In the context of the Royle and Nichols (2003) model, a trade-off between the number of
sites and the number of sampling occasions have to be made. However, biologists may also
enhance the quality of data collection by better field methods and can induce changes on a
parameter such as the animal-specific detection probability. With existing difficulties in animal
abundance estimation, Bayesian inferential procedures are likely to be more useful from a
management standpoint, especially with low sample sizes. In this chapter,
* I construct a Bayesian Markov Chain Monte Carlo simulation approach using the Gibbs
sampler (Gelman, Carlin, Stem & Rubin, 1995) to estimate the parameters in the Royle
and Nichols (2003) model.
* I investigate the problems associated with the likelihood-based inference procedure in this
model for low sample sizes and suggest the use of a Bayesian approach with an informed
prior to more appropriately deal with this problem.
Methods
Royle and Nichols (2003) Model
Royle and Nichols (2003) use the occupancy based approach and assume that the
detection probability of a given species at a particular site is directly dependent on the abundance
of that species in that site for a given animal-specific detection probability and nothing else.
Consequently, the heterogeneity in detection probabilities across a system of sites is caused by
the heterogeneity in abundance across those sites. And, by modeling the variation in abundances
according to some probability distribution model (e.g., Poisson), they build a model based on
maximum likelihood to arrive at estimates of abundance in these sites.
The Royle and Nichols (2003) model is as follows:
p,= 1-(1-r)N' (2-1)
Here p, is the probability of detecting at least one animal within the site i.
r is the probability of an animal being detected in site i.
N, is the actual animal abundance at site i.