The models and data structure we just considered are premised on the original idea of the RD, which was that all the 'open-ness' occurs between the primary periods, but during the primary periods the population is considered closed. But there arise situations in which it might be reasonable to allow the population to be open to certain types of transition, even during the primary periods. Bill Kendall, in the MARK book section 15.8, motivates these models with an example of nesting sea turtles, which can potentially arrive and depart from nesting beaches essentially continuously during a nesting season, leading to violation of the closure assumption (if we view a nesting season as a primary period). These models get even more complex than the "ordinary" RD and there are serious questions of parameter identifiability (so what can be legitimately estimated and what can't).
The Open RD is implemented via the model type "ORDMSState" in RMark, meaning that the model is actually a type of multi-state model (to be continued next). The idea is that one of the states (commonly denoted as "1" in the capture history) is observable whereas the other (e.g., "2") is not, and thus never appears in the capture history. I have reformatted the robust example here as an Open RD model in the attached script to illustrate. However, since the data were not collected under circumstances justifying the "open within primary" assumption, the parameter estimates will not be especially meaningful, and the example is just for illustrating the mechanics of how to run the model.
Anyone contemplating using these models will first need to know the Closed RD inside out, second get a very firm grip on the additional literature and notation, and third, likely consult with someone who actually has used these models. In general I do not recommend the use of the ORD models by anyone except advanced users of MARK/RMark, and again, this should be in consultation with someone who has experience with using these models for practical examples (which I do not).