Discriminant Analysis Worksheet

Discriminant Analysis Worksheet
Dennis Deck, Virtual Dirt Time
Purpose

Although most of the tracking guides offer averages for track and gait measurements, in practice you will find considerable variation in size for any species. Furthermore, there is often considerable overlap between two related species (e.g., fox and coyote). In these situations, it is helpful to determine what characteristics of a track or gait help distinguish the two.

Discriminant.xls is an Excel worksheet I designed to do a discriminant analysis of the track and gait measurements for two related species. As an example, I have included data from a little study I did conducted to compare elk and bison.

Description

There are two data entry sheets and three charts to display the results graphically:

Track scatterplot showing the distribution of track length and width for two species.
Gait scatterplot showing the distribution of stride and straddle for the two species.
Line graph showing how well the selected measure discriminates between the two species.

Each tab of the spreadsheet includes instructions about how to organize the data. Enter your observations for two species into the shaded area of the DataSheet tab. Then inspect the two track and gait charts and select the measure you want to compare them on. Copy that column to the DA Worksheet tab and follow the instructions to resort. Now inspect the line graph at the DA Chart tab to see if there is a cut point that discriminates well.

Your interpretation of the results should be tempered by the quality of your sample. To the extent that you were unable to collect a large and fully representative sample (age, gender, and regional variation in size), the results may not generalize.

Example

The worksheet includes sample data from a winter study I did comparing elk and bison in Yellowstone National Park. I sampled areas between the Bison Ranch and Soda Butte in the Lamar Valley for bison and east of Pebble Creek for bull elk. My protocol included:

Select clear hind tracks with no evidence of enlargement by melting or other distortion
Select walking strides with no evidence of turning that would widen the straddle measurement
Select only one set of tracks from each individual animal
Take minimum outline track measurements

In this little study, I found little overlap in track measures but considerable overlap in gait measurements. The bull elk in my sample had tracks under 110 mm. A different bison sample with young calves would likely have tracks smaller than that but the adults in this sample were consistently larger. Furthermore, the scatterplot reveals that bison tracks are consistently wider relative to their length. The ratio of width to length averages 1.0 (width=length) for the bison and 0.8 (width<length) for elk. As for gait measurements, straddle was generally less than 10 inches for elk and generally more than that for bison.