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).