By the properties of a gamma distribution,
Mean = ab
Variance = ab2
From the home range information of adjacent sloth bears (Joshi et al., 1999), a maximum
density of 6 male bears and 3 female bears were observed using a common area and each bear
shared 50% or more of its home range area within the area of other bears. I assume that the
degree of overlap is independent of home range size, based on the logic that sloth bear home
ranges overlap due to the energetic costs that are involved in sustaining territoriality and the
home range size is a function of resource distribution and abundance. Consequently, I assume
that bear abundance per home range is invariant of home range size. I use this idea in deciding
the shape and scale parameters for the prior gamma distribution.
Using the information from (Joshi et al., 1999), I set the mean as 9 for the gamma
distribution. However, there is no prior information on the degree of variation in abundance per
home range. While I tried various priors to evaluate the performance of the model, I include
results from only two prior distributions, one being more informative than the other.
Analysis of actual data
Sloth bear home range size in the Nagarahole-Bandipur region was expected to lie within
the range of 10-25 km2. To ensure independence between sites and incorporating these home
range classes of this order, the analysis had to be performed with relatively low sample sizes
(number of sites). By the simulation results from chapter 2 with low sample sizes, I chose to use
the Bayesian approach to derive the posterior distributions of 2 and r. Four home range classes
were selected for the analysis (10 km2, 18 km2, 25 km2 and 50 km2). Although I tried various
combinations of shape and scale parameters for the prior gamma distribution, I present the
results from two prior distributions: