Ecological Archives A016-053-A3

Jason E. Bruggeman, Robert A. Garrott, Daniel D. Bjornlie, P. J. White, Fred G. R. Watson, and John Borkowski. 2006. Temporal variability in winter travel patterns of Yellowstone bison: the effects of road grooming. Ecological Applications 16:1539–1554.

Appendix C. Descriptions of bison road travel and bison off-road travel response variables.

Road Travel Response Variable (ij)

To offer more insight into how we defined and calculated our road travel response variable (ij) we examine each component of the response variable and provide plots of the data.  Using data from our bison road use surveys we calculated the response as ij = ijij for each time interval (i) and year (j) to quantify the amount of bison road travel in units of bison groups observed per 100 km of road surveyed.  We calculated ij by summing the number of bison groups observed traveling on roads for the ijth period and dividing by the total distance of road surveyed for that period.  A plot of bison groups observed on roads over time for each period and for all eight years is presented in Fig. C1.  Since varying amounts of survey effort between periods could lead to observing more (or fewer) groups, we divided the number of groups observed per period by the distance of road surveyed per period to obtain ij.  A plot of ij vs. time is provided in Fig. C2.

Using ij alone as the response variable was not sufficient because the size of traveling bison groups can vary throughout the season as bison migrate into the Madison-Firehole area (Fig. C3) and all groups would be treated equivalently whether the size of the group was one or 50 bison.  Based upon our field observations we felt that ij alone did not provide an accurate representation and quantification of the variability in the amount of bison road travel between periods.  Therefore, we multiplied ij by a unitless road use weighting factor (ij) to account for the potential variability in group size over time.  We calculated ij as the total number of individual bison in road traveling groups for the ijth period divided by the total number of individual bison documented in road traveling groups for the entire season.  A plot of ij over time is presented in Fig. C4.  Our final road travel response variable (ij) accounted for the number of traveling road groups observed, variability in group size, and survey effort as depicted in Fig. C5.

Given this background on how we calculated our response variable, we now examine the alternatives that we did not use.  Two possibilities for the response were the number of individual bison traveling roads (Fig. C6) or the number of individual bison traveling roads per survey effort (Fig. C7).  However, these would have given an overestimation of the amount of road travel because bison in groups do not travel independently.  In large groups it is often the case that a few bison will begin traveling and the remainder of the group will follow until the lead animals stop.  By this rationale we did not calculate ij as the average group size per period because this ij, when multiplied by ij, would have given a response variable of number of individual bison per survey effort.

Off-Road Travel Response Variable (ij)

We defined and calculated our off-road travel response variable (ij) using the same rationale as for ij.  Using travel data from our ground distribution surveys, we quantified the amount of bison off-road travel for each period by defining an off-road travel response variable as ij, having units of bison groups observed traveling off-road per survey.  We defined the off-road response as ij = ijij, where aij is the total number of bison groups observed traveling off-road per ground distribution survey for the ijth period, calculated as the sum of off-road/off-trail and off-road/on-trail traveling groups.  A plot of ij over time for each period and for all eight years is presented in Fig. C8

Again, using ij alone as the response variable was not sufficient because the size of off-road traveling bison groups can vary throughout the season (Fig. C9).  Therefore, we multiplied ij by a unitless off-road travel weighting factor (ij) to account for the potential variability in group size over time.  We calculated ij as the number of bison observed traveling off-road during ground distribution surveys during the ijth period divided by the total number of bison observed traveling off-road for the entire season during ground distribution surveys.  A plot of ij over time is presented in Fig. C10.  Our final off-road travel response variable (ij) accounted for the number of off-road traveling groups observed, variability in group size, and survey effort as depicted in Fig. C11.

Appendix C Figures:

   FIG. C1. The number of bison groups observed traveling on roads for each period and year during bison road use surveys from 1997–1998 through 2004–2005.


 

   FIG. C2. The number of bison groups observed traveling on roads per 100 km of road survey effort (ij) for each period and year during bison road use surveys from 1997–1998 through 2004–2005.


 

 

   FIG. C3. The mean number of bison per group traveling on roads per period as observed during bison road use surveys from 1997–1998 through 2004–2005.  The 95% confidence intervals about the mean for each year are presented.


 

 

   FIG. C4. The road travel weighting factor (ij) for each period and year as calculated using data from bison road use surveys from 1997–1998 through 2004–2005.


 

 

   FIG. C5. The bison road travel response variable (ij) for each period and year as calculated using data from bison road use surveys from 1997–1998 through 2004–2005.


 

 

   FIG. C6. The number of individual bison observed traveling on roads for each period and year during bison road use surveys from 1997–1998 through 2004–2005.


 

 

   FIG. C7. The number of individual bison observed traveling on roads per 100 km of road survey effort for each period and year during bison road use surveys from 1997–1998 through 2004–2005.


 

 

   FIG. C8. The number of bison groups observed traveling off-roads per survey effort (ij) for each period and year during bison ground distribution surveys from 1997–1998 through 2004–2005.


 

 

   FIG. C9. The mean number of bison per group traveling off-roads per period as observed during bison ground distribution surveys from 1997–1998 through 2004–2005.  The 95% confidence intervals about the mean for each year are presented.


 

 

   FIG. C10. The off-road travel weighting factor (ij) for each period and year as calculated using data from bison ground distribution surveys from 1997–1998 through 2004–2005.


 

 

   FIG. C11. The bison off-road travel response variable (ij) for each period and year as calculated using data from bison ground distribution surveys from 1997–1998 through 2004–2005.


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