Bayesian analysis of abundance for binomial sighting data with unknown number of marked individuals

The mark-resight method for estimating the size of a closed population can
in many circumstances be a less expensive and less invasive alternative to traditional mark-recapture. Despite its potential advantages, one major drawback of traditional mark-resight methodology is that the number of marked individuals in the population available for resighting needs to be known exactly. In real field studies, this can be quite difficult to accomplish. Here we develop a Bayesian model for estimating abundance when sighting data are acquired from distinct sampling occasions without replacement, but the exact number of marked individuals is unknown. By first augmenting the data with some fixed number of individuals comprising a marked “super population,” the
problem may then be reformulated in terms of estimating the proportion of this marked super population that was actually available for resighting. This then allows the data for the marked population available for resighting to be modeled as random realizations from a binomial logit-normal distribution. We demonstrate the use of our model to estimate the New Zealand robin (Petroica australis) population size in a region of Fiordland National Park, New Zealand. We then evaluate the performance of the proposed model relative to other estimators via a series of simulation experiments. We generally found our model to have advantages over other models when sample sizes are smaller with individually heterogeneous resighting probabilities. Due to limited budgets and the inherent variability between individuals, this is a common occurrence in mark-resight population studies.WinBUGS and R code to carry out these analyses
is available from http://www.stat.colostate.edu/~jah/software.