Bayesian analysis of abundance for binomial sighting data with unknown marked index

Brett McClintock, Master's Candidate,

Department of Statistics, Colorado State University

Friday, May 16, 2008

9:30 a.m.-223 Weber


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 mark-resight methodology is that the number of marked individuals in the population available for resighting typically needs to be known exactly.  In reality, this can be quite difficult to accomplish.  Here we develop a Bayesian model of abundance for 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 using New Zealand robin (Petroica australis) data recently collected in Fiordland National Park, New Zealand.  We then evaluate its performance relative to other estimators via a series of simulation experiments.  We generally found our model to have advantages over other models when sample sizes were small with heterogeneous resighting probabilities.  Due to limited budgets and the inherent variability between individuals, this is a common occurrence in mark-resight population studies.




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