a comparison of regimes across West Arm Lake, Kootenays, British Columbia


 
Figure 4  
 

Figure 5
METHODS

I gathered spatial datasets from provincial and federal sources to build a Geographic Information System (GIS) for the
study area using ArcGIS v 9.3.0.1770 (Table 1).

Dataset Source Notes
Vegetation Resource Inventory (VRI) Ministry of Forests and Range, British Columbia (Geographic Data Discovery Service 2009) A vector layer derived through interpretation of aerial imagery to assign attributes, such as age projections, species compositions, and disturbance histories to discrete patches of forest vegetation, termed “polygons”.
Digital Elevation Model (DEM) Ministry of Natural Resources, Canada (Canadian Digital Elevation Data 2009) To align the DEM to the VRI, I converted the DEM to a raster with cell size of 25 m by 25 m before reprojecting using bilinear sampling.
Roads Natural Resources Canada (Natural Resources Canada 2009) A vector layer of road centre lines derived from multiple sources including GPS and verified through orthophotos.
HNFR Blackwell et al. 2003 A vector layer that estimates boundaries in Historic Natural Fire Regime according to aspect, elevation, slope, and dominant vegetation.
 Table 1. Datasets Built in GIS for Analyses.

Since my questions focus on the historic role of fire, I removed polygons from the vegetation layer that did not support
fire according to the layer of HNFR. These polygons fell into two categories:

        1.      water bodies and
        2.      rocky areas located in alpine areas (Figure 4).
 
I performed all subsequent analyses on polygons that contained vegetation and support fire. First, I subdivide the vegetated
polygons that support fire into two groups according to projected age to reflect stands that likely established prior to European
settlement (1860):

        1.       ≥ 200 years old (old) and
        2.        < 200 years old (young) .

For all polygons within each category, I assigned a point to each polygon centre to calculate slope, aspect, elevation, and
solar radiation by extracting values from my DEM to the points that represented each polygons. I computed a distance
from nearest road from each point using the Euclidean Distance tool using the roads layer. Since observations from the
field indicated a direct relation between age and elevation, I plotted these variables against each other on a scatter plot
to inspect the variance of age with elevation (Figure 5).

I used a chi-squared test to test for independence between age and elevation. Then I built a model to predict stand age
using elevation, aspect, solar radiation and distance from nearest road. In this model stand age is a the dependent response
variable and each stand is binomially distributed, where stands ≥ 200 years old are assigned a value of 1 and all other stands
are assigned a value  of 0. The logistic regression model predicts stand for all stands to parameterize a probability curve of age:





where Pr is the probability that stands are ≥ 200 years old and Mx is the model of the likelihood of old stands that contains
the independent variable(s). In the simplest case, the model of stand age (M1) includes only one independent variable:

Where t is time since fire in years, and α and β are calculated coefficients for the regression. I incorporated topographic
variables along with distance from road into the model in a forward step-wise process to determine influences on stand
age. I used Akaike's information criterion (AIC), a tool for model selection that assesses goodness of fit between
model by measuring the relative amount of information lost in a given model, to select the best model. AIC value
is calculated with the following formula:

AIC = -2(maximized log-likelihood) + 2K

where K is the number of parameters and the maximized log-likelihood is the natural logarithm of the likelihood function
for a particular model. All subsequent analyses were performed using Statistical Analysis System (SAS) v9.1 (SAS Institute,
Cary, NC, USA). All tests were significant using alpha = 0.05.