title: A comparison of abundance estimates from extended batch-marking and Jolly-Seber-type experiments.
abstract: Little attention has been paid to the use of multi-sample batch-marking studies, as it is generally assumed that an individual's capture history is necessary for fully efficient estimates. However, recently, Huggins et al. (2010) present a pseudo-likelihood for a multi-sample batch-marking study where they used estimating equations to solve for survival and capture probabilities and then derived abundance estimates using a Horvitz-Thompson-type estimator. We have developed and maximized the likelihood for batch-marking studies. We use data simulated from a Jolly-Seber-type study and convert this to what would have been obtained from an extended batch-marking study. We compare our abundance estimates obtained from the Crosbie-Manly-Arnason-Schwarz (CMAS) model with those of the extended batch-marking model to determine the efficiency of collecting and analyzing batch-marking data. We found that estimates of abundance were similar for all three estimators: CMAS, Huggins, and our likelihood. Gains are made when using unique identifiers and employing the CMAS model in terms of precision; however, the likelihood typically had lower mean square error than the pseudo-likelihood method of Huggins et al. (2010). When faced with designing a batch-marking study, researchers can be confident in obtaining unbiased abundance estimators. Furthermore, they can design studies in order to reduce mean square error by manipulating capture probabilities and sample size.
authors.affiliation: Department of Mathematics and Statistics, University of Victoria Victoria, British Columbia, Canada.
authors.forename: Laura L E
authors.initials: LL
authors.lastname: Cowen
authors.affiliation: Department of Statistics, Athens University of Economics and Business Athens, Greece.
authors.forename: Panagiotis
authors.initials: P
authors.lastname: Besbeas
authors.affiliation: School of Mathematics, Statistics and Actuarial Science, University of Kent Canterbury, Kent, U.K.
authors.forename: Byron J T
authors.initials: BJ
authors.lastname: Morgan
authors.affiliation: Department of Statistics and Actuarial Science, Simon Fraser University Burnaby, British Columbia, Canada.
authors.forename: Carl J
authors.initials: CJ
authors.lastname: Schwarz
keywords: Abundance; batch mark; mark–recapture; open population