A General Methodology for the Analysis of Capture-Recapture Experiments in Open Populations

We trace the development of a likelihood function representation for the open-population capture-recapture (Jolly-Seber) experiment. We find that the modelling of the birth process in the general model is not consistent with the reduced death-only model and that all formulations to date lead to difficulties in imposing constraints upon the parameters of the birth process. We propose a generalisation to the usual Jolly-Seber representation that models births using a multinomial distribution from a super-population. We show how this leads to simplifications in the numerical optimization of the likelihood and how constraints upon the parameters of the model can now be easily imposed. We show how covariate models using auxiliary variables such as sampling effort or weather conditions to explain capture or survival rates can also be easily added. We also show how this model can be generalised to more than one group of animals. Finally a numerical example is provided which fits a class of models where the capture probabilities, survival probabilities and birth probabilities can each vary over time or among groups or both. This permits sequential model fitting within a comprehensive model framework; an approach akin to that of Lebreton et al (Ecological Monographs, 62, 67-118).