Limited-Information Modeling of Loggerhead Turtle Population Size

We attempt to estimate the size of a population of female loggerhead turtles. In traditional capture-recapture experiments to estimate the size of an animal population, individual animals are tagged and the information about which individuals are captured repeatedly is crucial. For these loggerhead turtle data, information about individual turtles is not available. Rather, we observe only the counts of successful and failed nestings at a location over a series of days (in our case, three). We view the turtles’ nesting behavior as an alternating renewal process, model it using parametric distributions, and then derive probability distributions that describe the behavior of the turtles during the three days via a 3-way contingency table. We adopt a Bayesian approach, formulating our model in terms of parameters about which strong prior information is available. We use a Gibbs sampling algorithm to sample from the posterior distribution of our random quantities, the most crucial of which is the number of turtles remaining offshore during the entire sampling period. We illustrate the method using data sets from loggerhead turtle sites along the South Carolina coast. We provide a simulation study which illustrates the quality and robustness of the method and investigates sensitivity to prior parameter specification.