Methodology
Multi-criteria decision analysis is a useful tool to evaluate multiple factors including constraints affecting the outcome of a decision. These factors can also include competing views from different points of view. In this study, a multi-criteria evaluation (MCE) was used in order to identify the future habitat range of this invasive species due to climate change. In this sense, MCE’s provide a useful analysis for changing conditions of habitats and provide effective results for where to focus management plans to reduce the spread of the invasive species. ESRI ArcGIS 10 was used to conduct the MCE.
In general, there are 5 steps involved in an MCE:
1) Determining Important Criteria
In order to know the criteria to include in the MCE, I had to understand under what conditions hound’s tongue establishes. For a plant species there are key biotic and abiotic factors that will indicate its presences. The abiotic factors include elevation, slope, aspect, soil acidity, average yearly temperature, and average yearly precipitation [1]. The factors included in the MCE are: elevation, slope, aspect, temperature and precipitation. Soil acidity was excluded due to the lack of spatial data; instead biogeoclimatic (BEC) zones are used as constraints to simulate some of the same conditions that soil provides. The BEC zones that hound’s tongue is found in presently are: Interior Cedar-Hemlock, Sub-boreal Spruce, Interior Douglas fir, Montane Spruce, Ponderosa Pine and Bunchgrass (Klinkenberg). There is one biotic factor that is associated with hound’s tongue and that is Mogulones cruciger, a root weevil that negatively affects the survival of hound’s tongue (“Hound’s Tongue”). This factor was not included due to the fact that this weevil has become an invasive species when it was introduced as a biocontrol agent against hound’s tongue.
Hound’s tongue is commonly found in rangelands, agricultural and clear-cut lands, which is another constraint to its potential establishment. This constraint was not included because the study hopes to see the overall distribution change in British Columbia and did not want to restrict to only looking at agricultural and clear-cut lands.
2) Creating and Normalizing Layers
All the factors had to be normalized in order to compare and evaluate each factor on a similar scale. From using the point data of locations of houndstongue, I gathered information on the distribution of each factor to determine what the relationship was to each variable and carried out the fuzzy membership function in order to create the normalization scheme on a scale of 1 to 0, where 1 is most favoured and 0 is least favoured areas. Elevation was distributed in a normal curve way, with preference for lower elevations and the Gaussian function in the fuzzy membership tool was used and the midpoint value was set to 887m, and normalized at this point to be 1 and all other lower and higher values would decline to 0. For aspect, southern facing slopes are preferred by many plant species and in order to normalize this the Gaussian function in the fuzzy membership was used and the midpoint of highest membership (equivalent to 1) was set to 180 degrees (or “south”), with a decline in relation towards the east and west and north. For slope, an inverse linear relationship was selected where lower slopes are favoured over higher slopes. Houndstongue prefers warmer temperatures but has an optimal level at the mean of 51°C, so a normal Gaussian distribution was used for its relationship, where the mean was the midpoint with the highest relationship of 1 and the relation declines to zero towards hotter and cooler temperatures. Precipitation was normalized through an inverse relationship where lower precipitation at base level of 276mm are preferred over higher precipitation areas, as the data points provide evidence for a preference of lower precipitation areas.
3) Determining Weights for Each Layer
This is one of the more controversial steps in the MCE process because of the subjective nature of evaluating the importance of different factors. Determining the importance of the different factors for plants is not easy as all factors contribute to a species establishment. I used the analytical hierarchical process of determining the weights with “My choice, My decision” online tool. This process is where each criterion is weighted against each other to evaluate the importance of each criterion in relation to all other criteria. In my decision, I decided that climatic conditions (temperature, aspect and precipitation) were more important than physical features (elevation and slope). Below is a table outlining the weights of each criterion in which a consistency ratio of 0.0443 was achieved:
In general, there are 5 steps involved in an MCE:
1) Determining Important Criteria
In order to know the criteria to include in the MCE, I had to understand under what conditions hound’s tongue establishes. For a plant species there are key biotic and abiotic factors that will indicate its presences. The abiotic factors include elevation, slope, aspect, soil acidity, average yearly temperature, and average yearly precipitation [1]. The factors included in the MCE are: elevation, slope, aspect, temperature and precipitation. Soil acidity was excluded due to the lack of spatial data; instead biogeoclimatic (BEC) zones are used as constraints to simulate some of the same conditions that soil provides. The BEC zones that hound’s tongue is found in presently are: Interior Cedar-Hemlock, Sub-boreal Spruce, Interior Douglas fir, Montane Spruce, Ponderosa Pine and Bunchgrass (Klinkenberg). There is one biotic factor that is associated with hound’s tongue and that is Mogulones cruciger, a root weevil that negatively affects the survival of hound’s tongue (“Hound’s Tongue”). This factor was not included due to the fact that this weevil has become an invasive species when it was introduced as a biocontrol agent against hound’s tongue.
Hound’s tongue is commonly found in rangelands, agricultural and clear-cut lands, which is another constraint to its potential establishment. This constraint was not included because the study hopes to see the overall distribution change in British Columbia and did not want to restrict to only looking at agricultural and clear-cut lands.
2) Creating and Normalizing Layers
All the factors had to be normalized in order to compare and evaluate each factor on a similar scale. From using the point data of locations of houndstongue, I gathered information on the distribution of each factor to determine what the relationship was to each variable and carried out the fuzzy membership function in order to create the normalization scheme on a scale of 1 to 0, where 1 is most favoured and 0 is least favoured areas. Elevation was distributed in a normal curve way, with preference for lower elevations and the Gaussian function in the fuzzy membership tool was used and the midpoint value was set to 887m, and normalized at this point to be 1 and all other lower and higher values would decline to 0. For aspect, southern facing slopes are preferred by many plant species and in order to normalize this the Gaussian function in the fuzzy membership was used and the midpoint of highest membership (equivalent to 1) was set to 180 degrees (or “south”), with a decline in relation towards the east and west and north. For slope, an inverse linear relationship was selected where lower slopes are favoured over higher slopes. Houndstongue prefers warmer temperatures but has an optimal level at the mean of 51°C, so a normal Gaussian distribution was used for its relationship, where the mean was the midpoint with the highest relationship of 1 and the relation declines to zero towards hotter and cooler temperatures. Precipitation was normalized through an inverse relationship where lower precipitation at base level of 276mm are preferred over higher precipitation areas, as the data points provide evidence for a preference of lower precipitation areas.
3) Determining Weights for Each Layer
This is one of the more controversial steps in the MCE process because of the subjective nature of evaluating the importance of different factors. Determining the importance of the different factors for plants is not easy as all factors contribute to a species establishment. I used the analytical hierarchical process of determining the weights with “My choice, My decision” online tool. This process is where each criterion is weighted against each other to evaluate the importance of each criterion in relation to all other criteria. In my decision, I decided that climatic conditions (temperature, aspect and precipitation) were more important than physical features (elevation and slope). Below is a table outlining the weights of each criterion in which a consistency ratio of 0.0443 was achieved:
Criteria
Temperature Aspect Precipitation Elevation Slope |
Weights
41.68% 22.38% 13.89% 11.02% 11.02% |
4) Conducting an Overlay using MCE Algorithms
I conducted a linear weighted overlay using ArcMap’s Weighted Sum tool at an output raster resolution of 775 metres. The Weighted Sum tool overlays each criterion on top of one another through multiplying the associated weights outlined in the previous step and then summed together. The follow expression outlines the overlay method of the variables:
HSx = [(41.68 * (Tx)] + [22.38 * (Ax)] + [13.89 * (Px)] + [11.02 * (Ex)] + [11.02 * (Sx)]
where HS is the suitability of habitat, Tx is temperature, Ax is aspect, Px is precipitation, Ex is elevation potential and Sx is slope potential.
In addition, the constraint to the biogeoclimatic zones (BEC) was also added so to attempt to model the climate and physical conditions better.
5) Performing a Sensitivity Analysis
Following the weighted overlay, a sensitivity analysis was conducted using equal weights for al factors, set at 20%. The sensitivity analysis helps to see the affect that different weights would have on the outcome, especially because the determination of weights can be controversial.
The process of this MCE was performed twice with a change in 2 of the variables: the first used current temperature and precipitation data, and the second used temperature and precipitation projected for 2080 based Climate BC’s climate change model for changes. The present day MCE was restricted to the BEC zones mapped for the present day and the predicted climate change was restricted to the BEC zone changes predicted for 2080.
I conducted a linear weighted overlay using ArcMap’s Weighted Sum tool at an output raster resolution of 775 metres. The Weighted Sum tool overlays each criterion on top of one another through multiplying the associated weights outlined in the previous step and then summed together. The follow expression outlines the overlay method of the variables:
HSx = [(41.68 * (Tx)] + [22.38 * (Ax)] + [13.89 * (Px)] + [11.02 * (Ex)] + [11.02 * (Sx)]
where HS is the suitability of habitat, Tx is temperature, Ax is aspect, Px is precipitation, Ex is elevation potential and Sx is slope potential.
In addition, the constraint to the biogeoclimatic zones (BEC) was also added so to attempt to model the climate and physical conditions better.
5) Performing a Sensitivity Analysis
Following the weighted overlay, a sensitivity analysis was conducted using equal weights for al factors, set at 20%. The sensitivity analysis helps to see the affect that different weights would have on the outcome, especially because the determination of weights can be controversial.
The process of this MCE was performed twice with a change in 2 of the variables: the first used current temperature and precipitation data, and the second used temperature and precipitation projected for 2080 based Climate BC’s climate change model for changes. The present day MCE was restricted to the BEC zones mapped for the present day and the predicted climate change was restricted to the BEC zone changes predicted for 2080.
[1] For a more detailed explanation of each layer and its source, please see the References section
© Andrea Eisma, University of British Columbia, 2013