WestslopeCutthroat Trout   

Sampling Locations

    A total of fourty-nine stream localities in the Bow River Basin were sampled from southwestern Alberta during the summer (August to September) of  2007, 2008 and 2009.  The sites belong to ten different watersheds in four National Parks (Banff, Jasper, Yoho and Kootenay). 

Methods

Hybridization Assessment

    Genetic analysis to determine the degree of hybridization in each locality was performed using a 10-microsatellite DNA assay. In this procedure, 10 variable regions of the genome are amplified using a molecular technique called polymerase chain reaction.

    The amplified fragments are tagged with fluorescent dye and the size of fragment can be determined based on the amount of fluoresence. There are known differences between westslope cutthroat trout and rainbow trout in the size of these amplified fragments. Thus, at each of the 10 variable regions in a fish, we can determine whether it comes from a westslope cutthroat trout origin or a rainbow trout origin. 

    Bayesian statistics were used to calculate the probability that an individual fish is a pure westslope cutthroat trout, pure rainbow trout, a first generation hybrid, second generation hybrid, a backcross to westslope cutthroat or backcross to rainbow trout. Individual probabilities were averaged for each sample site to produce a hybridization index (HI) which ranges from 0 to 1. 

Hybridization Index	Classification Scheme
0.99-1.0	Pure westslope cutthroat trout
0.95-0.99	Hybridization evident
<0.95	Significant hybridization
0-0.1	Pure rainbow trout

Environmental Regulation of Hybridization

    13 different variables were classified into two broad categories: Human Impact  and Stream Environment.

Human Impact Variables (HiV)	Measured as:
Rainbow Trout Stocking (1950-1960)	Distance to nearest stocking location (m)
Rainbow Trout Stocking (1990-2000)	Distance to nearest stocking location (m)
Pure Rainbow Trout Sites	Distance to nearest sample site where pure rainbow were found (m)
Powerlines	Distance to nearest powerline (m)
Pipelines	Distance to nearest pipeline (m)
Railroads	Distance to nearest railroad (m)
Access Roads	Distance to nearest access road (m)

    All HiVs we calculated using  the Near tool in Arc Map10 using ArcGIS software. This tool determines the distance from each sample site to the nearest HiV.

Stream Environment Variables (SeV)	Measured in:
Water Temperature	Degrees celcius
Mean Depth	Metres
Maximum Depth	Metres
Elevation	Metres
Physical Barriers	Presence or absence
Stream Order	Stream order, see below for more details

    Mean  depth, maximum depth and temperature were measured for each sample site at the time of sampling.  

    Elevation values for each sample site was extracted using 25 metre DEM of southwestern Alberta provided by Alberta Sustainable Resource Development. 

    Sample locations were scored for the presence/absence of physical barriers. Physical barriers such as dams, waterfalls, chutes, cascades and sub-surface waterflow, may influence hybridization levels by  prevent introduced rainbow trout from entering the stream system.

    Each sample site was assigned a numerical stream order based on the branching complexity of the stream. In this analysis, I used the Strahler method of stream ordering. With this method, stream order only increases when streams of the same order intersect. For example, if two first order streams intersect, the resulting branch becomes a second order stream. However, if a first order stream intersects with a second order stream, the resulting branch remains a second order stream.

     This method can be contrasted with the Shreve method of stream ordering where branching values are additive based on magnitude. Because the branching of streams in southwestern Alberta can be rather complex in certain areas, I chose to use the Strahler method  of stream ordering so that the number or stream order values a sample site could take on remained relatively low. This difference in methodology is illustrated on the right. For the same branching pattern, the Shreve method has 5 possible values for stream order, while the Strahler method yields only 3.

Analysis

Regression

    Regression analysis was used to model the relationship between the observed pattern of hybridization (dependent variable; y) and environmental factors (explanatory variables; x).

    After variable processing,  a scatterplot matrix was used to identify key explanatory variables to produce a properly specified model. A scatterplot allows you to visualize the relationship between the dependent variable and each environmental variable. 

    Ordinary Least Squares Regression was run using ArcMap 10 to determine how well the a particular model variable could explain the observed hybrid index (HI).  I first ran a model which included  all environmental variables (human impact and stream environment). From the results of this model and with the help of the scatterplot matrix, I was able to identify six key explanatory variables to model the observed pattern of hybridization. 

Spatial Autocorrelation (Moran's Index)

    To evaluate how well my aspatial regression model (ordinary least squares regression) describes the relationship between hybridization levels and key environmental variables, I analyzed the spatial autocorrelation of the residuals using ArcMap 10. If the results of the spatial autocorrelation show that the residuals are spatially autocorrelated, they are clustering in a non-random way and the aspatial regression model is missing a key environmental variable.

Reliability of the Model

    After specifying the model with the greatest R^2 value (the proportion of observed hybridization levels explains by the model), and testing for spatial autocorrelation,  I assessed the reliability of the model using the following criteria: 

1) Are the coefficients showing the expected sign? 

            - Confirm that the type of relationship is what we expect

2) Is there redundancy amongst the variables? 

            - Determine whether two or more variables are telling the same story. This is     

              measured by the variance inflation factor (VIF). A value greater than 7.5     

              demonstreates redundancy. If there is redundancy, this canlead to a bias in the 

              model. 

3) Are all the coefficients reliable?

            - Is the relationship it depicts just due to random chance or are they reliable?

              This is given by the probability values of each coefficient.

4) Are the residuals normally distributed? 

            - like the spatial autocorrelation, this tests whether the residuals are random 

              (a histogram would produce a bell curve). If the chi-square value of the 

              Jarque-Bera test  is statistically significant (residuals are not random), the model is
              biased and missing a key variable.

(Click on images to see full maps)

Sample sites