Cormack-Jolly-Seber models: time and age perspectives

Survival is a key demographic characteristic in many areas including both human
demography and population ecology. However, it is often the case that data collection protocols are different in these areas, resulting in different models and methods of analysis. This paper is motivated for the different emphasis given to the elicitation of the temporal scale (and consequently, on the origin time) in ecological and medical survival studies. Specifically,
in medical studies, the origin time is often determined in advance with individuals followed over a period of time at regular (or irregular) intervals, thus focusing on time within study (or age to a given reference point). However, in ecological capture-recapture studies, the capture occasions are typically fixed in advance, with an imperfect detection process observing individuals at these times. Moreover, the temporal scale is often primarily specified at the capture occasion level. In this work we focus on an ecological capture-recapture study related to guillemots and compare and contrast two different temporal scales: (i) calendar (or capture occasion); and (ii) age (or time within study), in terms of the way the data may be represented and in relation to the ecological Cormack-Jolly-Seber-type model. The different temporal scales provides insights into the different underlying structures, which can then becombined into a joint (calendar and age) dependence model.