A Unified Theory for Release - Resampling Studies of Animal Populations

Both capture-recapture and band-recovery studies can be conveniently modelled by one approach. The key is to view these methods as studies of cohort survival processes. Thus, in capture-recapture, as in band-recovery, attention is focused on survival rate, not population size. Probability models for the data are conditional on the known releases initiating each cohort. The first resampling of an individual after a release (e.g., live-capture, dead-recovery, live-resighting) effectively removes that individual from its release cohort. That individual may then be re-released as part of a new cohort. The re-sampling data are modelled as multinomial counts with a standardized form for the cell probabilities. The different resampling methods (e.g., live-recapture vs. band-recoveries) correspond to different model parameterizations. For capture-recapture, the complete model also requires the probability distribution of the unmarked animals caught on each occasion. That distribution, which is given here under the time-specific assumptions of the Jolly-Seber model, incorporates the recruitment parameters. The full distribution of the minimal sufficient statistic for the Jolly-Seber model can be given as a product of conditionally independent binomials. This representation of the minimal sufficient statistic greatly facilitates deriving variances and covariances. Goodness of fit tests for such cohort-survival data have two basic components. One component is identical for capture-recapture data and band-recovery data. The second component exists only for capture-recapture data; it uses information in subcohorts as defined by capture histories within each released cohort. The basic notation required in this modelling approach is much less than is typically used to develop capture-recapture models and the derivation of theory is more straightforward. Several special cases of the Jolly-Seber model are easily dealt with using this approach. Also considered here is the generalization of the time-specific model to allow different parameters to apply during the time interval i to i+l for individuals released at time i as compared to individuals released before time i and not captured (resampled) at time i. PREFACE The purpose of this report is to present some essential elements, as the author perceives them, of a unified approach to the statistical modelling and analysis of data arising from animal marking studies. This subject is often referred to as capture-recapture for open populations. The subject is, however, much broader than just capture-recapture taken literally. The essence of the methods is that animals are being sampled, somehow, from populations open to the dynamics of entry and loss. Sampled animals are "marked" in any …