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 The CO2 fertilization hypothesis stipulates that rising atmospheric CO2 has a direct positive effect on net primary productivity (NPP), with experimental evidence suggesting a 23% growth enhancement with a doubling of CO2. Here, we test this hypothesis by comparing a bioclimatic model simulation of NPP over the twentieth century against tree growth increment (TGI) data of 192 Pinus banksiana trees from the Duck Mountain Provincial Forest in Manitoba, Canada. We postulate that, if a CO2 fertilization effect has occurred, climatically driven simulations of NPP and TGI will diverge with increasing CO2. We use a two-level scaling approach to simulate NPP. A leaf-level model is first used to simulate high-frequency responses to climate variability. A canopy-level model of NPP is then adjusted to the aggregated leaf-level results and used to simulate yearly plot-level NPP. Neither model accounts for CO2 fertilization. The climatically driven simulations of NPP for 1912–2000 are effective for tracking the measured year-to-year variations in TGI, with 47.2% of the variance in TGI reproduced by the simulation. In addition, the simulation reproduces without divergence the positive linear trend detected in TGI over the same period. Our results therefore do not support the attribution of a portion of the historical linear trend in TGI to CO2 fertilization at the level suggested by current experimental evidence. A sensitivity analysis done by adding an expected CO2 fertilization effect to simulations suggests that the detection limit of the study is for a 14% growth increment with a doubling of atmospheric CO2 concentration.
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 The CO2 fertilization hypothesis stipulates that rising atmospheric CO2 has a positive effect on net primary productivity (NPP) due to increasing availability of carbon, a limiting factor for the photosynthesis of C3 plants [Huang et al., 2007]. The concept of CO2 fertilization has a long experimental history and has been well demonstrated under laboratory or controlled conditions for a variety of C3 vascular plants, including trees (see reviews by Norby et al. , Ainsworth and Long , Huang et al. , Körner et al. , Wang , and Prentice and Harrison ). In a landmark paper, Norby et al.  have reported on the most extensive experiments on this topic involving multiyear free-air CO2 enrichment (FACE) in coniferous and deciduous plantations. In the four sites under study, they have found a 23% enhancement of NPP sustained over multiple years following a doubling of preindustrial CO2 concentrations. Given the current weight of experimental evidence, modelers have been including CO2 fertilization effects in their simulations of past and future forest productivity [e.g., Rathgeber et al., 2000, 2003; Chen et al., 2000; Balshi et al., 2007; Su et al., 2007; Peng et al., 2009], generally resulting in projected increases in forest growth under future atmospheric CO2 concentrations. The impact of this type of inclusion is important as predictions of forest carbon sequestration dynamics are increasingly coupled to global circulation models and CO2 emission scenarios [e.g., Notaro et al., 2007; O'ishi et al., 2009].
 In spite of the current wealth of experimental evidence on CO2 fertilization of tree growth, there is still some doubt as to the actual realization of this effect under natural conditions. Körner et al. , in a FACE experiment in a mature deciduous forest, have found no lasting growth stimulation by CO2 enrichment after 4 years of treatment. Caspersen et al. , in a study of long-term results from forest sample plots in the eastern United States, have found only a modest increase in tree growth over the past century. And recently, Norby et al. [2008, 2009] reported that nitrogen limitation was causing a dramatic reduction in growth enhancement in their hardwood FACE experiment from the 23% reported by Norby et al.  to a current value of 9%. Evidence of site fertility restrain on carbon sequestration was also found by Oren et al.  in their study of mature pine forests exposed to elevated atmospheric CO2. In their global simulations of CO2 enhancement on NPP, Hickler et al.  concluded that current FACE results do not apply to boreal forest, because of the strong temperature dependence of the relative affinity of the carboxylation enzyme Rubisco for CO2 and O2. The predominantly colder temperatures of boreal forests compared with FACE experiments would limit the CO2 effect, with a simulated increase of NPP of about 15% under a doubling of atmospheric CO2 [Hickler et al., 2008]. These reports raise the question of the importance of CO2 fertilization in natural forest environments where tree growth is limited by other factors.
 As mentioned above, CO2 fertilization effects on growth have already been included in many process-based models. Such models serve as direct links between the climate and tree growth [Hunt et al., 1991; Landsberg and Waring, 1997; Rathgeber et al., 2000, 2003; Misson et al., 2004] or ecosystem carbon dynamics [e.g., Balshi et al., 2007; Peng et al., 2009]. The challenge with any such inclusion, however, lies with the verification of the modeled change in growth against actual field measurements of realized growth. Because real-world CO2 enhancement is not a step function, but rather a long-term monotonic increase, the signal it generates in tree growth is not easily detectable. The signal is certainly far weaker than the large interannual variations caused by climate variability [D'Arrigo and Jacoby, 1993] and may be within the uncertainties related to forest inventory data [Joos et al., 2002]. In addition, global temperatures have also been increasing, along with atmospheric nitrogen deposition in some parts of the globe, further confounding the effect of CO2 fertilization. Finally, the response of plants to CO2 is also affected by the possible down-regulation of photosynthesis [e.g., Eguchi et al., 2008; Crous et al., 2008]. All these issues make the detection of CO2 fertilization effects particularly challenging.
 Here, we test the CO2 fertilization hypothesis by comparing tree growth increment data from 1912 to 2000 with simulation results using a simulator that does not incorporate CO2 fertilization effects, and is empirically adjusted to the current CO2 growth environment through field measurements of photosynthesis. We postulate that, in the event that a CO2 fertilization effect has occurred, climatically driven simulations of forest productivity will show increasing divergence with the measurement record over time as the atmospheric CO2 increases [Graumlich, 1991; Jacoby and D'Arrigo, 1989, 1997; Rathgeber et al., 2000]. For this purpose, we used tree ring increments of 192 jack pine (Pinus banksiana Lamb.) trees from the closed-canopy boreal forest of Duck Mountain Provincial Forest (DMPF) in Manitoba, Canada. Growth increment data were transformed into a tree growth index (TGI) using the regional curve standardization technique, such that low-frequency signals were retained in the data. The final tree ring chronology extends from 1717 to 2000. We used a two-level scaling approach to achieve estimates of forest productivity for the period of 1912 to 2000. At the finest scale, a leaf-level model of photosynthesis (FineLEAP) was used to simulate canopy properties and their interaction with the variability in radiation, temperature and vapor pressure deficit. Then, the StandLEAP model, a top-down plot-level model of forest productivity, was used to simulate landscape-level productivity over the twentieth century. The two levels of simulation are linked functionally as parameters of the coarser models are estimated from aggregated simulation results of the finer model, but neither model accounts for CO2 fertilization. Finally, the detection limit of our approach was investigated through a sensitivity analysis in which an expected CO2 fertilization was included in StandLEAP simulations via a response function.
2. Study Area
 The study took place in the DMPF (51°40′N; 100°55′W), which covers approximately 376,000 ha (Figure 1). Duck Mountain is located within the Boreal Plains ecozone, a transition zone between the boreal forest to the north and the aspen parkland and prairie to the south, and is topographically part of the Manitoba Escarpment, which is characterized by a higher elevation compared with the surrounding plains (300–400 m above sea level, with highest point at 825 m). Pure to mixed deciduous and coniferous stands, primarily composed of trembling aspen (Populus tremuloides Michx.) and white spruce (Picea glauca [Moench] Voss), constitute about 80% of the DMPF. Stands dominated by black spruce (Picea mariana [Mill.] BSP) and jack pine constitute about 14% and 6% of the area, respectively, and occur most commonly in the central, higher elevation regions of the DMPF. The DMPF has a midboreal climate with predominantly short, cool summers and cold winters. At lower elevation Swan River (52°03′N; 101°13′W, elevation: 346.6 m asl), mean monthly temperatures ranged from −18.2°C in January to 18.1°C in July for the reference period of 1971–2000. Average total annual precipitation was 530.3 mm, with most precipitation falling as rain between May and September.
3.1. Tree Ring Measurements
 During the summers of 2000 and 2001, the DMPF was surveyed with the objective of reconstructing fire history [Tardif, 2004]. The DMPF was systematically divided into UTM grids (10 × 10 km) and sites were sampled within each grid based on accessibility. Detailed information on data collection is found in the work of Tardif . For the current study, we analyzed a subset of jack pine cores (2 radii/tree) and stem cross sections consisting of 192 living and dead trees collected from 70 sampling sites located within 20 UTM grids. Only trees with complete ring measurements from pith to the last year of growth were included, which explains the lower sample replication compared to earlier studies (i.e., 291 trees in that of Girardin and Tardif ). The majority of samples were collected in the uplands in stands dominated by jack pine and black spruce. Each of the cores and sections were dried, sanded and cross-dated using the pointer-year method [Yamaguchi, 1991]. Annual growth increments were measured from the pith to the outermost ring at a precision of 0.001 mm using a Velmex measuring stage coupled with a computer, and both cross-dating and measurements were statistically validated using the COFECHA program [Holmes, 1983]. The final data set consisted of 332 ring width measurement series. Ring width measurements were recorded for a period extending from AD 1717 to AD 2000.
3.2. Meteorological Data
 Meteorological data used as input for the bioclimatic model were monthly means of daily maximum and minimum temperatures (from the Birtle (1905–1998) and Dauphin (1904–2003) meteorological stations; Figure 1) and total monthly precipitation data (from the Birtle (1918–2000), Dauphin (1912–2003), and Russell (1916–1990) meteorological stations) from Vincent and Gullett  and Mekis and Hogg , respectively. Data were corrected by the authors for nonhomogeneities associated with changes in instrumentation or weather station location. Regional climate data files were created by averaging data from all stations following the procedure described by Fritts  (homogeneity testing, station adjustments for mean and standard deviation, and station averaging).
3.3. Forest Inventories
 Biometric information was obtained from DMPF temporary sample plots (TSP) of the Forest Lands Inventory initiated by Louisiana Pacific Canada Ltd.–Forest Resources Division and Manitoba Conservation–Forestry Branch. Necessary information for driving the StandLEAP bioclimatic model includes soil texture and forest stand properties (forest composition and biomass estimates). For simplicity, we only modeled forest stands classified as “pure” jack pine stands (i.e., where more than 75% of plot basal area was contributed by jack pine). A total of ten plots (out of 1317) met the 75% criterion while also having all the necessary information for modeling purposes (Table S1, available as auxiliary material). For each of these TSPs, aboveground biomass was estimated using the national biomass equations of Lambert et al. . These functions were applied to each tree, and the individual tree biomass values were summed to estimate stand-level biomass density (Mg ha−1) in each TSP.
3.4. Atmospheric CO2 Data
 We used annual average of the atmospheric concentrations of CO2 reconstructed from ice cores [Etheridge et al., 1996] and recorded at Mauna Loa observatory since 1953 [Keeling et al., 1982]. The CO2 concentration increased from 300 ppmv in 1910, to 317 ppmv in 1960, and to 370 ppmv in 2000.
4.1. Development of the Tree Growth Index
 All ring width measurements were detrended using the regional curve standardization technique [Esper et al., 2003] in order to eliminate noise caused by site-related effects (e.g., competition and self-thinning) and biological effects (e.g., aging). This approach has the potential to preserve the evidence of long timescale forcing of tree growth (see reviews by Esper et al.  and Briffa and Melvin ) as it scales ring width measurements against an expectation of growth for the appropriate age of each ring (Figure 2). We first aligned the 332 measurement series by cambial age and calculated the arithmetic mean of ring width for each ring age. We then created a regional curve (RC) by applying a negative exponential smoothing [Cook and Kairiukstis, 1990] to the age series of arithmetic means (Figure 2). It is assumed that this RC created from the means of ring width for each ring age describes the functional form of the age-related growth trend. Note that our conclusions were insensitive to the use of other types of smoothing (e.g., the ‘Hugershoff’ or spline smoothing [Cook and Kairiukstis, 1990]) or to truncation of the measurement series by removal of the juvenile period (first 15–20 years of data) and downsampling of age cohorts (Figures S1–S3). Next, we divided each one of the original 332 ring width measurement series by the RC value for the appropriate ring age to create standardized series. These departures from the RC are interpreted as departures related to climate variability or some other induced forcing (e.g., insect herbivory). Finally, the 332 standardized series were realigned by calendar year and averaged using a bi-weight robust mean to create the jack pine tree growth index (TGI). TGI error was estimated by bootstrapping the standardized series and collecting the two-tailed 95% confidence interval from the distribution of the bootstrapped means. Robustness of the final jack pine chronology was assessed using a 30 year ‘moving window’ approach of the interseries correlation, and of the expressed population signal (EPS) [Wigley et al., 1984]. The EPS is a measure of the degree to which the mean chronology represents the hypothetical perfect, noise-free, chronology. The EPS ranges from zero to one. A value of 0.85 has been tentatively suggested as desirable [Wigley et al., 1984]. Program ARSTAN (version 40c) was used for processing of tree ring measurement series and for computation of statistics [Cook and Krusic, 2006].
4.2. Modeling of Forest Productivity
 The bioclimatic model StandLEAP version 2.1 [Raulier et al., 2000; Girardin et al., 2008] was used to simulate past forest productivity. StandLEAP is based on the 3PG model [Landsberg and Waring, 1997], and is a generalized stand model applicable to even-aged, relatively homogeneous forests. It is parameterized for individual species. Application of StandLEAP to any particular stand does not involve the use of error reduction techniques. We conducted monthly simulations of forest productivity (described below) for each of the ten temporary sample plots of the DMPF Lands Inventory (Table S1). Monthly simulation outputs were summed to seasonal and annual values, and plots were averaged to a regional level. Sampling error was estimated by bootstrapping the simulations and collecting the two-tailed 95% confidence interval from the distribution of the bootstrapped means.
 In StandLEAP, absorbed photosynthetically active radiation (APAR, mol m−2 month−1) is related to gross primary productivity (GPP, gC m−2 month−1) using a radiation use efficiency coefficient (RUE; gC/mol−1 APAR):
represents a species-specific mean value of RUE. The value of RUE differs among locations and through time because of the effects of environmental constraints on the capacity of trees to use APAR to fix carbon. Each constraint takes on the form of a species-specific multiplier (f1…fn) with a value usually close to unity under average conditions, but which can decrease toward zero to represent increasing limitations (e.g., soil water deficit), or increase above 1.0 as conditions improve toward optimum (e.g., temperature). Constraints related to mean maximum and minimum daily soil and air temperatures, vapor pressure deficit (VPD), monthly radiation, and leaf area index are expressed using a quadratic function:
where parameters βlx and βqx represent the linear and quadratic effects of the variable x on RUE and is the mean value of the variable over the period of calibration. The multipliers (f1…fn) account for nonlinearity in time and space that cannot be accounted for by a constant value of RUE.
 Parameter values of equation (3) for the fx multipliers are derived from prior finer-scale simulation results of canopy-level GPP and transpiration carried out using FineLEAP, a species-specific multilayer hourly canopy gas exchange model [Raulier et al., 2000; Bernier et al., 2001, 2002]. In FineLEAP, the representation of photosynthesis is based on the equations of Farquhar et al.  parameterized from leaf-level instantaneous gas exchange measurements, including the sensitivity of shoot photosynthesis to PAR, temperature and VPD, and the characterization of the shoot physiological and light-capturing properties with shoot age and surrounding average diffuse and direct light environment. Transpiration was computed using the energy balance approach of Leuning et al. . Sixty leaf angular classes were considered (five for the zenith and 12 for the azimuth).
 The FineLEAP model simulates canopies aspatially as layers of foliage of equal properties by using the frequency distribution of the leaf area by classes of shoot age. This aspatial approach rests on the strong relationship between leaf area per unit mass, and both the photosynthetic properties of the foliage and the average light climate impinging upon it [Bernier et al., 2001]. Ecophysiological and canopy structure data for jack pine were drawn mostly from the 1994 to 1996 BOREAS [Sellers et al., 1997] data sets for northern and southern study areas in old jack pine stands (98°37′19″W, 55°55′41″N and 104°41′20″W, 53°54′58″, respectively). These data are archived at the ORNL-DAAC [Newcomer et al., 2000]. FineLEAP simulations were repeated for each climate sequence and for a range of leaf area indices (2 to 8 m2/m2). Hourly values of transpiration, of GPP, and of environmental variables derived from or used in FineLEAP simulations were then rolled up into a monthly data set. This new synthetic data set was used to fit simultaneously equations (1) and (2), in which modifier variables were expressed as in equation (3). The fit was performed in an iterative procedure with the gradual inclusion of modifier variables in a declining order of significance. Only variables that reduced the residual mean square error by more than 5% were retained [Raulier et al., 2000]. The atmospheric CO2 concentration was assumed to be constant at 350 ppmv.
 Other basic climate influences on productivity are encapsulated in StandLEAP within the following functions. The multipliers used to represent the effect of soil water content (f) is as in the work of Landsberg and Waring , and that of frost (fF) is as in the work of Aber et al. ; both are limited to a maximum of 1.0. Bud burst and growth resumption in spring takes place after the accumulation of a certain heat sum above a specific base temperature [Hänninen, 1990]. Monthly APAR is adjusted throughout the growing season for changes in leaf area due to phenological development, as in the PnET model [Aber and Federer, 1992].
 Computation of NPP and respiration fluxes by the StandLEAP model is done as follows. NPP (gC m−2 month−1) is computed monthly after partitioning respiration into growth (Rg, a fixed proportion of GPP) and maintenance (Rm) quantities and subtracting these from GPP:
where M is the living biomass of each plant component and rm10 is their respective respiration rate per gN at 10°C and Q10rm is the temperature sensitivity of Rm, defined as the relative increase in respiration for a 10°C increase in temperature. This function is derived from the strong correlation between tissue nitrogen concentrations and plant maintenance respiration [Ryan, 1991]. Rm is calculated separately for stem sapwood, root sapwood, fine roots, and foliage. Similarly, net ecosystem productivity (NEP) is obtained from
where heterotrophic respiration (Rh) (gC m−2 month−1) is computed as
where T represents monthly mean temperature. Values of parameters y0, a and b were obtained from a least squares adjustment to monthly synthetic Rh data obtained by summing up simulations of half-hourly Rh computed as in the work of Lloyd and Taylor  and using the 10 year temperature records of the old jack pine stand obtained from the Fluxnet-Canada/Canadian Carbon Program Data Information System.
 The strength of this modeling approach is supported by the good performance of StandLEAP in a comparison of its simulation results with measurements by eddy-flux towers of GPP (data from Fluxnet-Canada [Margolis et al., 2006]), ecosystem respiration (Re) and NEP from 2000 to 2006 in a 95 year old stand in Saskatchewan, Canada (Figure 3). The model captured reasonably well the month-to-month variability in these variables (GPP-R2 = 0.92; Re-R2 = 0.92; NEP-R2 = 0.63; n = 84 months). The capacity of FineLEAP to simulate canopy-level gas exchanges has also been verified by comparing hourly [Bernier et al., 2001] and daily [Raulier et al., 2002] measurements of plot-level transpiration to simulated values for two different stands of sugar maple (Acer saccharum Marsh.).
4.3. Statistical Analyses
 Tree ring width measurements in boreal forests have an autocorrelation structure that can be expressed as an auto-regressive (AR) process of order p:
where It are the tree ring width measurements for year t, et are serially random inputs, and ϕi are the p autoregressive (AR) coefficients that produce the characteristic persistence seen in the tree rings [Monserud, 1986; Biondi and Swetnam, 1987; Cook and Kairiukstis, 1990; Berninger et al., 2004]. A strong AR process will cause the tree ring width measurements to be excessively smoothed, and vice versa. The AR process in tree rings reflects, among other things, how stored photosynthates are made available for growth in the following years. While this process can be mathematically described [Misson, 2004], its process basis remains difficult to express quantitatively so that one could predict empirically how much carbon produced a given month or year should be allocated to the growth in the following years [i.e., Kagawa et al., 2006]. The autocorrelation function in TGI can indeed go beyond an AR1 process [Monserud, 1986].
 In contrast, there is no such year-to-year carryover in yearly totals of simulated NPP by StandLEAP. In order to correct for this deficit and make the comparison of NPP and TGI possible, the two series must be brought to a similar AR process. In this study, we estimated the AR process of the jack pine TGI and applied the AR equation parameters [Cook and Kairiukstis, 1990] to the standardized yearly totals of simulated NPP, which were obtained by dividing annual NPP values by the long-term mean of NPP over 1912–2000. We hereafter refer to this new NPP series as the NPPAR series. The application of this transformation to NPP does not violate the assumption of independence between the two data sets, but allows them to have a similar time-dependent (or ‘smoothing’) behavior. Another approach would have been to remove the AR process in TGI through auto-regressive modeling (i.e., prewhitening). This, however, would have resulted in a significant loss of low-frequency changes in the TGI (for analyses of ‘prewhitened’ data, refer to Girardin and Tardif  and Girardin et al. ). The order of the autocorrelation process was determined using the Akaike Information Criterion (AIC) implemented in the program ARSTAN (version 40c) [Cook and Krusic, 2006].
 Long-term linear changes in TGI, climatic, and simulated data were detected using least squares linear regressions [von Storch and Zwiers, 1999]. Goodness of fit was described by the coefficient of determination (R2). Significance of the slope was tested against the null hypothesis that the trend is different from zero, using a variant of the t test with an estimate of the effective sample size that takes into account the presence of serial persistence (red noise bias) in data [von Storch and Zwiers, 1999, sections 8.2.3 and 6.6.8]. For those time series having an autocorrelation structure expressed as an AR process of order greater than one (AR > 1), the significance of trends was evaluated using Monte Carlo simulations. In this analysis, 1000 random time series with similar autocorrelation structure as the original data were tested for the presence of trends and 99%, 95% and 90% percentiles of the coefficient of determination were collected and used as a criterion for testing against the null hypothesis. When necessary, data were ranked prior to analysis to satisfy the normality distribution requirement in model residuals [von Storch and Zwiers, 1999]. The period of analysis for this study was 1912–2000 (e.g., limited to the earliest year of meteorological data and the latest year covered by tree ring data).
 As mentioned earlier, the StandLEAP simulator does not incorporate CO2 enhancement effects. In the event that a CO2 fertilization effect has occurred during the twentieth century, climatically driven simulations of NPP and TGI should show increasing divergence with increasing or decreasing atmospheric CO2 [Graumlich, 1991; Jacoby and D'Arrigo, 1989, 1997; Rathgeber et al., 2000]. To test this fertilization hypothesis, residuals of the difference between TGI and NPPAR were related to atmospheric CO2 data using correlation analysis and piecewise regression [Friedman, 1991]. In the regression analysis, the relationship between residuals and [CO2] was described by a series of linear segments of differing slopes, each of which was fitted using a basis function. Breaks between segments were defined by a knot in a model that initially over-fitted the data, and was then simplified using a backward/forward stepwise cross-validation procedure. This approach was preferred over a linear trend analysis because CO2 increases nonlinearly through time. The null hypothesis Ho of ‘no fertilization effect’ was to be rejected in the presence of a basis function with a positive slope post-1970 (i.e., when the rate of CO2 increase was most important). The R package ‘earth’ was used [R Development Core Team, 2007]. The Generalized Cross Validation (GCV) penalty per knot was set to four and the minimum amount of observations between knots was set to 25 to ensure numerical stability. Other parameters were kept as in the ‘earth’ default settings.
4.4. Sensitivity Analysis to Atmospheric CO2
 Empirical evidence indicating CO2 fertilization effects has often resulted from laboratory or controlled experiments following a doubling of preindustrial CO2 concentrations from approximately 300 ppmv to 700 ppmv [e.g., Norby et al., 2005]. The CO2 forcing acting on natural environments is much lower (from 300 ppmv in 1910 to 370 ppmv in 2000) and, hence, the response of forests cannot be expected to be as large as the one seen in experimental conditions [Joos et al., 2002]. The fertilization effect in natural environments could simply be under the limit of statistical detection [D'Arrigo and Jacoby, 1993]. We investigated this potential source of error through a sensitivity analysis in which an ‘expected’ effect of CO2 fertilization was added to simulations of NPPAR. The ‘expected’ effect of CO2 fertilization on forest growth is often quantified using a logarithmic response function that takes the form of
where NPPE and NPP0 refer to net primary productivity (equation (4)) in enriched (CO2E) and control (CO2O) CO2 environments, respectively [e.g., Friedlingstein et al., 1995; Rathgeber et al., 2000; Peng et al., 2009]. In this equation, β is an empirical parameter that ranges between 0.0 and 0.7, and is adjusted so that NPP under a doubled atmospheric CO2 concentration (from 350 to 700 ppmv) increases by approximately 23% (equation (9)) (based on experimental evidence from Norby et al. ). We used a value of 0.34 for β, as in the work of Peng et al. . Under the hypothesis that a fertilization effect in TGI has not occurred, residuals of the difference between TGI and ‘CO2-enriched NPPAR’ simulations should show a significant bias toward decreasing values with increasing atmospheric CO2 (i.e., negative slope). On the other hand, a slope that is not significantly different from zero would imply that the fertilization effect in TGI is possible but too small to be statistically detected by our modeling procedure. In such an eventuality, the CO2 fertilization effect could simply be masked by the high interannual variability in the TGI time series.
5.1. Temporal Changes in Tree Growth Index
 Most sampled jack pine trees originated from postfire recruitment episodes, as for example in the 1890s (∼60% of trees) and 1750s to 1770s (∼20%) (Figure 4b). The only information available on growth conditions prior to the 1890s was from dead trees. That being said, a close relationship between average ring width of dead and living trees and tree age (Figure 5) (R2 = 0.49; n = 332) suggested the existence of relatively homogeneous behavior in the tree population under study with regard to growth rates. Also, the age-related growth trend of trees originating from prior to 1880 was reasonably similar in level and slope to a curve obtained from trees originating after 1880 (Figure 2b). We also found little difference in the age-related growth trends under different classes of jack pine dominance (Figure S4). Therefore, one can assume that the trees belonged to the same population, a prerequisite for application of the regional curve standardization [Esper et al., 2003].
 First-order autocorrelation (AR1) of the jack pine record was 0.83 over 1717–2000, reflecting high biological memory (i.e., persistence of previous year growth conditions). The best AR model fit was obtained using an AR(5) process. However, an AR(2) model (described in Table 1) was considered the best for a subperiod covering 1880–2000.
Table 1. Summary of the Estimated Autoregressive Modela
Here p is autoregressive (AR) coefficients (see equation (8) in text). Period of analysis is 1880–2000.
Akaike information criterion for each AR order
Selected autoregression order
R2 due to pooled autoregression
 Expressed population signal (EPS) values meet signal strength acceptance for the full period covered by tree ring data (Figure 4d). Replication of ring width measurements may thus be considered sufficiently high to approximate a signal representative of a theoretical population of an infinite number of trees, i.e., an entire forest stand [Wigley et al., 1984]. However, the low correlation obtained during the 30 year ‘moving window’ analysis of the interseries correlation (Rbar < 0.32 over much of the nineteenth and twentieth centuries; Figure 4d) demonstrates the high variability among measurement series, and suggests the action of diverse biological and nonbiological forcing agents on the growth of the jack pine trees. This was further highlighted by a wide bootstrap confidence interval around the mean throughout much of the nineteenth century, when sampling replication was low (Figure 4a). As opposed to any previous time periods, the period submitted to our modeling experiment (i.e., 1912–2000) appeared minimally biased, as can be assessed from high EPS, relatively stable Rbar, and a narrow confidence interval around the mean. The final TGI chronology suggested marked variations in the growth of jack pine trees, with low growth from the 1910s to 1940 and around 1960, and highs in the 1950s and post 1970 (Figure 4a). Least squares linear regression applied to the TGI indicated a positive trend over 1912–2000 (Table 2). The trend explained 34.4% of the variance in data (Table 2).
Table 2. Summary of Linear Trend Models on Tree Growth Index, Gross Primary Productivity, Net Primary Productivity (and Net Primary Productivity After Application of the AR Model), Respiration (Growth Rg, Maintenance Rm, and Total Rt), Growing Degree Days Above 5°C, Vapor Pressure Deficit, and Soil Water Content at a Depth of 1 m Over the Period 1912–2000a
Here ***, significant at P ≤ 0.01; **, significant at P ≤ 0.05; *, significant at P ≤ 0.10; N.S., not significant; N.A., not available. TGI, tree growth index; GPP, gross primary productivity; NPP, net primary productivity; GDD, growing degree days; VPD, vapor pressure deficit; SWC, soil water content.
Significance of the linear trend was examined using least squares linear regressions [von Storch and Zwiers, 1999]. Goodness of fit is described by the coefficient of determination (R2). Significance was tested against the null hypothesis that the trend is different from zero, using a variant of the t test with an estimate of the effective sample size (effective n) that takes into account the presence of serial persistence in data.
Significance of trends was evaluated using Monte Carlo simulations (see section 4).
 Simulated annual GPP over 1912–2000 averaged 857 gC m−2 yr−1, and simulated respiration losses were about 52% of this amount (Figure 6). Annual simulated NPP averaged 460 gC m−2 yr−1, with a minimum of 212 gC m−2 yr−1 in 1961 and a maximum of 556 gC m−2 yr−1 in 1977 (Figure 7). About 60% of annual NPP was produced during the June to August period (average equals 270 gC m−2 yr−1). Summer NPP also showed a higher departure from the mean (standard deviation of 45 gC m−2 yr−1) than spring or fall (21 and 15 gC m−2 yr−1, respectively). Indeed, except perhaps in the 1970–1980s, most of the highs and lows in annual NPP (Figure 7) were found within the productivity during summer months. These variations were driven in the model by the climate modifiers affecting RUE (equation (2)) and, hence, GPP. The temperature constraints on respiration (equation (4)) were likely not sufficiently important to induce in NPP the large departures from the mean seen in Figure 7.
 The simulation suggested an increase in forest productivity over the century, with an increase of annual GPP estimated at 0.780 gC m−2 yr−1 and a linear trend explaining 9.7% of the variance in data (Table 2 and Figure 6). Nevertheless, carbon losses due to respiration have also significantly increased, but such losses were more than compensated by increased GPP, resulting in a significant rise in NPP of 0.502 gC m−2 yr−1. This rise in NPP explained 7.8% of the variance in data (Table 2 and Figure 7). Most of the increase was simulated to have taken place in the spring (by 0.233 gC m−2 yr−1).
 Climate factors encapsulated in the bioclimatic model were also tested for the presence of linear trends. Among factors that could explain the simulated upward trend in forest productivity were increases in the length of the growing seasons, as inferred from the annual sums of growing degree days above 5°C, and increased availability of soil moisture in the first meter of soil (Table 2 and Figure 8). Both variables had a significant positive trend over 1912–2000 (P < 0.05), explaining 6.0% and 6.8% of the variance in data, respectively.
5.3. Comparing Empirical Data With Simulations
 The AR process dominating the jack pine TGI (Table 1) was applied to the yearly totals of simulated NPP so that both series could share similar time-dependent behavior (see section 4.3). The two records, illustrated in Figure 9a, shared 47.2% of common variance over their common period of analysis, i.e., 1912–2000 (P < 0.01 according to Monte Carlo simulations). The amount of shared variance equaled 28.5% (P < 0.05) when both series were detrended prior to analysis. Most often, the simulation of NPPAR propagated well within the uncertainty band of the TGI data (Figure 9). Nevertheless, the simulation did not do well in 1921–1925 (overestimation), 1936–1937 (underestimation), 1975–1976 (underestimation), and 1992 (overestimation). These years were not found to be systematically related to a climatic factor (as investigated with Student-t tests on monthly climatic data) or to a biological agent acting on growth, such as outbreaks of the jack pine budworm (Choristoneura pinus Freeman) [McCullough, 2000; Volney, 1988] recorded in the DMPF from 1938 to 1942 and in 1985 [Canadian Forestry Service, 1986]. These years might reflect the influence of climatic extremes not taken into account by the simulator or of magnitudes outside the domain of calibration of the modifiers affecting RUE (see section 4.2). If we eliminate the ‘disconnected’ years 1936 and 1976 (with Studentized residuals >3.0) from the data comparison, the amount of shared variance between data rises to 59.0% (39.5% after detrending).
 A positive trend in productivity over the past century is clearly distinguishable in the NPPAR simulations and in TGI (Table 2 and Figure 9), indicating long-term changes in growing conditions. Both TGI and NPPAR shared similar regression slopes (i.e., no statistical difference) and amount of variance explained by the trend line (Table 2). Also clearly distinguishable in the jack pine TGI series were growth declines in the 1920s to 1930s and early 1960s (Figure 9a). Coincident with these episodes are notable drought events that are reflected in the index of available soil water at a depth of 1 m (Figure 8b). The influence of moisture availability on jack pine growth was readily apparent when correlating the TGI data over 1912–2000 with the smoothed version of available soil water (Figure 8b): the two records shared 42.7% of variance.
5.4. Testing for a CO2 Fertilization Effect
 Climatically driven simulations of NPPAR and TGI did not show evidence of increasing divergence with increasing atmospheric [CO2] as residuals of the difference between TGI and NPPAR (Figure 10a) were uncorrelated to long-term changes in the atmospheric [CO2] (R2 = 0.017, P > 0.30). In addition, the piecewise regression model did not detect a linear segment or a long-term trend in residuals capturing a missing effect of increasing atmospheric [CO2] on NPP (Figure 10a). When the effect of CO2 fertilization was added to NPP through the use of equation (9) and β = 0.34, the residuals of the difference between TGI and CO2-enriched NPPAR were negatively correlated to long-term changes in the atmospheric CO2 (R2 = 0.067, P < 0.05), and presented a significant bias according to the piecewise regression analysis (Figure 10b). Our results therefore suggest that long-term changes in the TGI were adequately reproduced by the climatically driven simulation of NPPAR without inclusion of a CO2 factor.
 We also conducted a sensitivity analysis in order to evaluate the statistical detection limit of our approach. Our analysis involved redoing the simulation of NPPAR with values of β varying between 0 and 0.7. Results of this analysis revealed that values of β greater than 0.20 generated an overestimation of the slope of the linear trend between NPPAR and TGI data (period 1912–2000) (Figure 11a). Residuals between NPPAR and TGI also increased with values of β greater than 0.20 (Figure 11b) and were increasingly correlated to CO2 (Figure 11c). A cutoff value of β = 0.20 corresponded to a growth enhancement of 14% with a doubling of CO2. We also found a slight improvement of model fit between TGI and NPPAR with the addition of a weak CO2 factor between 0.10 and 0.15, but this effect was nonsignificant (see minimum value in Figure 11b and Figures S5 and S6).
 It is an increasingly common practice for modelers to include CO2 fertilization effects when assessing the current and future impacts of global climate change (see section 1). This practice, which is done using empirical evidence from laboratory or controlled conditions, is often applied to large territories (e.g., continental scale) and over a range of habitats and species. Within the detection limit of the data-model approach used in this work, we find nothing to support the idea of a FACE-level CO2 growth enhancement (23% for a doubling of CO2) in jack pine trees of the DMPF during the twentieth century (β = 0.34). In addition, comparison between recent growth and growth prior to the 1890s in our jack pine TGI series of the DMPF fails to show the multicentury increase in growth that should be expected as a result of the CO2 fertilization effect [Jacoby and D'Arrigo, 1989, 1997; Huang et al., 2007]. As seen in Figure 2, the age-related growth trend of trees originating after 1880 is reasonably similar in level and slope to a curve obtained from trees originating prior to 1880 in spite of significant increases in atmospheric CO2 over the past century [Keeling et al., 1982; Etheridge et al., 1996]. Because of the detection limit of our approach, evaluated at 14% growth enhancement for a doubling of CO2 (maximum β = 0.20), our results do not invalidate suggestions for a lower CO2 fertilization effect, such as the value of 15% proposed by Hickler et al. . Our results do suggest the need to use caution when including CO2 fertilization effects in models.
 Empirical observations provide support to the correctness of our modeling results with respect to the factors driving the simulated twentieth century increase in NPP. Net ecosystem productivity of coniferous forests is increased by early spring warming [Arain et al., 2002; Grant et al., 2009] but reduced by hot summers and soil moisture depletion [Griffis et al., 2003; Dunn et al., 2007]. The pattern of year-to-year changes in tree growth reflects the underlying influences of variability in the climate and occurrence rate of weather episodes favorable or not to photosynthesis (equation (1)) and respiration (equation (4)). Our observed trends toward greater length of the growing season and greater available soil water are consistent with these short-term observations. Notably, springtime increases in simulated NPP suggest that growth conditions in the second half of the century have benefited from increasing growing season degree days, particularly through an earlier onset of spring (Figure 7). Extension of the growing season by up to 2 weeks in mid and high northern latitudes since the early 1970s is apparent in remotely sensed vegetation indices (NDVI) [Myneni et al., 1997; Zhou et al., 2001] and in seasonal trends of atmospheric CO2 drawdown [Keeling et al., 1996]. The positive influence of global warming on plant growth and establishment in high-latitude, cold-limited systems has widely been reported [e.g., Jacoby and D'Arrigo, 1989, 1997; Gamache and Payette, 2004; Briffa et al., 2008].
 Also clearly distinguishable in the jack pine TGI series of the DMPF were growth declines in the 1920s to 1930s and early 1960s coherent with intense or frequent drought years. These well-documented droughts [e.g., Girardin and Wotton, 2009] may have been relatively mild when examined in the context of past centuries [e.g., Cook et al., 2004], but the ‘Dust Bowl’ drought nevertheless severely affected almost two-thirds of the United States and parts of Mexico and Canada during the 1930s [Schubert et al., 2004]. It is apparent from our NPP simulations and empirical data that carbon uptake by the jack pine population of the DMPF was severely limited for much of the early twentieth century as a consequence of this extreme climatic anomaly. The year 1961, which was referred to by Girardin and Wotton  as the driest summer over the period 1901–2002 for Canada as a whole, also stands out as the year with the lowest simulated NPP (and measured TGI) for the entire simulated period.
 So why has CO2 fertilization of jack pine trees in the DMPF failed to be detected? It is apparent that constraints other than atmospheric CO2 concentration have been and are still limiting the growth of this forest. Temperature effects on growth are strongly mediated by nutrient availability and capture [Jarvis and Linder, 2000]. Although the drop in forest productivity with increasing latitude highlights the primary controlling role of climate across the spatial domain (e.g., temperature dependence of the CO2-enhancement effect as discussed in section 1), secondary factors, such as soil fertility and stand age, that operate on a longer time lag may be attenuating the immediate impact of climate warming and CO2 fertilization in these forests [e.g., Körner et al., 2005]. One constraint would be the insufficient availability of nitrogen in soils to meet the increasing demand under elevated CO2 [Oren et al., 2001; Johnson et al., 2004; Norby et al., 2008, 2009], particularly on sites with low to moderate soil nitrogen availability [Reich et al., 2006]. In general, coniferous forests are believed to have lower availability of nitrogen due to slower nutrient turnover than deciduous forests [Jerabkova et al., 2005; Ste-Marie et al., 2007].
 An additional constraint on the detection of the CO2 fertilization effect is the expected size of this effect in comparison to the detection limit. The effect may not yet be detectable in natural forest environments, in part because it may be much smaller than what is found in controlled experiments, and in part because the CO2 increases during the studied interval were relatively modest, again in comparison to controlled experiments. These findings concur with those of Joos et al. . The results of the sensitivity analysis revealed that our analysis cannot detect a fertilization effect of up to β = 0.20, which corresponds to a growth enhancement of 14% with a doubling of CO2. However, this value of β as a detection cutoff results in part from our choice of pretreatment method for the TGI measurement series that retained the most amount of trend possible (Figure S1). This choice enhances the probability of generating false positive or Type 1 errors at lower values of β (i.e., accept the fertilization hypothesis when in fact there is none). The use of other detrending methods would have resulted in a detection cutoff value of β lower than 0.20 (Figure S6).
 Other uncertainties may also weaken our inference. In particular, the method relies on the use of a data set with a uniform distribution of tree establishment and mortality dates over time in order to allow common climate/CO2 signals to be canceled and averaged out when the series are aligned by cambial age (Figure 3a). In our experimentation this condition is not necessarily met as a large proportion of trees germinated within a short period in the 1890s. Nonetheless, results of a sensitivity analysis (Figure S2) that involved a downsampling of the number of trees established during that interval suggest that our inference is robust against this source of error. Finally, the instrumental weather data used as input for the simulator were subject to homogenization and this could induce some uncertainty in the measurement trend, which might also be carried over into the modeled estimates. In our estimation, however, none of these sources of uncertainty weaken the basic inference from this study that, in our boreal forest environment, we could not detect the level of CO2 fertilization effect that has been reported in controlled FACE experiments [Norby et al., 2005] and that is often included in simulations of future forest productivity [e.g., Chen et al., 2000; Peng et al., 2009].
7. Concluding Remarks
 This study suggests that empirical evidence from controlled experiments on CO2 fertilization cannot be directly extrapolated to large forested areas without a good understanding of local constraints on forest growth. Inclusion of such additional constraints on growth in the models remains a daunting task when they are to be applied to large heterogeneous landscapes such as the boreal forest. Adding complexity to models without empirical supporting evidence as to the applicability of the additional relationships may in the end become counterproductive and generate unrealistic projections of future forest states. In spite of all their shortcomings, field-based studies such as this one remain one of the best guarantees that we indeed understand forest growth and can adequately predict its future.
 We currently do not know if our inference with respect to the absence of long-term CO2 fertilization applies to all of Canada's closed-canopy boreal region but widespread replication of this type of study is currently challenging. The technique employed in the processing of our jack pine tree ring data (regional curve standardization) has high capabilities for preserving long-term growth changes [e.g., D'Arrigo et al., 2006]. Nevertheless, the technique can only be applied in specific circumstances [Esper et al., 2003] and requires high within-site replication (D'Arrigo et al., 2006). Many tree ring data sets across closed-canopy forests of boreal Canada have been developed in the past [Girardin et al., 2006; St. George et al., 2009]. However, few of these data have been collected from productive forests following a dense sampling scheme that includes sampling of multiple age cohorts. Expansion of this work is further limited by the absence of plot-level data necessary to run process-based models on stands in which growth increment data were collected. While the applicability of species-specific process-based models may be fairly narrow in scale owing to the complexity of input data, they are of valuable help in answering specific questions that are relevant to modelers of carbon exchanges of broad spatial scales. Estimates of stand attributes, such as biomass and soil types, through remote sensing could help address some of these issues in the future. There is, however, clearly a need for additional tree ring sampling campaigns coupled with complete plot-level information if we are to successfully document and attribute long-term growth trends in the circumboreal forests.
 Funds for this research were provided by the Canadian Forest Service operating budgets, the Canada Research Chairs Program, the Natural Sciences and Engineering Research Council of Canada, and the University of Winnipeg. Special thanks are extended to Allan Barr and to Fluxnet-Canada/Canadian Carbon Program and associated funding agencies for the generation and provision of eddy-flux tower measurements. We thank Mike Lavigne, Dennis Baldocchi, the Associate Editor, Mark J. Ducey, Greg King, Flurin Babst, and an anonymous reviewer for providing valuable comments on an earlier draft of this manuscript.