Kernel Home Range Estimation for ArcGIS, using VBA - Fish and ...

4.5. Standardization
Not all datasets are created equal. It is often the case that data will have greater variance in a
particular direction. This may be caused by the behavior of the animal or it may be a result of a
geographic constraint to movement – as might be the case for linear barriers such as mountain
ranges, streams or coastlines (for terrestrial species). In such cases it may be better to search
further in the direction with the greater variance to find points that will contribute to the density
estimate for an evaluation point. Complex kernels are one method of overcoming this bias in the
data, and an alternative technique is described in section 4.5.2. A better solution would be to
standardize the data, run the kernel density analysis (using a single smoothing parameter) and
then re-project the final home range contours to match the original scale of the data. Unit
(Section 4.5.1.) and X Variance Standardization (Section 4.5.2.) have been suggested for this.
ABODE allows the user to incorporate standardization in the analysis using the aforementioned
methods and a thrid option, Covariance Bias (Section 4.5.3).
4.5.1. Unit Variance Standardization
Standardizing data to have a unit covariance matrix was proposed by Silverman (1986). The
original data (Figure 4.5.1.1.a.) are standardized using the variance measures in the x and y
directions. The x coordinate for each point is divided by the standard deviation in X (σBxB).
Similarly, y is scaled by σByB. This results in a set of standardized data (Figure 4.5.1.1.b.). In this
simple example, the relationship between points is preserved, since the variance is equal in both
X and Y (Figure 4.5.1.2.a.). In cases where the variance in X and Y is not equal (Figure
4.5.1.2.b.), the relationship between the points is altered such that the variance in each direction
is equal. The kernel density estimation would typically be done on the standardized data to
produce a home range estimate (Figure 4.5.1.3.a.). This allows for the use of a single smoothing
factor. The final product would be transformed back to the original scale of the data (Figure
4.5.1.3.b.).
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