Study area
To examine the simultaneous effects of endogenous processes and climate change, we used data from a network of Permanent Sample Plots (PSPs), established throughout Alberta and Saskatchewan. We selected plots according to four criteria (i) PSPs had a known origin date of stand replacing wildfire, and were unmanaged; (ii) PSPs had all trees marked and tagged with diameter at breast height (DBH) and species identification accurately tracked over multiple censuses; and, (iii) PSPs had to have a minimum of three censuses; and (iv) plot size, soil drainage class, and spatial location were available. All plots were established in visually homogenous well-stocked stands greater than 1 ha in size, at least 100 m from any openings to minimize the impacts of edge effects (Frey 1981). The selection process resulted in 1279 plots. These plots range in latitude from 49.0o to 59.7 oN and in longitude from 119.7o to 95.3 oW (Additional file 1: Figure S1). Plots were established between 1958 and 2001, final censuses were conducted on the selected plots from 1963 to 2009, and time between censuses varied from 3 to 28 years, with a mean of 9.5 years. Plot sizes varied from 202 m2 to 2023 m2 with a mean of 976 m2. Time since stand-replacing wildfire varied from 15 years to 316 years, with a mean of 100 years. Across space and time, annual temperatures ranged from −5.77 to 11.67 °C, and annual precipitation ranged from 187 mm to 882 mm between 1957 and 2014, determined using the BioSIM 10 software (Réginère et al. 2014). Over the course of the observations, the study region underwent several persistent droughts, and a general increase in temperature (Diffenbaugh and Field 2013). The dominant species of the region include deciduous Populus tremuloides (Michx.), Populus balsamifera (L.), and Betula papyrifera (Marshall) as well as the coniferous Pinus banksiana (Lamb.), Pinus contorta (Douglas), Picea mariana (Mill.), Abies balsamea ((L.) Mill) and Picea glauca ((Moench) Voss.). Wildfire typically occurs in the region every 15–90 years (Larsen 1997; Weir et al. 2000).
As the provinces had different criteria for measuring trees (Alberta ≥9.1 cm DBH, Saskatchewan ≥9.2 cm DBH), a threshold of 9.2 cm DBH was used. If a tree subject to a mortality event had a smaller DBH than its last previous alive measurement, it was assigned the previous DBH. If a tree was missing from one census to another, it was deemed dead and assigned its previous (alive) DBH. Finally, if a tree’s growth was greater than 2 cm a year, it was examined for data entry mistakes (e.g., an incorrect decimal).
Biomass calculations
Similar to previous studies (Chen and Luo 2015; Chen et al. 2016; Hogg et al. 2017; Searle and Chen 2017a), above-ground biomass for each individual stem was calculated for individual trees using species’ specific allometric equations developed for all major boreal tree species (Lambert et al. 2005; Ung et al. 2008). The biomass of individual stems were summed across each plot to obtain stand-level estimates. The annual net aboveground biomass change (ΔAGB) was calculated as the total live biomass at the census minus the total live biomass at the previous census divided by the time between censuses (interval). Annual change in above-ground biomass growth (ΔAGBGI) was calculated as the biomass gain of live trees between censuses plus biomass gain from recruited trees divided by the interval. Annual change in above-ground biomass loss due to mortality (ΔAGBM) was calculated as the biomass lost due to mortality divided by the interval. Relative biomass growth, mortality, and net biomass change were calculated as the absolute value divided by the mean standing biomass between the two focal census periods.
Explanatory variables
We used calendar year to represent temporal changes in climatic conditions as a whole, following previous studies (Brienen et al. 2015; Chen et al. 2016; Searle and Chen 2017a), corresponding to each observation of ΔAGB, relative ΔAGB and their related components. This encompasses not only the systematic increases in atmospheric CO2 concentration and temperature and a decrease in climate moisture index, but also the changes in other climatic and non-climatic drivers.
Soil drainage class of each plot was categorized into three major groupings: well-drained, moderately-drained, and poorly-drained. These values correspond to a soil drainage class value of 1–3, 4 & 5, 6 & 7, respectively. These values were inferred from the pore pattern and depth of mineral soils, the topographic position of the site, and physical characteristics of the soil profile including humus depth, location of the water table, permeability, and water storage capacity (Frey 1981; Alberta Sustainable Resource Development 2005). Of the 1279 plots selected for this analysis, 161 were well drained, 1071 were moderately drained, and 47 were poorly drained. Of the 47 poorly drained sites included in our analysis only two were identified as fully saturated for the entirety of the growing season.
Similar to our previous studies (Luo and Chen 2013; Chen et al. 2016; Searle and Chen 2017a), we used forest age to account for endogenous stand processes, interpretable as time since fire as all selected stands originated from wildfire. Forest age for each PSP was determined according to a known fire or by coring at least three dominant/co-dominant trees of each tree species inside or outside the plot at the time of plot establishment. When coring was used, the average ring counts of the tree samples for the species with the oldest age was used to determine time since fire by species-specific relationships between forest age and time since fire developed for boreal forests (Gutsell and Johnson 2002; Huang et al. 2009). With all data pooled, there was a weak positive correlation between forest age and calendar year (r = 0.12, R2 = 0.014). There are three possible approaches to disentangle their joint variation. The first is to model their effects simultaneously. The second is to use residual and sequential regressions by assigning the priority to forest age and then modelling the effects of year and its interaction with forest age on the residuals (Graham 2003; Cohen et al. 2013). The third is to reverse the priority in the second approach. However, as we have no logical or theoretical basis for considering any variable to be prior in terms of a hypothetical causal structure of the data (Cohen et al. 2013), and assigning priority to forest age would marginalise the year effect, and vice versa (Brown et al. 2011; Chen et al. 2016), we reported the results from simultaneously modelling effects of forest age and year.
To understand the influence of individual climate change drivers on ΔAGB and its related components, we derived CO2 measurements from the Mauna Loa Earth System Research Laboratory in Hawaii (http://www.esrl.noaa.gov/gmd/ccgg/trends/co2_data_mlo.html) and from the Law Dome DE08 and DE08–2 ice cores (http://cdiac.ornl.gov/ftp/trends/co2/lawdome.smoothed.yr20). We also calculated the annual temperature anomaly (ATA) for each census, defined as the annual mean annual temperature of a plot minus the average annual temperature for the plot throughout the study period. To assess temporal changes in climate moisture availability, we calculated the standardized precipitation evapotranspiration index (SPEI). The index is standardized to a location and has been shown to be an excellent indicator of water availability that is directly comparable across large spatial and temporal gradients (Vicente-Serrano et al. 2010). We used monthly precipitation and evapotranspiration derived from BioSIM to calculate a yearly SPEI, using the SPEI, version 1.6, package in R (Vicente-Serrano et al. 2010). We then calculated the average value of each driver over the census interval. Over the study period, there was a general increase in temperature, decrease in SPEI, and increase in atmospheric CO2 (Additional file 1: Figure S2).
Data analysis
To address how drainage classes might affect climate change associated trends in stand level ΔAGB, relative ΔAGB and their related components, we tested the effects of forest age, calendar year (climate change as a whole), soil drainage and all two-way interactions using the following linear mixed effects model:
$$ {\displaystyle \begin{array}{c}\varDelta {\mathrm{AGB}}_{\mathrm{ij}}={\beta}_0+{\beta}_1\cdot {D}_j+{\beta}_2\cdot {Y}_{ij}+{\beta}_3\cdot f\left({A}_{ij}\right)+{\beta}_4\cdot {D}_j\times {Y}_{ij}+\\ {}{\beta}_5\cdot {D}_j\times f\left({A}_{ij}\right)+{\beta}_6\cdot {Y}_{ij}\times f\left({A}_{ij}\right)+{\pi}_j\end{array}} $$
(1)
where D is the soil drainage class of the plot, Y is the mid-calendar year, and f(A) is natural logarithm of forest age for absolute ΔAGB models and is the inverse of the natural logarithm of forest age for relative ΔAGB. π is the random plot error, which accounts for plot specific effects other than drainage class, such as plot size, nutrient regime, and species composition. Similar to previous studies using plot networks consisting of plots of varying sizes and census lengths (Brienen et al. 2015; Chen et al. 2016), we weighted each observation by the square root of the plot size in hectares times the total plot census length. All variables were centered prior to analysis to speed convergence and aid in interpretation. In order to derive overall temporal trends, we fit a similar model to eq. 1 but omitted the drainage class year interaction (β6).
To better understand the influences of temporal changes in climate on ΔAGB, relative ΔAGB and their components, we substituted Y in Eq. 1 with atmospheric carbon dioxide concentration, ATA, and SPEI and modeled each driver independently. Our analysis is parametric and assumes normality of residuals; however, model residuals for ΔAGB were left-skewed, model residuals for ΔAGBGI and ΔAGBM were right-skewed and residuals of relative ΔAGB and its components were leptokuric. To account for this, all models were bootstrapped 1000 times to generate 95% confidence intervals. Graphical representation of the trends was performed according to methods developed by Chen et al. (2016). Analysis was conducted in R 3.4.0 (R Core Development Team 2017), using the lme4 package (Bates et al. 2015).