Estimating Abundance of Antler Rubs

1
Estimating Abundance of Antler Rubs
Eric S. Long

• Antler rubs by white-tailed deer are a means of
  communication among deer during the breeding
  season.
• Their density (abundance) is thought to be
  influenced by a number of factors, including
  habitat type, topography, food sources, and
  social mechanisms
• PA implemented changes in harvest regulations
  that were expected to increase the density of
  male deer (and decrease no. female deer)
• What change in density of antler rubs might
  result from changes in population demographic
  structure?

2
Pilot Study

• A study area in northcentral Pennsylvania was
  selected to assess the logistics and statistical
  precision required to assess changes in antler
  rub density
• A study by Miller et al. (1987) provided
  information for estimating sample size
  requirements

Miller, K. V., K. E. Kammermeyer, R. L.
Marchinton, E. B. Moser. 1987. Population and
habitat influences on antler rubbing by
white-tailed deer. Journal of Wildlife Management
5162-66.
3
Centre County
Defined Study Area Moshannon State Forest -
65.02 km2
4
If we have L0 (total line length), n0 (number
objects detected, CV (desired coefficient of
variation for density estimate), and
(probability density function of the
perpendicular distance data) - from a pilot study
- we can estimate total line length required to
obtain a given CV with the following equations
However, obtaining a reasonable value for b from
small studies may be difficult. Use b 3 for
planning purposes (in general, b 2 to 4)
5

• Miller et al. (1987) provide density estimates
  and standard errors
• Range of densities 183-580 rubs/sq. km
• Range of CVs 0.16 0.43
• The paper provides no information on transect
  length walked, number of rubs detected (except
  total for all study sites), nor the estimated
  detection probability
• However, if we make some guesses about maximum
  detection distance, and detection probability we
  could estimate the missing information

6

• Est. maximum detection distance 20 m
• Est. detection probability 0.50
• Then, we would expect to detect
• 3.66 rubs/km at 183 rubs/sq. km
• 11.60 rubs/km at 580 rubs/sq. km
• We desire a CV 0.1 (precision acceptable for
  research purposes)
• Giving us an estimated total transect length to
  walk of somewhere between 26 and 82 km!

7
Random Pt
Randomly placed one point in Study Area. Placed
systematic grid of points 3 km (N,S,E,W) from
this starting point
8
Clipped those points to include only those within
the study area This yielded 19 transects
9
Arbitrarily defined those points as the lower
left point of a square transect 500m on a
side Each transect 2 km. 2 km x 19
transects 38 km
10
Logistics vs Statistics

• An estimated 140-440 antler rubs are expected to
  be detected
• Buckland et al. (2001) recommend 60-80 detections
  for modeling the detection function reasonably
  well
• 19 transects gives us a reasonable sample size
  (note that the number of transects is an
  important component of the variance of density
  and is usually contributes more than the
  component associated with estimating the
  detection function)
• Buckland et al. (2001) recommend 20 transects
• 38 km is possible to walk by 1 person (but Eric
  Long was still very tired after it all!)

11
Some squares, however, extended beyond the study
area
12
Why a square transect?

• You finish at the same location where you start
• Especially helpful if access to the transect is
  limited
• You can start anywhere on the transect
• Especially helpful if access to the transect is
  limited
• You just need to make sure the size of the square
  (500 m x 500 m) is much greater than the maximum
  detection distance (20 m)
• Recording distances of detections at corners are
  problematic, but if rare not an issue
• Simply use the shortest distance to the transect
  line

13
For these, those sections outside the boundary
were reflected back in to keep transect length
constant.
14
Locations of all rubs were geo-referenced although
this is not necessary for standard distance
sampling, geo-referenced data collection has
advantages and can be utilized for
spatially-mapped density estimates but requires
more complex analyses
15

• In database, recorded
• Study area name
• Area size
• Rub ID
• Transect ID
• Transect Length
• Perpendicular Distance (ft)
• Perpendicular Distance (m)
• Direction (N,S,E,W)
• Cluster Size
• Diameter of tree (mm)
• KL) Observer Latitude and Longitude (in UTM)
• MN) Rub Latitude and Longitude (calculated from
  columns K,L,J, and H)

16
Analysis Tasks

• Import data into DISTANCE (see class website for
  links)
• Treat antler rubs as clusters is that
  necessary?
• Does the covariate, rub diameter, influence
  detection?
• Is the precision of density estimates as
  predicted? If not, by how much would one have to
  increase total transect length to obtain the
  desired precision?
• Are there other design or protocol issues that
  need to be addressed if the study were to
  continue?