Closed Robust design - how closed?

[JonL]

This refers to the Robust design as described in sections 16.1 to 16.6 of "the gentle introduction" and analysed in MARK chosing "Select data typ; Robust design; Closed captures".

Under "Assumptions" (section 16.5) it seems closure refers to the catchable population within a primary sampling period (several secondary samples). In my toad case (you are probably familiar with these creatures by now...) this means within a breeding season. This is a slight problem but can be reasonably fixed by pooling early or late capture occasions.

But what about the full study period, several primary samples (years/breeding periods)? The example (16.6.1) explicitly assumes no immigration or recruitment to the superpopulation but this is not really mentioned in the general introduction. For most multi-year studies addition of recruits (in this case first year breeders) is an important feature. Intuitively, it seems to me the model (unfortunately) should have difficulties handling a situation with new recruits arriving each year. Or does it manage? If so, are recrutiment rates hidden as some derived parameter?

The "Pradel Robust Design Survival and Recruitment" looks like an alternative but this does not seem to allow for temporary emmigration.

Am I stuck or is there a model where I can use a sample design with primary and secondary sampling periods to analyse survival and temporary emmigration when I have to assume a substantial recruitment.

Any suggestions are welcome.

[JonL]

I forward this reply in an email from Bill Kendall, at his request:

Don't be fooled by the example in 16.6.1. Evan generated the data that way for simplicity. Tha assumption of no recruitment is how the data were generated, but is not an assumption of the model. The RD model (Pradel version excepted; you're correct that it cannot handle unobservable states; this leads back to your original question about estimating superpopulation size) does not model recruitment. It uses closed models to get p* and population size, then conditions on first primary period of capture and models recaptures (and thus survival and transitions) in forward time. So new recruits are allowed, but they just get added to the critters being monitored once they are captured. Evan or I will insert a note in that example to avoide this understandable confusion in the future.

[cooch]

I forward this reply in an email from Bill Kendall, at his request:

Don't be fooled by the example in 16.6.1. Evan generated the data that way for simplicity. Tha assumption of no recruitment is how the data were generated, but is not an assumption of the model. The RD model (Pradel version excepted; you're correct that it cannot handle unobservable states; this leads back to your original question about estimating superpopulation size) does not model recruitment. It uses closed models to get p* and population size, then conditions on first primary period of capture and models recaptures (and thus survival and transitions) in forward time. So new recruits are allowed, but they just get added to the critters being monitored once they are captured. Evan or I will insert a note in that example to avoide this understandable confusion in the future.

I've been away, and just saw this. Bill is of course entirely correct. I used the simulation capability in MARK to generate the data for the example. As noted in Appendix A, simulation of the robust design model (discussed in Chapter 16) requires that the user enter parameters for the simulation that are interpreted differently than what is estimated. This issue occurs for the population estimates for the second and later primary sessions. The user would expect that the values entered for the population sizes for each primary session would be the actual population sizes. This assumption is true for the first primary session. However, for the second and later primary sessions, the value of N entered is the number of *new* animals entering the population at that point, i.e., N is now the number of animals available for capture that have never previously been available for capture (which could comprise recruits, for example). So, for the example, I simply set the number of new recruits to zero (as I recall) - made coding/analysis/interpretation simpler.