## Materials and Methods
### Model Development
#### 2.2.2 Tree Mortality Resulting from Defoliation  
Observed annual defoliation (AD) can be considered as a measure of the percentage of leaf biomass lost to insects. Since this variable causes a decrease in LAI, it subsequently impacts forest ecosystem photosynthesis. Every year, SBW produces one generation that is divided into nine life stages comprised of eggs, larvae (which include stage one through six), pupa, and moth. Damage from the SBW mainly occurs from May to July when the larvae are in stage three through six [44; 45; 46]. Temperature impacts the beginning of SBW feeding. We estimated that defoliation commenced in May when the mean temperature is generally greater than 5 \({}^{\circ}\)C in the study area [44; 47; 48]. Thus, AD was distributed over a period of two to three months by setting different weights to AD in our model (see Table 2) to account for differences in SBW phenology [49]. Figure 1: Framework and flow chart of TRIPLEX-Insect model (modified from [PERSON] et al. (2002) [25]). Rectangles represent pools or state variables; ovals represent simulated processes; diamond-shaped boxes represent judgment process; dotted lines represent controls; and solid lines represent carbon (C), nitrogen (N), and water flow. Defoliation caused mortality (DM; %/year) is defined in our model and described by Equation (2):  
\[\text{DM}=\text{K}\times(\exp(\text{DS}\times\text{S}\times\text{A}\ )-7)/100 \tag{2}\]  
where K = 6.6774 is a parameter derived from empirical data taken from literature [50]. The defoliation stress (DS) index was calculated by cumulative defoliation (CD) and the weight of current annual defoliation (WAD) using Equation (3):  
\[\text{DS}=\text{CD}\times\text{WAD} \tag{3}\]  
If annual current defoliation levels for the last five years were 0.25, 0.25, 0.5, 0.75, and 1, then CD would be 0.25, 0.5, 1, 1.75, and 2.75 [51]. The WAD estimates will equal 3 \(\times\) AD, 1.07 \(\times\) AD, 1.6 \(\times\) AD, and 0.52 when annual defoliation levels are 1 (AD: 0%-5%), 2 (AD: 6%-30%), 3 (AD: 31%-60%), and 4 (AD: 61%-100%), respectively. Additionally, both tree species (S) and ages (A) influence mortality during SBW outbreaks [52]. For balsam fir forests, we used observed basal area data from 2010-2016 for the North Shore region of Quebec to compare with model simulation results from the model (see Table 1) and then calibrated S = 0.4 and A as Equation (4):  
\[\text{A}=1.27/(1.75+\exp(-0.001\times\text{Age}\ )) \tag{4}\]  
There are two mortality rates in the original TRIPLEX 1.0 model: natural mortality (NM; %/year) and competition mortality (CM; %/year). The CM rate is estimated based only on canopy competition for sunlight [28] and be given an initial value as 1.2%/year. In addition, we assume that DM rates greater than 3%/year means all dead trees are caused by severe defoliation, where the rates of NM and CM are zero (Table 3). Note that in this study we did not add new trees when defoliation caused mortality and dead trees were transferred to the litter pool in the next iteration. SBW preferentially eaters flower cones, resulting in little to no seed production during an outbreak [53]. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mean Temperature in May**} & \multicolumn{3}{c}{**Proportion of Annual Defoliation**} \\ \cline{2-4}  & **May** & **June** & **July** \\ \hline \textless{}5 \({}^{\circ}\)C & & 50\% AD & 50\% AD \\ \(\geq\)5 \({}^{\circ}\)C & 10\% AD & 40\% AD & 50\% AD \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Monthly distribution of annual defoliation (AD) in May, June, and July based on the mean temperature in May.