved.

Annual ring width (RW) measurements were made along

each trajectory from each scanned image using WINDEN-

DROTM software (Regent Instruments, Inc. Quebec, QC,

Canada). The perpendicular distance between two successive

rings was used as an annual radial growth. Annual RW mea-

surements of every tree from each plantation site were cross-

dated with respective master chronologies for the site. Mean

sensitivity (Fritts, 1976), which measures percentage change of

each measured annual ring width value to the next was

assessed for each tree for both species. Brief summaries of in-

terseries correlation, and first- and second-order autocorrela-

tions of RW of 25 jack pine and black spruce plantations and

mean sensitivity of RW of each tree for both species are pre-

sented in Table 1.

Past annual diameter growth (inside bark) was calculated

using cross-dated tree-ring widths. This resulted in diameter

increment data from 927 jack pine and 1173 black spruce trees

from 75 stands in 25 plantations. From each plantation, two

stands were randomly selected for each species and the diam-

eter (i.e., ring width) measurements of trees from these stands

were used to calibrate the models (calibration data set). The

diameter measurements from trees of the remaining stands

were used to evaluate the model (validation data set). Average

annual diameter growth from each tree was calculated using

5 year increments, so that the model prediction interval would

match the interval at which the forest resource inventory/

management plans are updated in Ontario. Summary statistics

of tree and stand characteristics for the calibration and valida-

tion data sets for each species are given in Table 2.

© 2012 Blackwell Publishing Ltd, Global Change Biology, 19, 505–516

506 N. SUBEDI & M. SHARMA

Climate data

The climate of the region is continental with cold winters and

warm summers. Temperature decreases toward the east and

north in Ontario, but temperature differences are much smal-

ler in summer than winter. Maximum precipitation occurs in

the region during summer and the amount of precipitation is

affected by proximity to the Great Lakes, prevailing winds,

and the elevation and slope of the terrain (Phillips, 1990).

Annual precipitation is relatively consistent from year to year.

Periods of excessively dry or wet weather are infrequent,

although periods of drought are more likely to occur in the

late summer (i.e., at the end of growing season) (Phillips,

1990).

For each of the study plantations, the long-term average of

a suite of climate variables was estimated for the period 1971–

2000 using thin-plate smoothing splines, as implemented in

the ANUSPLIN climate modeling software (e.g., Hutchinson,

2011). Initially, Daniel McKenney (Canadian Forest Service,

pers. comm., 2012) estimated 65 climate variables, primarily

related to temperature and precipitation, for each plantation

location. The climate variables included average values of

minimum and maximum temperature and precipitation, for

each month, the entire growing season and various quarters,

Table 1 Summary of chronology statistics for tree rings of jack pine and black spruce from boreal Ontario used in this study

Species

Statistic

Plot level Tree level

Interseries

correlation

First-order

autocorrelation

Second-order

autocorrelation

Mean

sensitivity

Jack pine

N 25 25 25 927

Mean 0.978 0.905 0.810 0.096

Min 0.687 0.855 0.711 0.045

Max 0.997 0.932 0.864 0.230

SD 0.061 0.022 0.044 0.023

Black spruce

N 25 25 25 1173

Mean 0.972 0.901 0.798 0.138

Min 0.796 0.853 0.698 0.055

Max 0.996 0.926 0.851 0.307

SD 0.053 0.024 0.049 0.042

Fig. 1 Distribution of jack pine and black spruce plantation sites sampled across northern Ontario, Canada.

© 2012 Blackwell Publishing Ltd, Global Change Biology, 19, 505–516

CLIMATE –GROWTH RELATIONSHIPS OF BOREAL TREES 507

growing degrees days, and Julian day at the start and end of

the growing season (see McKenney et al., 2011 for details). Of

these variables, those that were temperature- and moisture-

related and spanned the growing season and various quarters

were selected to analyze climatic effects on diameter growth.

The average mean temperature during growing season

(MT), average total precipitation during growing season (TP),

and average precipitation during wettest quarter (i.e., the

three consecutive months receiving the maximum precipita-

tion) for the period of 1971–2000 estimated for Ontario using

ANUSPLIN are displayed in Fig. 2. For the 1971–2000 period,

the wettest quarter occurred during June to August in north-

western Ontario, but arrived 1 month later (i.e., July to Sep-

tember) in northeastern Ontario [National Climate Data &

Information Archive (NCDIA), 2012]. The growing season was

determined using temperature-based rules, starting when the

mean daily temperature was greater than 5 °C for five consec-

utive days, and ending when the average temperature fell

below �2 °C after the first day of August. For the jack pine

and black spruce plantations, respectively, average annual

mean temperatures were 1.58 °C and 0.97 °C, annual precipi-tation ranged from 676 to 785 mm, and average growing

degrees days ranged from 1077 to 1454 and 694 to 841.

Diameter growth equation

Diameter/basal area growth models generally include tree

size-, site-, and individual-tree competition-related variables

(Wykoff, 1990). Recently, Subedi & Sharma (2011) compared

two composite and one potential growth-based diameter

equations (Wykoff, 1990) to predict diameter growth of jack

pine and black spruce using the same data set as this study.

They reported that the composite growth equation, which

expresses tree size and competition effects as an exponential

function, provided better predictive accuracy across tree size

(diameter at breast height; DBH) and age for both species than

the other models tested. The exact form of the composite

diameter growth equation they used was:

ADG ¼ exp�b0 þ b1 lnðDBH1 þ 1Þ þ b2DBH2

1

þb3Age1 þ b4 lnðSIÞþb5ðDBH1=DBH1Þþb6

�Age1 �DBH1

�þ b7LNG�þ e

ð1Þ

where, ADG is annual inside-bark diameter growth (cm yr�1)

at breast height (1.3 m), b0–b7 are model coefficients, DBH1,

DBH1 and Age1 are tree inside-bark diameter (cm), the stand

level average inside-bark diameter (cm), and tree age, respec-

tively, at breast height at the start of growth period. Similarly,

SI is the site index (m) at index age (i.e., 25 years) above breast

height, LNG is longitude, and e is error term. As mentioned

earlier, Eqn (1) does not include any climatic variables, so

would not reflect responses to change in climate. Therefore,

we modified Eqn (1) by incorporating temperature- and mois-

ture-related variables (as described above) to account for cli-

matic effects.

Model fitting and evaluation

Data used to develop diameter growth models generally origi-

nate from multiple measurements on trees from a number of

stands. These observations are commonly hierarchical (i.e.,

trees within stands). Observations among sampling units

(stands) are independent, but observations within a sampling

unit (stand) are dependent (i.e., correlated) because they are

from the same subpopulation (Pinheiro & Bates, 2000;

Demidenko, 2004). As a result, two sources of variation

exist among sampling units and within a sampling unit. To

address the problem of autocorrelation within a sampling

unit, researchers have used the mixed-effects modeling tech-

nique (Subedi & Sharma, 2011) or correlation structure

Table 2 Summary statistics for diameter at breast height (DBH), total height (height), breast height age (BHA), basal area per hect-

are (BAPH), trees per hectare (TPH), and site index (SI; top height of dominant or codominant trees at BHA 25 years) for planta-

tion-grown jack pine and black spruce trees/stands in the calibration and validation data sets used in this study

Species/variable

Calibration Validation

N Mean SD Min Max N Mean SD Min Max

Jack pine

DBH (cm) 616 17.69 4.43 7.40 31.00 311 15.47 6.41 0.00 33.80

Height (m) 616 15.63 2.38 8.55 23.17 311 15.66 2.14 9.62 23.02

BHA (years) 616 38.15 9.44 17 60 311 38.34 9.92 21 83

BAPH (m2) 50 27.70 5.81 16.25 42.25 25 27.15 5.90 15.28 37.46

TPH (no.) 50 1753 647 884 3302 25 1859 707 960 3102

SI (m) 50 12.86 1.27 10.44 15.85 25 12.87 1.19 10.31 15.37

Black spruce

DBH (cm) 781 13.53 3.54 3.60 24.50 392 13.05 3.90 2.50 24.80

Height (m) 781 11.00 2.39 4.38 17.00 392 10.58 2.59 2.98 17.85

BHA (years) 781 30.75 7.85 12 74 392 30.40 7.68 13 52

BAPH (m2) 50 30.21 8.79 12.00 48.87 25 29.02 9.08 12.62 45.43

TPH (no.) 50 2865 857 1500 4678 25 3027 995 1471 5579

SI (m) 50 10.19 1.18 8.00 12.55 25 9.76 1.38 6.43 12.13

© 2012 Blackwell Publishing Ltd, Global Change Biology, 19, 505–516

508 N. SUBEDI & M. SHARMA

(Dieguez-Aranda et al., 2006), or both (Trincado & Burkhart,

2006). Details about mixed-effects modeling are provided by

Vonesh & Chinchilli (1997), Pinheiro & Bates (2000), and

Demidenko (2004).

Equation (1) was first fitted to the calibration data set for

each species using the generalized least-squares method in R

(R Development Core Team, 2011). Then, a combination of

temperature- and precipitation-related variables were

included in the model and evaluated for their contribution to

model improvement. Climate variables that were both signifi-

cant (alpha = 0.05) and improved model fit were selected for

both species. Hereafter, the diameter growth model that

includes the combination of selected climatic variables will be

referred to as the full model.

The full model was then fitted using the mixed-effects mod-

eling approach (i.e., ‘nlme’ (Pinheiro et al., 2011) and ‘lme4’

packages (Bates et al., 2011) in R) for both species. Random-

effects parameters were added sequentially starting at one

coefficient as a random effect for each species. The model with

random effects was evaluated based on goodness-of-fit criteria

such as log likelihood (twice the negative log-likelihood),

assessment of model residuals, and Akaike Information Crite-

rion (AIC) (Akaike, 1978). The model with the smallest good-

ness-of-fit value is considered best.

The residuals of the diameter prediction model with random

group (i.e., stand) effects were analyzed for possible temporal

and spatial autocorrelations and heteroscedasticity for each

species. The Moran’s I of residuals indicated that spatial auto-

correlation did not occur among residuals within species. How-

ever, for both species temporal autocorrelation was evident

among residuals within stands. As a result, the final model was

fitted as a nonlinear mixed-effects model, and within-stand

autocorrelation (Pinheiro & Bates, 2000) was modeled directly

for both species. Two autocorrelation structures, AR1 (autore-

gressive process of order one) and ARMA (autoregressive

moving average process), were evaluated, and the one which

gave the best fit (i.e., smaller AIC) and provided expected

behavior of residuals was selected. Even after incorporating the

autocorrelation structure in the mixed-effects model, residuals

indicated some signs of heteroscedasticity (unequal variances).

The problem of heteroscedasticity was resolved by specifying a

within-stand variance function (Pinheiro & Bates, 2000). The

coefficients of the final models were determined using the

REML (reducedmaximum likelihood) method.

(a)

(b) (c)

Fig. 2 Surface maps of (a) average mean temperature during growing season (MT), (b) average precipitation during growing season

(TP), and (c) average precipitation during wettest quarter (PWQ) for period from 1971 to 2000 in Ontario.

© 2012 Blackwell Publishing Ltd, Global Change Biology, 19, 505–516

CLIMATE –GROWTH RELATIONSHIPS OF BOREAL TREES 509

Model predictions were evaluated using the independent

model evaluation data set. For each stand, records of all the

diameter growths of a randomly selected tree were used to

localize the mixed-effects coefficients (Vonesh & Chinchilli,

1997) for that stand. Details about localizing the mixed-effects

coefficients can be found in Trincado & Burkhart (2006) and

Subedi & Sharma (2011). Using both fixed- and random-effects

coefficients, the rate of annual diameter growth of the trees in

the stand was predicted for each species. The mean residual

(observed diameter increment – predicted diameter increment;

�ei) and the sample variance (vi) of residuals were calculated

across tree size (i.e., DBH class) and age using 100 simulations

for each species. These were considered estimates of bias and

precision, respectively. Finally, an estimate of mean square

error (MSEi) was obtained for each DBH class and age group

using the formula (Trincado & Burkhart, 2006):

MSEi ¼ �e2i þ vi i ¼ 1; 2; 3; :n:

where n is the number of DBH classes or age groups.

To estimate future diameter growth under changing climate

scenarios, two plantations, one from northeastern (NE) and

the other from northwestern (NW) Ontario, were selected for

each species. The details of these four plantation locations,

and associated climate variables, are given in Table 3. Future

temperature and precipitation for two scenarios (A2 and B2;

Intergovernmental Panel on Climate Change (IPPC), 2001)

during the period 2041–2070 for these locations were esti-

mated using climate predictions summarized by Colombo

et al. (2007), who predicted future temperature and precipita-

tion for Ontario using version 2 of CGCM model.

Some caveats related to our analysis are that the estimates

were based on the rates of growth of an average-sized tree (i.

e., individual tree) and did not include mortality from either

competition or disturbances.

Results

The evaluation of a combination of temperature- and

precipitation-related variables indicated that the mean

growing season temperature (MT), precipitation of wet-

test quarter (PWQ; the precipitation of the three consec-

utive wettest months), and total growing season

precipitation (TP) were significant (alpha = 0.05) in

explaining the variation in diameter growth of jack pine

and black spruce trees. After including these variables,

the full diameter growth model can be represented as:

ADG ¼ exp�b0 þ b1 lnðDBH1 þ 1Þ þ b2DBH2

1 þ b3Age1

þb4 lnðSIÞþb5ðDBH1=DBH1Þ þ b6�Age1 �DBH1

�

þb7MTþ b8PWQþ b9TP�þ e

ð2Þwhere b0–9 are model coefficients, MT is mean tempera-

ture (°C) during the growing season, PWQ and TP are

precipitation during the wettest quarter (mm) and total

growing season precipitation (mm), respectively, and

other parameters are as defined above.

When the long-term average (1971–2000) of three cli-

mate variables were included in the model (i.e., Eqn 1),

the longitude (LNG) variable was no longer significant.

After including climate variables, the fit statistics (root

MSE, AIC (smaller is better), and log likelihood)

improved for both species (Table 4). Thus, Eqn 2 not

only incorporated climate variables but also improved

the fit statistics, and the full model would be useful in

explaining the climate–growth relationship of jack pine

and black spruce trees. When the model with coeffi-

cients b1 and b3 was treated as mixed-effects, model fit

was improved (smaller AIC) for both species. Thus, the

final mixed-effects diameter growth model for jack pine

and black spruce can be represented as:

ADG¼ exp�b0þðb1þb1Þ lnðDBH1þ1Þþb2DBH2

1

þðb3þb3ÞAge1þb4 lnðSIÞþb5ðDBH1=DBH1Þþb6

�Age1 �DBH1

�þb7MTþb8PWQþb9TP�þe

ð3Þ

where b1 and b3 are stand level random-effects coeffi-

cients and other parameters are as defined above. As

mentioned earlier, to resolve the problem of temporal

autocorrelation and heteroscedasticity among residuals,

Table 3 Site index (SI; top height of dominant or codominant trees at 25 years at breast height), and estimates of long-term

(1971–2000) averages of mean growing season temperature (MT), precipitation of wettest quarter (PWQ), and total growing season

precipitation (TP) of two jack pine and two black spruce plantations in northern Ontario, Canada

Species/location Latitude Longitude SI (m) MT (°C) PWQ (mm) TP (mm)

Jack pine

Timmins (NE) 47°28′12″N 81°55′12″W 14.5 13.06 239 434.9

Fort Frances (NW) 47°54′36″N 91°54′36″W 13.0 13.53 289 493.1

Black spruce

Cochrane (NE) 49°48′0″N 80°6′0″W 9.0 12.35 291 474.8

Dryden (NW) 49°57′36″N 92°29′24″W 9.0 13.39 289 492.2

NE and NW refer to northeastern and northwestern Ontario, respectively.

© 2012 Blackwell Publishing Ltd, Global Change Biology, 19, 505–516

510 N. SUBEDI & M. SHARMA

the finalmixed-effects diameter growthmodel was fitted

with AR1 autocorrelation structure and a power vari-

ance function (Pinheiro & Bates, 2000) of AGE1 (i.e.,

Varðejb1; b3Þ ¼ r2 AGE1j j2d). Estimates of studentized

residuals (observed–predicted) from annual diameter

growth were calculated for all 5 year growth periods for

each tree for both species and plotted against the pre-

dicted annual diameter growth (Fig. 3). Trends in error

structure did not suggest any signs of heteroscedasticity.

The estimated coefficients of the final mixed-effects

diameter growth model for jack pine and black spruce

trees are given in Table 5. All coefficients of the model

were significant (alpha = 0.05) for both species, except

b0 for black spruce (P-value = 0.07). However, because

it was related to the asymptote, the coefficient b0 was

retained in the black spruce diameter growth model.

The sign of the coefficients, including the variance of

random effects, was similar for both species, except for

coefficient b7. The difference in signs associated with b7for the two species (Table 5) suggested that the rise in

mean temperature during the growing season would

affect the diameter growth of jack pine and black

spruce differently. The warmer growing season should

favor radial growth of jack pine, but reduce that of

black spruce. Similarly, the coefficients of b8 were posi-

tive for both species, which inferred that the increase in

PWQ favors radial growth in both species. In contrast,

the coefficient b9 was negative suggesting that excessive

rain during the growing season may decrease radial

growth of both species. The positive sign associated

with q (the first-order autoregressive autocorrelation

structure) indicated that model error terms were posi-

tively correlated with the residual of prediction from

previous period.

Equation (3) was further evaluated using the valida-

tion data set. Measure of bias, precision, and RMSE

–10

–8

–6

–4

–2

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Stud

entiz

ed re

sidu

al

Predicted annual diameter increment (cm/year)

–10–8–6–4–2

02468

10

0 0.2 0.4 0.6 0.8 1

Stud

entiz

ed re

sidu

al

Predicted annual diameter increment (cm/year)

(a)

(b)

Fig. 3 Studentized residuals (observed–predicted) from pre-

dicting diameter increments of (a) jack pine and (b) black spruce

trees using a non-linear mixed-effects method.

Table 4 Fit statistics [root mean square error (RMSE), Akaike

Information Criterion (AIC), and twice the negative log-likeli-

hood (�2 ln (L)] for Eqns (1) and (2) by tree species

Statistic Jack pine Black spruce

Goodness of fit Eqn (1) Eqn (2) Eqn (1) Eqn (2)

RMSE 0.12515 0.12473 0.10459 0.10296

�2 ln (L) �6527.1 �6562.5 �8567.1 �8729.0

AIC �6509.1 �6540.5 �8549.1 �8707.0

Table 5 Parameter estimates and fit statistics (SE = standard

error) of Eqn (3) fitted using a nonlinear mixed-effects method

for black spruce and jack pine plantation data from boreal

Ontario

Parameters

Jack pine Black spruce*

Estimates SE Estimates SE

b0 �5.8480 0.61773 �0.9749 0.55252

b1 0.2935 0.02203 0.6539 0.02499

b2 �0.0044 0.00020 �0.0070 0.00035

b3 �0.1042 0.00322 �0.1230 0.00441

b4 1.3709 0.15203 0.7276 0.08415

b5 0.1439 0.02359 0.0563 0.02373

b6 0.0045 0.00017 0.0064 0.00028

b7 0.1762 0.02916 �0.1558 0.03573

b8 0.0081 0.00168 0.0049 0.00171

b9 �0.0055 0.00120 �0.0019 0.00093

Variance components

r2 0.05722 0.03103

var(b1) 0.01399 0.01170

var(b3) 0.00020 0.00038

cov(b1, b3) �0.00092 �0.00192

Autocorrelation structure

q 0.59865 0.45383

Weight (power of age)

d �0.33576 �0.29423

AIC �10861.3 �10202.9

Log likelihood 5446.6 5117.5

*b0 was not significant.

© 2012 Blackwell Publishing Ltd, Global Change Biology, 19, 505–516

CLIMATE –GROWTH RELATIONSHIPS OF BOREAL TREES 511

(root mean square error) for the localized responses

were calculated across tree size (DBH) and age for both

species (Table 6). Random-effects coefficients were

localized using diameter growth measurements from a

randomly selected tree. The mean biases in diameter

(inside bark) prediction were smaller for both species

across tree size and age. For example, the average

biases were less than �0.02 cm for jack pine and

�0.03 cm for black spruce across diameter classes.

Results indicated that for both species diameter predic-

tions were more precise (i.e., smaller RMSE) for larger

or older trees than for smaller or younger trees.

To predict future diameter growth under a changing

climate scenario, the diameter growth of an average-

sized (i.e., diameter) tree was estimated for both

species. The estimated diameter growth of an average

tree under the A2 and B2 climate scenarios during

2041–2070 for the selected plantation sites (Table 3) for

both tree species is given in Fig. 4. These estimates were

made using only fixed-effects coefficients. Model results

suggested that, under both climate scenarios, the

diameter growth of jack pine would be faster during

2041–2070 than the existing rate of diameter growth

(1970–2000) in both northeastern (NE) and northwestern

(NW) Ontario. The observed rates of diameter growth

were slightly faster in NW Ontario than those in the NE

Ontario and this trend is expected to continue, at least

during 2041–2070. For jack pine, the rate of diameter

growth will be more rapid (i.e., averaging 25 and 29%

increases in NE and NW Ontario, respectively) under

the A2 scenario than that (i.e., average 7% increase for

both NE and NW) under the B2 scenario.

For black spruce, current rates of diameter growth

were slower in NW than in NE Ontario. Under both

the A2 and B2 climate scenarios, the rate of diameter

increment would decrease for black spruce, with more

a pronounced decrease under the A2 than the B2 sce-

nario. Under the A2 scenario, the average rate of diam-

eter increment would be 32% and 40% lower for black

spruce trees in NE and NW Ontario, respectively, than

the existing rate (1970–2000). Under the B2 scenario, the

average rate of diameter increment would be 9% and

10% lower in NE and NW Ontario, respectively.

Discussion

Our results indicated that climatic variables could be

included in the existing diameter growth models to

make them climate sensitive. This can be accomplished,

at least in the composite model form (Wykoff, 1990), by

expanding the intercept term (e.g., b0 in Eqn (1)). We

found that a combination of temperature- and precipi-

tation-related variables (i.e., MT, PWQ, and TP) was

significant in explaining variation in diameter growth

of jack pine and black spruce trees across plantations in

the study area. After including climate variables, the fit

statistics of the individual-tree diameter growth model

improved significantly for both species. However, the

longitude variable, which was significant in the original

diameter growth model (e.g., Subedi & Sharma, 2011)

was no longer significant. This suggests that the longi-

tude of a plantation site was acting as a surrogate of cli-

mate variables in the original model.

Beyond climate variables, site index explained a sig-

nificant part of the variability in tree diameter growth

in jack pine and black spruce plantations. However, in

the study by Crookston et al. (2010), site index was

assumed to be a function of climate variables, and

growth rates in Forest Vegetation Simulator were

adjusted by constructing a function linking site index to

climate rather than directly incorporating climate vari-

ables and site index into the growth models. As the var-

iability in site index that can be explained using climate

variables is not very high (�25% as mentioned in

Crookston et al., 2010), accounting for site productivity

using growth components did not seem promising.

Similarly, Pokharel & Froese (2009) compared two

basal area growth models (one included mean annual

temperature and ecological land classification variables

and the other site, index only) for four boreal tree spe-

cies, including jack pine and black spruce in natural

stands. They reported that, for all species, the model

with mean annual temperature and ecological land clas-

sification variables outperformed that with only site

index. As Pokharel & Froese (2009) indicated, for some

data sets estimating site index was impossible and

where it was possible the estimates were not sufficiently

accurate to be of much use. However, the trees in our

study were sampled from jack pine and black spruce

plantations and the site indices for these plantations

were directly measured from stem analysis data. There-

fore, site index was an important variable in the diame-

ter growth model that accounted for the difference

between sites with different soil conditions but identical

climate variables. The importance of site index was also

obvious from the values of RMSE calculated with and

without site index variable in the models for evaluation

data sets for both species. These values for the models

with the climate and site index variables were 0.031 and

0.014 cm compared to 0.182 and 0.126 cm for the models

without site index for jack pine and black spruce, respec-

tively, across the tree size (dbh).

Relationship between mean growing season temperatureand radial growth

We found that a warmer growing season favors the

radial growth of jack pine trees, which is consistent

© 2012 Blackwell Publishing Ltd, Global Change Biology, 19, 505–516

512 N. SUBEDI & M. SHARMA

with findings from previous studies (e.g., Brooks

et al., 1998; Huang et al., 2010). Thus, prolonging the

growing season, either during spring warm up or late

fall, favors jack pine growth (Hofgaard et al., 1999).

This is the case for black spruce as well, but here the

negative temperature correlation is related to drought

sensitivity. The warmer growing season will increase

evapotranspiration during summer, which reduces

the availability of soil moisture. Jack pine is known to

be more drought resistant. Hofgaard et al. (1999) indi-

cated that the key factor separating these two species

extending the growing season into late fall, which

favors jack pine growth but not black spruce. Our

results for black spruce were consistent with those of

previous studies (e.g., Dang & Lieffers, 1989; Brooks

et al., 1998; Way & Sage, 2008; Wilmking & Myers-

Smith, 2008).

Another potential reason for the opposite response to

warmer growing season between species may be their

site preference. It is known that jack pine favors drier

sites whereas black spruce grows well on wet sites. The

warmer growing season may quickly raise the soil

temperature on drier sites but not on wet sites (Dang &

Lieffers, 1989; Brooks et al., 1998). On wet sites, spring

warm up of the soil is delayed by a thick organic hori-

zon, and despite warmer air temperatures the onset of

growth in black spruce trees may have been delayed

(Fraser, 1956). Timing of onset of the growing season

was determined for Scots pine (Pinus sylvestris L.) based

on the number of warm days during spring warm up

(Suni et al., 2003). Therefore, spring warm up might

favor the radial growth of black spruce (Hofgaard et al.,

1999) more than the warmer periods during either the

middle or later parts of growing season.

Table 6 Mean bias (observed–predicted), precision, and root mean square error (RMSE) in predicting annual diameter increments

using validation data set by tree size (A) and age (B)

Species DBH (cm)

Number of

observations

Average

bias (cm) Precision RMSE

A

Jack pine <3 392 �0.01630 0.0310 0.03130

4–6 314 0.00335 0.0183 0.01834

7–10 377 0.00375 0.0102 0.01022

11–13 489 0.00006 0.0071 0.00714

13–15 454 0.00594 0.0041 0.00418

16–18 288 0.00946 0.0028 0.00288

>19 196 �0.00140 0.0039 0.00390

Black spruce <3 811 0.00737 0.0141 0.01418

4–6 444 �0.00166 0.0069 0.00689

7–9 504 �0.00111 0.0057 0.00571

10–12 410 0.00004 0.0035 0.00356

13–15 256 �0.01215 0.0023 0.00250

>16 104 �0.00818 0.0023 0.00244

Age (years)Number of

observations

Average

bias (cm) Precision RMSE

B

Jack pine <5 622 �0.0127 0.02766 0.0278

6–10 312 �0.0024 0.01330 0.0133

11–15 312 �0.0052 0.00857 0.0086

16–20 312 �0.0041 0.00475 0.0048

21–25 288 0.0158 0.00386 0.0041

26–30 239 0.0239 0.00357 0.0041

31–35 190 0.0117 0.00220 0.0023

>36 235 0.0013 0.00253 0.0025

Black spruce <5 784 0.0052 0.01456 0.0146

6–10 392 �0.0083 0.00913 0.0092

11–15 384 �0.0056 0.00504 0.0051

16–20 337 0.0020 0.00446 0.0045

21–25 279 0.0071 0.00242 0.0025

26–30 211 0.0006 0.00182 0.0018

>31 142 �0.0047 0.00147 0.0015

© 2012 Blackwell Publishing Ltd, Global Change Biology, 19, 505–516

CLIMATE –GROWTH RELATIONSHIPS OF BOREAL TREES 513

Moreover, a recent study in which black spruce

plants were grown at lower temperature (22/16 °Cday/night temperature) and higher temperatures

(30/24 °C day/night temperature) indicated that those

grown at higher temperatures were 20% shorter, 58%

lighter, and had a 58% lower root : shoot ratio than

those grown at lower temperatures (Way & Sage, 2008).

The authors mentioned that the reason for heat-induced

growth reduction in black spruce seedlings was more

due to increased respiration rates than photosynthesis

rates during growth periods.

Relationship between precipitation during wettest quarterand radial growth

Understanding of seasonal growth patterns of boreal

trees is important to explain the relationship between

moisture availability and radial growth. The cumula-

tive radial growth of boreal tree species (including jack

pine and black spruce) can be described using three

distinct phases (Belyea et al., 1951; Tardif et al., 2001).

In early- to mid-May, an initial period of swelling of

the stem occurs that lasts for at least a week, indicating

the upward passage of water. This is followed by a

period of active cell division indicating the ‘grand per-

iod’ of growth. During the third period, growth stops,

the cells dehydrate, and the cambial tissue prepares for

its winter rest (Belyea et al., 1951). It was reported that

the cambial activity in the stem of trees, including yel-

low birch (Betula alleghaniensis Britton), American

beech, and white spruce [Picea glauca (Moench) Voss],

ceased by early September, even on sites where neither

moisture nor temperature was limiting (Fraser, 1956).

Similarly, a study of early wood and late wood forma-

tion in growth rings of balsam fir [Abies balsamea (L.)

Mill] from a boreal forest near Lac-Saint-Jean, Quebec,

Canada, indicated that complete earlywood formation,

including cell wall thickening, required 10–14 weeks

(Deslauriers et al., 2003). Thus, optimal growing

conditions during the ‘grand period’ are very impor-

tant for boreal trees species. Northern Ontario receives

its maximum precipitation during summer (Phillips,

1990), so the precipitation during wettest quarter

parameter applies to the early part of growing season.

The positive relationship that we found between

increased moisture availability during ‘grand period of

growth’/earlywood formation and radial growth was

as expected.

Relationship between growing season total precipitationand radial growth

Our model results indicated that more precipitation

during the entire growing season might negatively

affect radial growth of both tree species. Previous stud-

ies (Schuur et al., 2001; Hsu et al., 2012) indicated that

the relationship between the mean annual precipitation

and net primary productivity (NPP), at majority of

sites, could be described by a nonlinear, concave down

function. Alternatively, water initially acted as a

resource to increase NPP, then became neutral, after

which further increases in water availability decreased

NPP in humid forests (Schuur et al., 2001). The decline

in the NPP was likely an indirect effect on plant growth

mediated by the availability of other resources.

Whereas water acts mainly as a resource in dry-to-

(a)

(b)

Fig. 4 Diameter growth profiles of an average size (a) jack pine

tree in northeastern (Timmins) and northwestern (Fort Frances)

Ontario and (b) an average size black spruce tree (b) in north-

eastern (Cochrane) and northwestern (Dryden) Ontario for the

period 2041–2070 given IPCC’s (2001) A2 and B2 scenarios and

current climate (no change; 1970–2000).

© 2012 Blackwell Publishing Ltd, Global Change Biology, 19, 505–516

514 N. SUBEDI & M. SHARMA

mesic ecosystems, increased precipitation may reduce

radial growth of trees (i.e., NPP) by decreasing radia-

tion inputs, increasing nutrient leaching, or reducing

soil oxygen availability in humid ecosystems (Schuur,

2003). More rainfall reduces the diffusion of oxygen

through water-filled pores to match the aerobic needs

of roots and microbes, and reduces decomposition

rates. Although oxygen limitation did not appear to

affect plant growth directly, slower decomposition rates

decreased nutrient availability and limited the supply

of nutrients for plant growth (Schuur et al., 2001). These

relationships support our model predictions.

Climate–growth relationships and forest managementplanning

Our results suggested that changes in climate, as pre-

dicted by version 2 of CGCM [Intergovernmental Panel

on Climate Change (IPPC), 2001], would increase diam-

eter growth of jack pine and reduce that of black spruce

trees. Goldblum & Rigg (2005) reported that rising tem-

perature and precipitation would increase the growth

rate of sugar maple (Acer saccharum Marsh.) and white

spruce, but not balsam fir, as higher fall temperatures

did not increase balsam fir growth on a deciduous-bor-

eal forest ecotone site near the northeastern shore of

Lake Superior in Ontario, Canada. Therefore, the

performance of individual-tree species may vary under

a changing climate and future growth rates of boreal

trees may differ from historical rates. Moreover, a

changing climate may affect natural disturbance pat-

terns including fire, drought, introduced species,

insects and pathogen outbreaks, hurricanes, ice storms,

and landslides (Dale et al., 2001), which may change

the composition and structure of forests at landscape

levels (Hansen et al., 2001; Chmura et al., 2011).

Current forest management planning practices in

North America, including Ontario, are based on the

assumption that by emulating patterns of natural dis-

turbance, long-term forest sustainability is being main-

tained. However, in the context of a changing climate,

we cannot rely on past forest conditions to provide ade-

quate targets for future management decisions (Millar

et al., 2007). Various models, such as climate–growth

relationships and climate envelopes of species (e.g.,

Crowe & Parker, 2011), can play a significant role in

helping us to understand the dynamics of change and

develop strategies to meet the management objectives

at landscape, ecosystem, and planning (i.e., forest man-

agement unit) levels.

Quantitative models can provide estimates for a

range of future climate change scenarios and forest

responses, but rarely can they predict the future with

certainty with the level of accuracy and precision

needed by resource managers (Pilkey & Pilkey-Jarvis,

2007). The models developed in this study can be used

to predict how two species may respond and can be

used to help guide decision making. In this context,

the models should not be used to predict future out-

comes, but rather to narrow the possible range of plau-

sible outcomes, identify the range of uncertainty, and

suggest appropriate management alternatives (Littell

et al., 2011). Predictions made using climate-based

growth models need to be coupled with continuous

learning through adaptive management to reduce the

uncertainty associated with the forest management

decisions.

Acknowledgements

This study was supported by the Ontario Ministry of NaturalResources. Data collection was funded by the Forestry FuturesTrust Enhanced Forest Productivity Science Program. Theauthors are grateful to Daniel McKenney and Pia Papadopol,Canadian Forest Service, for providing estimates of climate vari-ables for study sites; John Parton, Ministry of NaturalResources, for his assistance with field work; and Lisa Buse,Ontario Forest Research Institute, for editing an earlier versionof the manuscript.

References

Aber J, Neilson RP, McNulty S, Lenihan JM, Bachelet D, Drapek RJ (2001) Forest pro-

cesses and global environmental change: predicting the effects of individual and

multiple stressors. BioScience, 51, 735–751.

Akaike H (1978) A Bayesian analysis of the minimum AIC procedure. Annals of the

Institute of Statistical Mathematics, 30, 9–14.

Bates D, Maechler M, Bolker B (2011) lme4: Linear Mixed–Effects Models using S4 Clas-

ses. R Package Version 0.999375-42. Available at: http://cran.r-project.org/web/

packages/lme4/lme4.pdf (accessed 10 December 2011).

Belyea RM, Fraser DA, Rose AH (1951) Seasonal growth of some trees in Ontario. The

Forestry Chronicle, 27, 300–305.

Brooks JR, Flanagan LB, Ehleringer JR (1998) Responses of boreal conifers to climate

fluctuations: indications from tree-ring width and carbon isotope analyses. Cana-

dian Journal of Forest Research, 28, 524–533.

Burton BJ, Messier C, Weetman GF, Prepas EE, Adamowicz WL, Tittler R (2003) The

current state of boreal forestry and the drive for change. In: Towards Sustainable

Management of the Boreal Forest (eds Burton PJ, Messier C, Smith DW, Adamowicz

WL), pp. 1–40. NRC Press, Ottawa, Canada.

Chmura DJ, Anderson PD, Howe GT et al. (2011) Forest responses to climate change

in the northwestern United States: ecophysiological foundations and adaptive

management. Forest Ecology and Management, 261, 1121–1142.

Clark J, Gibbs D (1957) Studies in tree physiology IV. Further investigations of sea-

sonal changes in moisture content of certain Canadian forest trees. Canadian Jour-

nal of Botany, 35, 219–253.

Colombo SJ, McKenney DW, Lawrence KM, Gray PA (2007) Climate Change Projec-

tions for Ontario: Practical Information for Policymakers and Planners. Ontario Ministry

of Natural Resources, Applied Research and Development Branch, Climate

Change Research Report CCRR-05, Sault Ste. Marie, ON, Canada.

Crookston NL, Rehfeldt GR, Ferguson DE, Warwell M (2008) FVS and global warm-

ing: a prospectus for future development. In: Third Forest Vegetation Simulator Con-

ference: 2007 February 13–15 (eds Havis RN, Crookston NL), pp. 7–16. Proceedings

RMRS-P-54, USDA, Forest Service, Fort Collins, CO.

Crookston NL, Rehfeldt GE, Dixon GE, Weiskittel AR (2010) Addressing climate

change in the forest vegetation simulator to asses impacts on landscape forest

dynamics. Forest Ecology and Management, 260, 1198–1211.

Crowe KA, Parker WH (2011) Conserving the diversity of Ontario tree species

under multiple uncertain climatic futures. Canadian Journal of Forest Research,

41, 533–542.

© 2012 Blackwell Publishing Ltd, Global Change Biology, 19, 505–516

CLIMATE –GROWTH RELATIONSHIPS OF BOREAL TREES 515

Dale VH, Joyce LA, McNulty S et al. (2001) Climate change and forest disturbances.

BioScience, 723–734.

Dang QL, Lieffers VJ (1989) Climate and annual ring growth of black spruce in some

Alberta peatlands. Canadian Journal of Botany, 67, 1885–1889.

Daniels LD, Veblen TT (2004) Spatiotemporal influences of climate on altitudinal tree-

line in northern Patagonia. Ecology, 85, 1284–1296.

D’Arrigo RD, Jacoby GC, Free RM (1992) Tree-ring width and maximum latewood

density at the North American tree line: parameter of climate change. Canadian

Journal of Forest Research, 22, 1290–1296.

Demidenko E (2004) Mixed Models: Theory and Applications. John Wiley & Sons, Inc.,

Hoboken, NJ.

Deslauriers A, Morin H, Begin Y (2003) Cellular phenology of annual ring formation

of Abies balsamea in the Quebec boreal forest (Canada). Canadian Journal of Forest

Research, 33, 190–200.

Dieguez-Aranda U, Burkhart HE, Amateis RL (2006) Dynamic site model for lob-

lolly pine (Pinus taeda L.) plantations in the United States. Forest Science, 52,

262–272.

Duchesne L, Houle D (2011) Modelling day-to-day stem diameter variation and

annual growth of balsam fir (Abies balsamea (L.) Mill.) from daily climate. Forest

Ecology and Management, 262, 863–872.

Fraser DA (1956) Ecological studies of forest trees at Chalk River, Ontario, Canada.

II. Ecological Conditions and Radial Increment Ecology, 37, 777–789.

Fritts HC (1958) An analysis of radial growth of beech in a central Ohio forest during

1954–55. Ecology, 39, 705–719.

Fritts HC (1976) Tree Rings and Climate. The Blackburn Press, Caldwell, NJ.

Goldblum D, Rigg LS (2005) Tree growth response to climate change at the decidu-

ous-boreal forest ecotone, Ontario, Canada. Canadian Journal of Forest Research, 35,

2709–2718.

Hamann A, Wang T (2006) Potential effects of climate change on ecosystem and tree

species distribution in British Columbia. Ecology, 87, 2773–2786.

Hansen AJ, Neilson RP, Dale VH et al. (2001) Global changes in forests: responses of

species, communities, and biomes. BioScience, 51, 765–779.

Huang J, Tardif JC, Bergeron Y, Denneler B, Berninger F, Girardins MP (2010)

Radial growth response of four dominant boreal tree species to climate along a

altitudinal gradient in the eastern Canadian boreal forest. Global Change Biology,

16, 711–731.

Hofgaard A, Tardif J, Bergeron Y (1999) Dendroclimatic response of Picea mariana and

Pinus banksiana along a longitudinal gradient in the eastern Canadian boreal forest.

Canadian Journal of Forest Research, 29, 1333–1346.

Hsu JS, Powell J, Adler PB (2012) Sensitivity of mean annual primary production to

precipitation. Global Change Biology, 18, 2246–2255.

Hutchinson MF (2011) ANUSPLIN version 4.3. Available at: http://fennerschool.anu.

edu.au/research/publications/software-datasets/anusplin (accessed 6 December

2011)

Intergovernmental Panel on Climate Change (IPPC) (2001) Climate change 2001.

Synthesis report. In: A contribution of Working Groups I, II, and III to the Third

Assessment Report of Intergovernmental Panel on Climate Change (eds Watson RT,

Albritton DL, Baker T, Bashmakov IA, Canziani O, Christ R). Cambridge Univer-

sity Press, Cambridge, UK, 398 pp.

Lacerte V, Larocque GR, Woods M, Parton WJ, Penner M (2006) Calibration of the for-

est vegetation simulator (FVS) model for the main forest species of Ontario, Can-

ada. Ecological Modelling, 199, 336–349.

Littell JS, McKenzie D, Kerns BK, Cushman S, Shaw CG (2011) Managing uncertainty

in climate-driven ecological models to inform adaptation to climate change. Eco-

sphere, 2, 1–19.

McDowell NG, Beerling DJ, Breshears DD, Fisher RA, Raffa KF, Stitt M (2011) The

interdependence of mechanisms underlying climate-driven vegetation mortality.

Trends in Ecology and Evolution, 26, 523–532.

McKenney DW, Hutchinson MF, Papadopol P et al. (2011) Customized spatial cli-

mate models for North America. Bulletin of the American Meteorological Society, 92,

1161–1622.

Millar CI, Stephenson NL, Stephens S (2007) Climate change and forests of the future:

managing in the face of uncertainty. Ecological Applications, 17, 2145–2151.

National Climate Data and Information Archive (NCDIA) (2012). Environmental

Canada. Available at: www.climate.weatheroffice.gc.ca/climateData/canada_

e.html (accessed 10 February 2012).

National Forest Database (NFD) (2012). Canadian Forest Service, Natural Resources

Canada. Available at: http://nfdp.ccfm.org/dynamic_report/dynamic_repor-

t_ui_e.php (accessed 4 January 2012).

Parker WC, Colombo SJ, Cherry ML et al. (2000) Third millennium forestry: what cli-

mate change might mean to forests and forest management in Ontario. The Forestry

Chronicle, 76, 445–463.

Peterson DW, Peterson DL (2001) Mountain hemlock growth responds to climatic

variability at annual and decadal time scales. Ecology, 82, 3330–3345.

Phillips D (1990) The Climates of Canada. Ministry of Supply and Services Canada,

Ottawa, Canada.

Pilkey O, Pilkey-Jarvis L (2007) Useless Arithmetic: Why Environmental Scientists Can’t

Predict the Future. Columbia University Press, New York, NY.

Pinheiro JC, Bates DM (2000) Mixed-Effects Models in S and S-PLUS. Springer-Verlag,

New York, NY.

Pinheiro JC, Bates DM, Debroy S, Sarkar D (2011) nlme: Linear and Nonlinear Mixed

Effects Models. R Package Version 3.1-102. Available at: http://cran.r-project.org/

web/packages/nlme/index.html (accessed 10 November 2011).

Pokharel B, Froese RB (2009) Representing site productivity in the basal area incre-

ment model for FVS-Ontario. Forest Ecology and Management, 258, 657–666.

R Development Core Team (2011) R: A Language and Environment for Statistical Com-

puting. R Foundation for Statistical Computing, Vienna, Australia. Available at:

http:/www.r-project.org (accessed 4 September 2011).

Schuur EAG (2003) Productivity and global climate revisited: the sensitivity of tropi-

cal forest growth to precipitation. Ecology, 84, 1165–1170.

Schuur EAG, Oliver CA, Matson PA (2001) Carbon cycling and soil carbon storage in

mesic to wet Hawiian montane Forests. Ecology, 82, 3182–3196.

Sojo AJ, Tchebakova NM, French NHF et al. (2007) Climate-induced boreal forest

change: predictions versus current observations. Global and Planetary Change, 56,

274–296.

Stromgren M, Linder S (2002) Effects of nutrition and soil warming on stemwood

production of a boreal Norway spruce stand. Global Change Biology, 8, 1195–1204.

Subedi N, Sharma M (2011) Individual-tree diameter growth model for black spruce

and jack pine plantations in northern Ontario. Forest Ecology and Management, 261,

2140–2148.

Suni T, Berninger F, Markkanen T, Keronen P, Rannik U, Vesala T (2003) Interannual

variability and timing of growing-season CO2 exchange in a boreal forest. Journal

of Geophysical Research, 108, ACL 2-1–ACL 2-7.

Tardif J, Flannigan M, Bergeron Y (2001) An analysis of the daily radial activity of 7

boreal tree species, northwestern Quebec. Environmental Monitoring and Assess-

ment, 67, 141–160.

Trincado G, Burkhart HE (2006) A generalized approach for modeling and localizing

stem profile curves. Forest Science, 52, 670–682.

Vonesh EF, Chinchilli VM (1997) Linear and Nonlinear Models for the Analysis of

Repeated Measurements. Marcel Dekker Inc., New York, NY.

Way DA, Sage R (2008) Elevated growth temperatures reduce the carbon gain of

black spruce [Picea mariana (Mill.) B.S.P.]. Global Change Biology, 14, 624–636.

Wilmking M, Juday GP (2005) Longitudinal variation of radial growth at Alaska’s

northern treeline�recent changes and possible scenarios for the 21st century. Glo-

bal and Planetary Change, 47, 282–300.

Wilmking M, Myers-Smith I (2008) Changing climate sensitivity of black spruce (Picea

mariana Mill) in a peatland�forest landscape in Interior Alaska. Dendrochronologia,

25, 167–175.

Wilmking M, Juday GP, Barber VA, Zald HSJ (2004) Recent climate warming forces

contrasting growth responses of white spruce at treeline in Alaska through tem-

perature thresholds. Global Change Biology, 10, 1724–1736.

Worbes M (1999) Annual growth rings, rainfall-dependent growth and long-term

growth patterns of tropical trees form the Caparo Forest Reserve in Venezuela.

Journal of Ecology, 87, 391–403.

Wykoff WR (1990) A basal area increment model for individual conifers in the north-

ern Rocky Mountains. Forest Science, 36, 1077–1110.

© 2012 Blackwell Publishing Ltd, Global Change Biology, 19, 505–516

516 N. SUBEDI & M. SHARMA