Open population mark-recapture models including ancillary sightings : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University
A model is proposed for a mark-recapture experiment with ancillary observations obtained from marked animals any time between capture periods and throughout the geographic range of the animals. The model allows three types of emigration from the site where recaptures are made: (1) random emigration, where the probability an animal is at risk of capture at i does not depend on whether it was at risk of capture at i - 1, (2) permanent emigration where animals can leave the area where they are at risk of capture but not return, and (3) Markov emigration, where the probability an animal is at risk of capture at i depends on whether it was at risk of capture at i - 1. Under random emigration the likelihood function can be factored into a set of conditionally independent binomial terms used to estimate the parameters and a set of conditionally independent multihypergeometric terms that do not involve the parameters. Closed-form maximum likelihood estimators are derived under random emigration for models with age-dependence and a temporary marking effect. Contingency table based goodness-of-fit tests are derived from the multihypergeometric terms in the likelihood function. Contingency table tests of the age-dependence and temporary marking effect models are also derived. Explicit estimators do not appear to exist for permanent or Markov emigration. It is shown that the estimator suggested by Jolly (Biometrika 52:239, 1965), and as a consequence the estimator suggested by Buckland (Biometrics 36:419-435, 1980), is only valid if there is no emigration from the study area or if emigration is random. The estimator suggested by Mardekian and McDonald (Journal of Wildlife Management 45:484-488, 1981) for joint analysis of recapture and tag-recovery data is also only valid under no emigration or random emigration. By making appropriate constraints on parameters the models reduce to previously published models including the Jolly-Seber model (with age-dependence and a temporary marking effect), tag-resight models, tag-recovery models, and joint live-recapture/ tag-recovery models. Thus, the model provides a common framework for most widely-used mark-recapture models and allows simultaneous analysis of data obtained in several ways. Advantages of the new models include improved precision of parameter estimates, and the ability to distinguish between different type of emigration. FORTRAN programmes are developed for fitting the models to data with an application to a data set for brown trout (Salmo trutta) tagged in spawning tributaries of Lake Brunner, Westland between 1987 and 1991.