The model used to determine future vulnerability of Eastern Hemlock to the spread of Hemlock Woolly Adelgid consisted of: weighted multi-criteria evaluation (MCE) to determine the area Hemlock Woolly Adelgid is most likely to spread, and a multiplication of spread with hemlock density to determine what hemlocks are at risk of exposure to Hemlock Woolly Adelgid. This allowed for the inclusion of continuous data and of multiple criteria of varying significance. The MCE functioned by adding all weighted criteria together and multiplying the sum by the constraints:

MCE equation: Constraints*(Weight_{1}Criteria_{1} + Weight_{2}Criteria_{2 }+ Weight_{3}Criteria_{3} + Weight_{4}Criteria_{4})

There were other models considered for the analysis, such as binary models and process models, but the MCE was found to be the most appropriate. This is because binary models must satisfy all criteria fully, and therefore would not provide the likelihood of spread based on low and high values of each criterion. Process models were also not suitable for this type of analysis because they use existing knowledge in a set of equations that quantify the process, and this was not applicable to the research question.

The data of the layers contained different units and therefore were standardized in order to be compared against each other. For this, all the data was standardized to a range of 0-100 with higher values being more suitable. Two equations were used to achieve this:

x = 100 * ( x_{i } - x_{min}) / (x_{max} - x_{min}) *where higher scores are better*

x = 100 * (1 - ( x_{i} - x_{min}) / (x_{max} - x_{min})) *where lower scores are better*

Where x represented the standardized score for the pixel, x_{i} represented the initial pixel value, and x_{max}/x_{min} represented the maximum and minimum pixel value for the data layer.

Temperature, current Hemlock Woolly Adelgid distribution, distance to roads and road types were classified as criteria. To determine the weight of each factor, a pairwise comparison was used. Temperature was also classified as a constraint with a score of 0 being unsuitable and 1 suitable.

**Table 2: Nine point pairwise comparison scale (Bonnycastle et al., 2017).**

To calculate the suitability scores the following equation was used for each criterion:

Suitability = Σw_{k}x_{k}

Where w_{k} represented weight and x_{k} represented the layer

**Figure 2: Broad model of the process used to determine the vulnerability of Eastern Hemlocks**