## 3 Results
### Sensitivity Analysis  
Simulated outputs of GPP and Ra exhibited significant sensitivity to the level of defoliation. Five or 10 years after the beginning of an outbreak, we found a greater increase in GPP than Ra with 20% AD, while a greater loss in GPP compared to Ra with 60% AD and 80% AD (Table 4). Changes in GPP compared to no defoliation (control) increased from 1.32% to 4.25% while changes in Ra ranged from 0.74% to \(-\)1.64% as 40%AD levels after 5 years of an outbreak starting (Table 4). In addition, in all scenarios, with 60% and 80% AD, total GPP and Ra loss reached 100% because no trees survived. Indeed, medium and severe defoliation (40%-80% AD) led to the mortality of all trees when the SBW outbreak was programmed to last for 20 years. Therefore, we ended the simulation when all trees were dead.  
The sensitivity experiments simulated negative NEP following defoliation for all scenarios evaluated (Figure 3A-F). Although we observed a pattern of rapid decline for all defoliation levels,  
Figure 2: Comparison of observed and simulated values of (**A**) tree mortality (%), and (**B**) the current annual volume increment (CAI) (cm\({}^{3}\) year\({}^{-1}\)).  
more severe AD (from 20% to 80%) led to a greater decrease in annual NEP in balsam fir forests (Figure 3A-F).  
We found that the duration of the outbreak and stand age also influence forest recovery. Following the end of the outbreak, younger (ages range from 40 to 60 years) stands (Figure 3A,D) recovered C sinks (NEP \(>\) 0) more rapidly and achieved higher levels of NEP compared to scenarios with older stands. Shorter duration of outbreaks resulted in a greater tree survival (20% AD and 40% AD in Figure 3A-C). For outbreaks lasting 20 years, only scenarios with 20% AD were able to recover (Figure 3D-F) because the other scenarios resulted in total tree mortality.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**5 Years of GPP Change**} & \multicolumn{4}{c}{**5 Years of Ra Change**} \\ \hline
**Tree Ages** & 20\% AD & 40\% AD & 60\% AD & 80\% AD & 20\% AD & 40\% AD & 60\% AD & 80\% AD \\ \hline
41–60 ages & 5.80\% & 1.32\% & \(-\)55.78\% & \(-\)53.68\% & 4.81\% & 0.74\% & \(-\)32.18\% & \(-\)46.36\% \\
101–120 ages & 6.25\% & 2.16\% & \(-\)78.02\% & \(-\)54.95\% & 3.91\% & \(-\)0.49\% & \(-\)65.04\% & 76.07\% \\
161–180 ages & 11.15\% & 4.25\% & \(-\)93.16\% & \(-\)95.42\% & 6.23\% & \(-\)1.64\% & \(-\)89.62\% & 93.01\% \\ \hline \multicolumn{10}{c}{**10 Years of GPP Change**} & \multicolumn{4}{c}{**10 Years of Ra Change**} \\ \hline
**Tree Ages** & 20\%AD & 40\%AD & 60\%AD & 80\%AD & 20\%AD & 40\%AD & 60\%AD & 80\% AD \\ \hline
41–60 ages & 4.94\% & \(-\)6.76\% & \(-\)100\% & \(-\)100\% & 4.30\% & \(-\)8.06\% & \(-\)100\% & 100\% \\
101–120 ages & 7.88\% & \(-\)4.76\% & \(-\)100\% & \(-\)100\% & 4.86\% & \(-\)8.62\% & \(-\)100\% & 100\% \\
161–180 ages & 12.74\% & \(-\)23.37\% & \(-\)100\% & \(-\)100\% & 7.37\% & \(-\)29.47\% & \(-\)100\% & 100\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Simulated total changes of GPP and Ra at 5 years and 10 years after the beginning of an outbreak compared to no defoliation (control) in the balsam fir forest. AD denotes annual defoliation.  
Figure 3: Simulated annual NEP started from different stand ages (41, 101 or 161 years) under two different durations of outbreaks (10 or 20 years) and five different defoliation scenarios (no defoliation (control), 20% AD, 40% AD, 60% AD, and 80% AD). AD denotes annual defoliation. (**A**) Short-Young; (**B**) Short-Mature; (**C**) Short-Old; (**D**) Long-Young; (**E**) Long-Mature; and (**F**) Long-Old.