Data Analysis
The cost-effectiveness of restoration was calculated by dividing above-ground carbon by the cost of restoration. Cost-effectiveness was calculated based on above-ground carbon only (e.g. Birch et al., 2010; Strassburg et al., 2019), because no information on the net soil carbon changes attributable to forest restoration was available in this study, and soil carbon dynamics following restoration in the Atlantic Forest remains poorly known (Mendes et al., 2019). The explored model was as follows:
\(Y\ \sim\ MT\ \times stem_{\text{density}}+MT\times clay+MT\ \times age\)
where Y is above-ground carbon accumulation, soil carbon accumulation or cost-effectiveness for above-ground carbon accumulation - models were adjusted separately for each dependent variables. MT is management type (categorical variable). stemdensity, clay and age are density of stems per hectare (#stem/ha), clay content (%) and stand age (years), respectively (covariates).
For each dependent variable, two models were adjusted, where MT factor was used to test for differences between reference and restored forests, and between plantations and naturally regenerated forests. When comparing reference and restored forests, stand age was not included in the models. The models were simplified using F-tests. Data from different sites were considered as independent observations. Log-log transformation was used when necessary to linearize relationships among variables and/or correct for residual heteroscedasticity. When log-log transformation was applied, model fit was presented with its natural power form in the figures. We did not report critical autocorrelation of the explanatory variables in our dataset (VIF<4). The compliance to linear model assumptions was checked using standard procedures (Zuur, Ieno, Walker, Saveliev, & Smith, 2009).
We further explored the drivers of above-ground biomass and soil carbon accumulation by conducting a model selection procedure (Burnham & Anderson 2002). For each variable, competing models including all possible combinations of explanatory variables were adjusted and ranked using ∆AICci. ∆AICci is the difference between the Akaike Information Criteria corrected for small samples (AICc) of a given model and the AICc of the best-fitting model (minimum AICc). To assess the contribution of explanatory variables, we retained for each forest carbon stock components a subset of best-fitting models (∆AICc<2). The averaged coefficient, standard error and relative importance of explanatory variables (the weighted proportion of the models ∆AICc ≤ 2 that contain the driver) were calculated from the final model subsets. The soil characteristics considered in this analysis included sum of bases, cation exchange capacity, and texture. Soil carbon content was analyzed separately at depths 0-10 cm and 10-20 cm. All analyses were carried out in the R 3.0 environment (R Development Core Team, 2013), using the package “MuMIn” (Barton, 2016).