Try to include as much empirical data in your model as possible :)

Dear Quinn Carvey

May be you must used a multi variate analysis bu using your data about breeding colony and inserted nearby breeding colony as supplementary data.

Also, if you can estimate migration between colony, you can added this parameter as factor to your analysis.

Good luck

A "site" is nothing more than a potential "state" where one of your animals, a puffin in this case, might be observed during a sampling period, summer months in your case. When you start thinking in states versus sites then the generality and purpose of the multi-state (aka but a poor replacement, multi-site) model should become much more apparent.

Although many of the earliest applications of this mark-recapture model-type involved multiple sites, such as a few from Jeff Spendelow's research, "site" was never intended to be a requirement or limitation of this model. Instead, any "state", such as a site, can be integrated into this model type as well as combinations of "states" such as site and sex as you're hoping to model.

Let's say you go to site b and observe a marked puffin that happens to be a known female. In your model, you'll define / name a state for observations of known females at site b, could be something like Fb. Elsewhere, on site c, you observe a marked puffin that is of unknown sex, that's another state in your model, you might name that one Uc. And on and on.

Names need to be kept as simple as possible to accommodate limitations of modeling software and the capacity of a human brain to keep track of lot's of info all at one time. If you're reading the lit on multi-state models, including those from Jeff's studies, then you'll have run into naming conventions. I advise adopting those regardless of my suggestions, above, that I provided off the top of my head.

You're going to use your model states to disentangle apparent survival ("apparent" makes implicit that survival, in this case, is confounded by permanent emigration from the study area) from dispersal by estimating transition probabilities between them. For example, what's the probability that a known female moves from site (islands in our case) b to c?

Once the concept of a multi-state model is clear in your mind then define all your states. Once you do that, you'll notice that some transitions are impossible, such as FB to MB, a female never becomes a male. You'll fix that state to zero in the software that you choose, such as Program MARK. By doing so, you'll reduce the number of parameters that will actually be estimated by, eg, Program MARK, when you run each model. Several transition probabilities will be set to zero in your base / starting model and those will remain this way all the way up to the most complex model that you integrate / consider in your model set.

Regarding the data set, by no means use only sexed birds, use ALL the marked birds you have access to.

Now let's review The BIG Rule in mark-recapture: get p high. P refers to detection probability. I mention this because of how you'll handle those "other sites", other islands in your case. If you rely on birds that originate / are marked on MSI versus those marked on any island then you run the risk of generating very low and poorly estimated (wide SEs) detection probabilities on those other islands. And worst case, the model may not even converge (be able to attain) estimates given how few birds will be detected on those islands on any given sampling occasion.

If instead, you use ALL marked birds from those islands then you'll get a much better estimate of p (relatively tight SE) and that estimate will likely be much higher and closer to truth than you'll accomplish in the absence of data from all islands.

Something else to think hard about is the concept of heterogeneity and what that means in the context of estimation of population parameters in a mark-recapture analysis. I refer here specifically to heterogeneity in p, detection probability.

To take an extreme, if a bird has a burrow next to the research cabin and so it's detection probability is 1; and another lives at a place rarely visited by the field team, it's detection probability 0.25. When you combine many of these two types of birds into a model without any concern for heterogeneity in detection probability then the model will suggest detection of ANY bird is about 1+.25/2 = 0.625.

Note that this isn't even close for either case, bird close to the cabin or the one in no-mans-land. The problem here is if you blow estimation of p, detection probability, because of this sort of heterogeneity then your population parameter estimates, such as apparent survival, will also be total crap!

The puffin collaboration in the Gulf of Maine has generated an enormous amount of potential for 1) generating very biased / misleading estimates of survival, dispersal, etc because of enormous variation in detection probability across islands and years; but also 2) enormous potential for generating very useful and rare population parameter estimates as long as heterogeneity, in particular, is modeled with care.

Note, there may be a multi-state model that integrates pop growth rate and abundance so that your analysis can be one step versus two. I've been out of the lit and the system from some time. I advise posting questions like this one to the Program MARK forum to get the latest advice.

Ahead of you is a very deep rabbit hole, but the wonders that reside there are well worth exploring if you have the time. If you decide to go there, then I wish you much more than luck.

It is not my profession please ask the concerned body