Supplementary Material for
Estimation of Black-tailed Prairie Dog Colonies in Montana
RYAN L. RAUSCHER,1,2 Montana Fish, Wildlife and Parks, 54078 United States Highway 2
W, Glasgow, MT 59230, USA
SCOTT J. STORY, Montana Fish, Wildlife and Parks, P.O. Box 200701, Helena, MT 59620,
USA
JUSTIN A. GUDE, Montana Fish, Wildlife and Parks, P.O. Box 200701, Helena, MT 59620,
USA
ROBIN E. RUSSELL,3 Montana Fish Wildlife and Parks, 1400 19th Street, Bozeman, MT
59717, USA
1
E-mail: rrauscher@mt.gov
2
Present address: Montana Fish, Wildlife & Parks, 514 S Front Street, Suite C, Conrad, MT
59425, USA
2
Present address: United States Geological Survey National Wildlife Health Center, Madison,
WI 53711, USA
Appendix The following is derived from White et al. (2005) and Odell et al. (2008) and
describes the modeling approach used in the manuscript. Estimates for correcting colony lengths
measured from the air (CLA) for each colony i were calculated by assuming CLA (y_lengthi)
were normally distributed with error and that colony lengths on the ground (CLG) represented
the true lengths (z_lengthi).
y _ lengthi ~ dnorm (µi , τ); where τ  1/ σ2 , the prior on σ ~ uniform  0,10 , and µi  z _ lengthi  β.
Here τ represents the precision parameter, and β is the estimate of the ratio of true length to
estimated length from the air. The inverse of the estimates of β were used as a correction factor
for all y_lengthi to estimate z_lengthi. Then corrected lengths were summed for each individual
transect, and the sum was divided by the transect length to calculate the ratio (rt) of active colony
to surveyed transect for each transect t (Odell et al. 2008). Mean ratios, μ_ratios, for each strata s
were calculated by averaging rt within a strata.
To correct for the misidentification of inactive colonies as active from the air, we
assumed that the designation of ‘active’ or ‘inactive’ on the ground represented the true state of
the colony (za) and za ~ Bern(ψ), where the prior on ψ ~ Beta(1,1) and is the probability that a
colony is active. This represents the latent or unobserved probability that a given colony transect
is active. The observed classifications (ya) are Bernoulli-distributed ya ~ Bern(pi), where pi is the
probability of classifying a colony as active. This formulation represents the observation process;
that is, the probability of identifying a colony as active versus the probability the colony truly is
active (ψ).
pi = za + cspec ×(1 − za); with a prior on cspec ~ Beta(1,1,) equals 1-specificity, or the
false positive rate (the proportion of inactive colonies that were classified as active from the air).
Therefore the probability of identifying a colony as active from the air is equal to 1 if the colony
is active on the ground (there were no active colonies identified as inactive from the air; i.e., no
false positives), and equal to cspec, the false positive rate, if the colony was not active on the
ground.
To calculate the proportion of occupied and unoccupied area for each stratum, we first
calculated the proportion of active and inactive towns on each transect (rt and ri). Then we
calculated the mean rt and ri for each stratum (county), μ_ratios. Finally, we multiplied the area of
each stratum by the stratum-specific ratio, μ_ratios, to determine the total area of active and
inactive colonies in each stratum.