The effect of carbon fertilization on naturally regenerated and planted US forests
MaterialsInformation on wood volume and the physical environment of the plots were obtained from the US Forest Service Forest Inventory and Analysis (USFS-FIA)22. The FIA database categorizes each plot into one of 33 forest groups, but 23 groups do not have sufficient data in the control period (before 1990) to enable robust matching and so were dropped from this study. As a result, several western forest groups (e.g., Douglas-fir) were not included in our study. The following ten forest groups [(1) Loblolly/Shortleaf Pine, (2) Slash/Shortleaf Pine, (3) White/Red/Jack Pine, (4) Spruce/Fir, (5) Elm/Ash/Cottonwood, (6) Maple/Beech/Birch, (7) Oak/Hickory, (8) Oak/Gum/Cypress, (9) Aspen/Birch, and (10) Oak/Pine] all had more than 5000 observations and large numbers of observations both from before 1990 and from 2000 on. Data for the 48 conterminous states from evaluation years between 1968 and 2018 were included in the study. We limited our analysis to plots with trees from 1 to 100 years of age, resulting in trees that had been planted somewhere between 1869 and 2018—a period during which atmospheric CO2 increased from roughly 287 to more than 406 ppm32,33,34. The geographic distribution of the ten forest groups presented in Fig. 2 shows in orange all counties in which the USFS recorded in at least one year between 1968 and 2018 the presence of a plot of the respective forest group that met the age requirements for inclusion in this study. Precipitation and temperature data were obtained from the PRISM Climate Group41.MethodsResults in Tables 1 and 2 are based on estimated exponential tree-volume functions of the generalized form shown in Eq. 1. The left-hand side is the natural log of the volume per hectare in the central stem of trees on each plot in cubic meters. Volume is assumed to be a function of age, the logged cumulative lifetime concentration of CO2, and other variables, including plot-specific variables that vary across plots but not time (Xi), weather variables that vary across plots and time (Wit), and time-specific fixed effects that vary across time but not plots (Et).$${{{{mathrm{Ln}}}}},{left(frac{{{{{{rm{Volume}}}}}}}{{{{{{rm{Hectare}}}}}}}right)}_{it}= ,alpha+{beta }_{0}frac{1}{{{{{{{rm{Age}}}}}}}_{{{{{{rm{it}}}}}}}}+{beta }_{1},{{{{mathrm{Ln}}}}}({{{{{rm{CumCO}}}}}}2{{{{{{rm{Life}}}}}}}_{{{{{{rm{t}}}}}}})\ +{beta }_{2}{{{{{{rm{X}}}}}}}_{{{{{{rm{i}}}}}}}+{beta }_{3}{{{{{{rm{W}}}}}}}_{{{{{{rm{it}}}}}}}+{beta }_{4}{{{{{{rm{E}}}}}}}_{{{{{{rm{t}}}}}}}+{varepsilon }_{it}$$
(1)
The nonparametric smearing estimate method was used to transform logged-volume results into a volume in cubic meters per hectare42. The climate variables, obtained from the PRISM Climate Group41 and described in Supplementary Table 1, enter as cubic polynomials of the lifetime seasonal temperature and precipitation averages that a plot of a given age at a given time experienced.The variable for atmospheric carbon was constructed as the logarithmic transformation of the sum of yearly atmospheric CO2 exposures over the lifetime of the stand. Other site-specific covariates were obtained from the FIA data (Supplementary Table 2), such as the availability of water, the quality of the soil, the photoperiod of the plot, whether disturbances had impacted the land, and whether the land was publicly or privately owned43,44.The time-specific fixed effects (Et) in the model control for episodic factors like nitrogen deposition and invasive species, which are correlated with time but cannot be observed over space for the whole time period. These time-dummy variables account for underlying, unobservable systematic differences between the 21st-century period when atmospheric CO2 was higher and the pre-period when levels were much lower. Controlling for these factors aids the identification of the impact of elevated CO2, which varies annually.A potential concern is that wood volume changes over time could be related to an increased number of trees per hectare rather than increased wood volume of the trees. To assess whether controls for the stocking condition were needed, we examined data on the number of trees per acre of each forest type. First, we looked at a group of southern states (Supplementary Table 3) and found double-digit percentage changes in tree stocking between 1974 and 2017 for seven of the nine forest groups. However, the changes were mixed, with four having increased tree density and five decreasing tree density. The FIA data do not record the Aspen/Birch forest group as present in these southern states in these evaluations.Examination of a group of northern states involved a comparison of the average stocking conditions around 1985 with those in 2017. The changes in tree density for these forest types (Supplementary Table 4) were also split with four showing increased stocking and five having less dense stocking. The change for Loblolly/Shortleaf pine was relatively large, with stocking density increasing by 27.2%. Slash/Longleaf was not recorded as present in these states in these evaluations.Next, we analyzed changes, over the period from around 1985 to 2017, in all states east of the 100th meridian, as those states comprised the bulk of the data in our study (Supplementary Table 5). Results for seven of the ten forest groups showed a less dense composition. Loblolly/Shortleaf pine again was shown to have become more densely stocked, with an increase of 13.2%.The last check included all of the 48 conterminous states and compared changes in stocking conditions from years around 1985 to 2017 (Supplementary Table 6). Seven of the ten forest groups showed decreased stocking density over time. Not surprisingly (because most Loblolly/Shortleaf is located in the Eastern US), the change in Loblolly/Shortleaf pine density is the same for this check as was shown in the results in Supplementary Table 5. Based on the results from all these comparisons and given that stocking density has changed over time, we controlled for it both in the matching and in the multivariate-regression analysis.Genetic matching (GM), the primary approach used for this analysis, combines propensity score matching and Mahalanobis matching techniques45. The choice of GM was made after initially considering other approaches, such as nearest-neighbor propensity score matching with replacement and a non-matching, pooled regression approach. These three options were tested on the samples for Loblolly/Shortleaf pine and Oak/Hickory, and the regression results are presented in Supplementary Data 3-4.The results across these different approaches were quite similar, suggesting that the results are not strongly driven by methodological choice. We focused on matching rather than a pooled regression approach to help reduce bias and provide estimates closer to those that would be obtained in a randomized controlled trial. When choosing the specific matching approach, we considered that standard matching methods are equal percent bias reducing (EPBR) only in the unlikely case that the covariate distributions are all roughly normal46 and that EPBR may not be desirable, as in the case where one of two covariates has a nonlinear relationship with the dependent variable16. We also noted that GM is a matching algorithm that at each step minimizes the largest bias distance of the covariates24 and that GM has been shown to be a more efficient estimator than other methods like the inverse probability of treatment weighting and one-to-one greedy nearest-neighbor matching24,47,48,49. Additionally, when the distributions of covariates are non-ellipsoidal, this nonparametric method has been shown to minimize bias that may not be captured by simple minimization of mean differences50. Lastly, as sample size increases, this approach will converge to a solution that reduces imbalance more than techniques like full or greedy matching48,51,52. Given the support that this choice has in the literature, we decided to employ GM to create all the matched data used in this study using R software53.Artificial regeneration of forest stands, noted as planting throughout the text is used as the main proxy for the impact of forest management. The other indicator of management activity is what can be described as interventions, which are a range of human on-site activities that the USFS details22. We define unmanaged land as stands with natural regeneration and where no interventions occurred on the plot.To create Table 1, we first excluded all plots on which there had been either planting activities or some type of human intervention. Then, we created treatment and control groups by forming two time periods separated by an intervening period of ten years to ensure a more than a marginal difference between the groups in terms of lifetime exposure to atmospheric CO2. The control period used forest plot data sampled between 1968 and 1990, and the treatment period used forest plots sampled between 2000 and 2018. Note that even though the earlier period contains more years, there are fewer overall observations.Matches were then made to balance the treatment and control groups based on the following observable covariates: (1) Seasonal Temperature, (2) Seasonal Precipitation, (3) Stocking Condition, (4) Aspect, (5) Age, (6) Physiographic Class, and (7) Site Class. The propensity score was defined as a logit function of the above covariates to generate estimates of the probability of treatment. Calipers with widths less than or equal to 0.2 standard deviations of the propensity score were also employed to remove at least 98% of bias49.Balance statistics for the primary covariates are presented in Supplementary Data 1–2 and show a strong balance for all covariates across all forest groups. Thus for each forest group, our sample of plots includes control plots (pre-1990) and treatment plots (post-2000) that are comparable (balanced) in climate and other biophysical attributes.After trimming our sample using this matching process and obtaining strongly balanced matches, we turned to regression analysis, where we employed Stata software54. To confirm that we had the most appropriate model structure, tests of the climate and atmospheric carbon variables were undertaken using various polynomial forms, and the main variable of interest, atmospheric carbon, was tested both using a linear lifetime cumulative CO2 variable and a logarithmic transformation of that variable. Results (Supplementary Data 5–10) show that the climate variables were not improved with complexity beyond cubic form. Moreover, selection tools, like the Akaike and Bayesian information criterion, favored the cubic choice, and so we utilized the cubic formulation throughout this study. Results for the CO2 variable were similar in both sign and significance for the linear and logged form. We use the logged form as it allows easier interpretation of the effect, suppresses heteroscedasticity, and removes the assumption that each unit increase in CO2 exposure will have a linear (constant) effect on volume.The estimated effect of CO2 exposure for each forest group (Supplementary Data 12–21) was estimated using alternate specifications of the independent variables included in Eq. 1. For each forest type, the Model (1) specification (Eq. 2) is the basis for the results presented in Table 1. The β0 coefficient details the impact on the volume of the main variable of interest, atmospheric carbon.$${{{{mathrm{Ln}}}}}left(frac{volume}{hectare}right)= alpha+{beta }_{0},{{{{mathrm{Ln}}}}}({{{{{{rm{Lifetime}}}}}}{{{{{rm{CO}}}}}}}_{2})+{beta }_{1}frac{1}{{{{{{rm{Age}}}}}}}+{beta }_{2}{{{{{rm{Site}}}}}},{{{{{rm{Class}}}}}}\ +{beta }_{3}{{{{{rm{Seasonal}}}}}},{{{{{rm{Temperature}}}}}}+{beta }_{4}{{{{{rm{Seasonal}}}}}},{{{{{{rm{Temp}}}}}}}^{2}+{beta }_{5}{{{{{rm{Seasonal}}}}}},{{{{{{rm{Temp}}}}}}}^{3}\ +{beta }_{6}{{{{{rm{Seasonal}}}}}},{{{{{rm{Precipitation}}}}}}+{beta }_{7}{{{{{rm{Seasonal}}}}}},{{{{{{rm{Precip}}}}}}}^{2}+{beta }_{8}{{{{{rm{Seasonal}}}}}},{{{{{{rm{Precip}}}}}}}^{3}\ +{beta }_{9}{{{{{rm{Stocking}}}}}}+{beta }_{10}{{{{{rm{Disturbances}}}}}}+{beta }_{11}{{{{{rm{Physiographic}}}}}},{{{{{rm{Class}}}}}}+{beta }_{12}{{{{{rm{Aspect}}}}}}\ +{beta }_{13}{{{{{rm{Slope}}}}}}+{beta }_{14}{{{{{rm{Elevation}}}}}}+{beta }_{15}{{{{{rm{Latitude}}}}}}+{beta }_{16}{{{{{rm{Longitude}}}}}}+{beta }_{17}{{{{{rm{Ownership}}}}}}\ +{beta }_{18}{{{{{rm{Time}}}}}},{{{{{rm{Dummies}}}}}}+{beta }_{19}{{{{{rm{Seasonal}}}}}},{{{{{rm{Vapor}}}}}},{{{{{rm{Pressure}}}}}},{{{{{rm{Deficit}}}}}}\ +{beta }_{20}{{{{{rm{Length}}}}}},{{{{{rm{of}}}}}},{{{{{rm{Growing}}}}}},{{{{{rm{Season}}}}}}+{{{{{rm{varepsilon }}}}}}$$
(2)
After estimating Eq. 2 for each forest type individually (Supplementary Data 12–21), all plots were pooled across forest groups, with additional forest-group dummy variables, to estimate a general tree-volume function (Supplementary Data 22).Our main Model (1) results are provided in Supplementary Data 12–22, along with three additional models that assess the robustness of the elevated CO2 effect to different specifications. The simplest specification, Model (4), included only stand age, CO2 exposure, and a time-dummy variable. Model (3) took the Model (4) base and added in an array of site-specific variables, including those for the climate. Model (2) was similar to Model (1) in that it included the impact of vapor pressure deficit and the length of the growing season on the variables included in Model (3), but it differed from Model (1) in that it tested an alternate approach to capturing the impact of underlying, unobservable systematic differences like nitrogen deposition.Using the estimated coefficients from the preferred Model (column 1) specification (Eq. 2), the estimated change in growing-stock volume between two CO2 exposure scenarios was calculated at ages 25, 50, and 75. The first scenario examined CO2 exposure up to 1970 (that is, when calculating growing-stock volume for a 25-year-old stand, the CO2 exposure would have the summation of the yearly values for the years from 1946 to 1970 [310 to 326 ppm CO2]). The second scenario examined CO2 exposure up to 2015 (that is, when calculating growing-stock volume for a 25-year-old stand, the CO2 exposure was the summation of the yearly values for the years from 1991 to 2015 [347 to 401 ppm CO2])32,33,34. In both scenarios, climate variables were maintained at their 1970 exposure levels, covering the same historical years (e.g., for a 25-year-old stand, 1946 to 1970 were the years of interest), while using seasonal, not annual values and calculating average values, not lifetime summations.Forest dynamics in the Western US differ from those in the East (e.g., generally drier conditions; greater incidence of large wildfires) and as most of the observations for this study are of forest groups located in the 33 states that the USFS labels as comprising the Eastern US, robustness tests were conducted to assess whether results would differ were only eastern observations utilized. Three forest groups [(1) Loblolly/Shortleaf pine, (2) Oak/Gum/Cypress, and (3) Slash/Longleaf pine] have no observations in the Western US. A fourth, White/Red/Jack Pine, has a slight presence in a few Western states, but no western observations were selected in the original matching process (Supplementary Data 2). For the other six forest groups, all observations from Western US states were dropped. As can be seen from Fig. 2, this had the biggest impact on Aspen/Birch and Elm/Ash/Cottonwood. With this data removed, the GM matching algorithm was again used. Balance statistics are presented in Supplementary Data 23 and again show a strong balance for all covariates across all forest groups. With matches made, the average treatment effect on the treated was estimated using the Model (1) specification used to create Table 1. Regression results are presented in Supplementary Data 24,25, and a revised version of Table 1 for just the observations from the Eastern US is presented as Supplementary Table 7.As an additional robustness check on the results in Table 1, we tested an alternative functional form of the volume function. This alternative volume function is shown in Eq. 3. It has a similar shape as the function used for the main results in the paper, however, this equation cannot be linearized with logs in a similar way. Thus, it was estimated with nonlinear least squares, using the matched samples of naturally regenerated forests for individual forest groups, as well as the aggregated sample.$$frac{{{{{{mathrm{Volume}}}}}}}{{{{{{mathrm{Hectare}}}}}}}=a/(b+exp (-c,ast ,{{{{{rm{Age}}}}}}))$$
(3)
We began by estimating two separate growth functions, one for the pre-1990 (low CO2) period and one for the post-2000 (high CO2) period using Eq. 3. That is, observations from the pre-1990 (low CO2) control period and from the post-2000 (high CO2) treatment period were handled in separate regressions. For this initial analysis with the nonlinear volume function, we did not control for CO2 concentration or other factors that could influence volume across sites (e.g., weather, soils, slope, aspect), and thus, results likely show the cumulative impact of these various factors. Using the regression results (Supplementary Data 26), we calculated the predicted volume for the pre-1990 and post-2000 periods and compared the predicted volumes (Supplementary Table 8).Next, we tested this yield function on the combined sample (containing both control and treatment observations) and all forest groups. Here the model was expanded to better identify the impact of elevated CO2 by including all covariates. Instead of using a dummy variable for each forest group, though, a single dummy variable was used to differentiate hardwoods from softwoods. Once again, the equation was logarithmically transformed for ease of comparison with the results presented in Table 1. All covariates were originally input, but those which were not significant were removed. That process yielded the functional form shown in Eq. 4. Results for the regression are presented in Supplementary Data 27. The predicted change in volume due to CO2 fertilization from 1970 to 2015 is shown in Supplementary Table 9.$$frac{{{{{{mathrm{Volume}}}}}}}{{{{{{mathrm{Hectare}}}}}}}= big(a0+a1,ast ,{{{{{rm{Time}}}}}},{{{{{rm{Dummy}}}}}}+a2,ast ,{{{{mathrm{Ln}}}}}({{{{{rm{LifetimeCO}}}}}}2)+a{3},ast ,{{{{mathrm{Ln}}}}}({{{{{rm{Seasonal}}}}}},{{{{{rm{Temperature}}}}}})\ +a{4},ast ,{{{{mathrm{Ln}}}}}({{{{{rm{Seasonal}}}}}},{{{{{rm{Precipitation}}}}}})+a{5},ast ,{{{{{rm{Site}}}}}},{{{{{rm{Class}}}}}}\ +a6,ast ,{{{{{rm{Physiographic}}}}}},{{{{{rm{Dummy}}}}}}+a{7},ast ,{{{{{rm{Aspect}}}}}},{{{{{rm{Dummy}}}}}}+a{8},ast ,{{{{{rm{Stocking}}}}}},{{{{{rm{Code}}}}}}\ +a9,ast ,{{{{{rm{Disturbances}}}}}}+a{10},ast ,{{{{{rm{Hardwood}}}}}}/{{{{{rm{Softwood}}}}}},{{{{{rm{Dummy}}}}}}left.right) /left(right.b{0}+b{1},ast ,{{{{{rm{Time}}}}}},{{{{{rm{Dummy}}}}}}\ +b{2},ast ,{{{{mathrm{Ln}}}}}({{{{{rm{Lifetime}}}}}},C{O}_{2})+b3,ast ,{{{{mathrm{Ln}}}}}({{{{{rm{Seasonal}}}}}},{{{{{rm{Temperature}}}}}})\ +b{4},ast ,{{{{mathrm{Ln}}}}}({{{{{rm{Seasonal}}}}}},{{{{{rm{Precipitation}}}}}})+b5,ast ,{{{{{rm{Site}}}}}},{{{{{rm{Class}}}}}}\ +b6,ast ,{{{{{rm{Physiographic}}}}}},{{{{{rm{Dummy}}}}}}+b{7},ast ,{{{{{rm{Aspect}}}}}},{{{{{rm{Dummy}}}}}}+b8,ast ,{{{{{rm{Stocking}}}}}},{{{{{rm{Code}}}}}}\ +b9,ast ,{{{{{rm{Disturbances}}}}}}+b{10},ast ,{{{{{rm{Hardwood}}}}}}/{{{{{rm{Softwood}}}}}},{{{{{rm{Dummy}}}}}}\ +exp left(right.-left(right.c{0}+c{1},ast ,{{{{{rm{Time}}}}}},{{{{{rm{Dummy}}}}}}+c{2},ast ,{{{{{rm{Lifetime}}}}}},{{{{{{rm{CO}}}}}}}_{2}\ +c{3},ast ,{{{{mathrm{Ln}}}}}({{{{{rm{Seasonal}}}}}},{{{{{rm{Temperature}}}}}})+c{4},ast ,{{{{mathrm{Ln}}}}}({{{{{rm{Seasonal}}}}}},{{{{{rm{Precipitation}}}}}})+c{5},ast ,{{{{{rm{Site}}}}}},{{{{{rm{Class}}}}}}\ +c{6},ast ,{{{{{rm{Physiographic}}}}}},{{{{{rm{Dummy}}}}}}+c{7},ast ,{{{{{rm{Aspect}}}}}},{{{{{rm{Dummy}}}}}}+c{8},ast ,{{{{{rm{Stocking}}}}}},{{{{{rm{Code}}}}}}\ +c{9},ast ,{{{{{rm{Disturbances}}}}}}+c{10},ast ,{{{{{rm{Hardwood}}}}}}/{{{{{rm{Softwood}}}}}},{{{{{rm{Dummy}}}}}}left.right),ast ,{{{{{rm{Age}}}}}}left.right)left.right)$$
(4)
As the results using the nonlinear volume functions were similar in sign and magnitude to the multivariate-regression results and as the practice of matching and then running a multivariate-regression represents a doubly robust econometric approach that has been shown to yield results that are robust to misspecification in either the matching or the regression model47,55,56,57, the main text results are based on estimations utilizing multivariate-regression analysis post-matching.To develop Table 2, which compares naturally regenerated stands with planted stands, we used the same general approach as was used to create Table 1. The analysis and comparison of planted and naturally regenerated stands was conducted only for stands with enough observations of both to make a comparison: White/Red/Jack, Slash/Longleaf, and Loblolly/Shortleaf pine. We followed the same matching and regression procedures as above, but conducted the matching separately for naturally regenerated and planted stands. We also limited the data to stands less than or equal to 50 years of age, as there are few planted stands of older ages due to the economics of rotational forestry35,36,37,38,39,40. Balance statistics for the matched samples are presented in Supplementary Data 28–30. Again, the matching process resulted in a good balance in observable plot characteristics, which implies that we achieved comparable treatment and control plots.Using the matched data, we estimated the same regression as in Eq. 2. Estimation results, which use the Model (2) specification from Supplementary Data 19–21 that was used with the data for these three forest groups from ages 1–100, are presented in Supplementary Data 30–32. A comparison of the parameter estimates on the natural log of lifetime CO2 exposure between the results for ages 1–50 (from Supplementary Tables 31–33) and those for ages 1–100 (from Supplementary Data 19–21) is presented in Supplementary Table 10.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More
