# Capture recapture for only two visit assuming a open population model

I have a study system where I’m doing a capture recapture analysis. I mark fish in one year and I’m recapturing a subset of them the next year.

I only have 2 capture events. Since a lot of time has passed, relative to the fish, between the two episode of recapture, I cannot assume a closed population model. Is there an alternative?

What mark-recapture model would be best for this situation given that I want to compute a recapture probability?

• I would assume your goal is to estimate the population size, is that right? Do you have any idea of the migration rate in and out of your population? – Remi.b Feb 5 '16 at 23:22
• Oh! Sorry, I forgot to mention that it's the recapture probabilities that I want. No I don't have the migration rate. – M. Beausoleil Feb 5 '16 at 23:27
• If the migration is 0, then it is the standard model. If the migration rate is 1, then the probability of recapture is 0. There is no way to estimate the recapture probability without having any information on the migration rate. – Remi.b Feb 5 '16 at 23:57
• What do you mean then by the standard model? – M. Beausoleil Feb 6 '16 at 6:04
• I randomly referred to one of the multiple existing models. But it was misleading. Sorry about that. If you only want to estimate the probability of recapture knowing the population size, then this probability is just the fraction of those marked and the probability to recapture a given number of them follows a binomial or hypergeometric distribution depending on whether there is replacement. I am not sure I understand your question... – Remi.b Feb 6 '16 at 6:34

In a classic closed population model, you can estimate population size with k=2 (where k is the number of events) but it's impossible to separate survival from recapture probability. Seeing this formula you could expect to be able to estimate recapture probability dividing R by S but it would be an error since S = M*survival (ø) *probability of recapture (p) . Therefore it's imposible to separate p from ø when k<2.

Hope it helps !

Cheers

If you have unique ID's on each of the fish (instead of just marked and not marked) then you could use the Cormack-Jolly-Seber open population model.

• Welcome to Biology.SE. Please provide some background to your answer, for example by providing an explanatory reference (and please also briefly describe what you reference which would be the CJS open population model in this case). I suggest you take the tour and have a look at how to provide what we consider good answers or your answer might be downvoted. Thank you. – AlexDeLarge Jul 17 '16 at 15:12