All of the approaches in this section have in common that, whereas previously we were focused on estimating survival (accounting for detection variation, covariates, etc.) , now interest includes estimating "recruitment", as well as potentially estimating abundance at each sampling occasion if possible.
Before going too much further we should be clear on what we mean by "recruitment". Broadly speaking, we are referring to any entry into the population between marking periods of (by definition) unmarked animals. So recruitment can include births from within the local population, but also movement (immigration) of either adults or young from other areas. Depending on the study design sometimes we can separate these components, sometimes not.
The change in focus from survival estimation under CJS models (which was based only upon recaptures of marked animals) to recruitment and abundance estimation (which by definition includes unmarked animals) has important implications. Number one, obviously we now have to include the unmarked animals explicitly in the estimation model, a departure from CJS. Number two, in order to estimate anything we have to make some assumptions about the capture and survival processes and whether these are the same or different for unmarked and marked animals, or heterogeneous among animals. That is, in addition to CJS assumptions, we are now going to have to assume (most of the time ) that:
Unmarked and previously marked animals have the same probability of recapture, i.e,. capture does not behaviorally affect animals
All individuals in the population have the same probability of capture, i.e., there is not individual capture heterogeneity among animals.
You should recognize these strong assumptions as being essentially the same as the Lincoln-Petersen assumptions, and that is no accident.
Essentially, what has happened is that by having multiple capture occasions, we can either
Assume the population is closed, focus on abundance estimation, and robustly model capture heterogeneity or
Allow the population to be open, estimate abundance, survival and recruitment, but make very restrictive assumption about the capture process.
We cannot do both with a the basic, multiple CMR design, because there is no statistical free lunch.
Keep the above in mind as we go through some neat sounding approaches that produce estimates, to follow.