The above examples fit the "classic" CJS age-specific analysis, but situations can and do arise that deviate significantly from these designs and data structures. Here are a few:
>2 age classes- These can be accommodated if the initial ages are all known (back to our original example). Better yet, if (say) young, subadult, and adult classes can be identified, and there are releases of each age class each occasion, then age- and time-specific analysis extends in an obvious way. One upshot will be that now we generally will have to include age structure in modeling p (e.g., animals released as young will be recaptured at subadult rates the next occasion and adult rates subsequent occasions).
Some indeterminate ages- This happens when, for example, we are able to distinguish young from older animals, but not age classes within the 2nd year and older animals. This is very common (the usual situation with birds) and only really matters when it result in significant heterogeneity (e.g., SY and ASY birds have very different survival rates). There is not much that can be done about this, other than possibly to diagnose it through lack of CJS model fit.
Age transition and recapture intervals differ- This happens because capture/recapture is occurring either at faster or slower intervals than transition to the next age class, and which way this happens determines what can be done about it.
Recapture more frequent than age transition-This would happen if for example we are trapping >1 time per year but age transition is defined annually. This is easy to deal with, by simply keeping the age index constant over the appropriate interval, e.g, 1 1 2 2 3 3 instead of 1 2 3 4 5 6.
Recapture less frequent than age transition- This creates a more difficult problem, because we are actually collecting data at a different temporal scale than the process we are trying to model. The upshot in most cases will be the creation of "latent states" that can only be indirectly observed, and is probably best dealt with through Bayesian state-space or (possibly) multi-state models.
Stage vs. age transition - Multi-state models - All of the above is predicated on a predictable (deterministic) type of transition between states (ages): e.g., if 1 year (or whatever interval we define) elapses, an organism of age(i) goes to age(i+1). We could vary the interval (e.g., say that it takes 2 intervals for transition) without materially changing the problem. However, if we are dealing with developmental or other stages we have several possibilities:
Some individuals may transition over a given interval and others may not.
In some organisms, the state (or stage) transition can even operate in reverse.
When transition can be stochastic, bi-directional, or both, standard CJS methods no longer will suffice, and we are in the realm of multi-state models (MSM). MSM are an important but difficult area, and demand a level of data complexity beyond most study designs in order to operate. We will return to MSM later in the course.
Next: Review exercises