encounter history for "no immediate release"

[Natterjack]

Hey,
I have a short question:
My data don't meet one of the CJS assumptions (individuals are released immediately after sampling) and I wonder if I can still use them for a MARK analysis.
For tagging the individuals had to be kept inside over night and were released the next day after the next sampling occasion.
Could I
a) ignore the fact, resulting e.g. in the encounter history 001001... for an individual that was cought on the third sampling occasion, released on the fourth occasion and seen again on the sixth?
b) count the release occasion as "encountered", so the same case would look like this 001101...?
c) count the individual as unmarked on the first capture occasion and as marked after it had been released (000101...)? (although this doesn't make much sense in my opinion)

Couldn't find a model with an option for cases like that and would be glad about some help. Thanks!

[ganghis]

Hi,
In CJS you condition on release, so you could simply adjust encounter histories as you've suggested in (c). The approaches (a) and (b) will result in biased inference.

Paul

[JonL]

1. I do not really understand how Natterjack"s suggestion c above could be the correct solution. Suppose there were 3 recaptures and 3 new captures on day 3. For this day there were thus 50% marked toads in the sample. If new captures were not listed as 001xx but as 0001x MARK should assume there was 100% (all 3) marked toads in the sample of day 3. To me it seems very strange that MARK could make a dorrect estimate out of this. Can you give me a clue or is this situation elaborated somewhere, to your knowledge?

2. An alternative suggestion (as you understand I am also involved in this particular project): Because all toads (yes, this is about toads) were released the night after initial capture and their release always involved some search for new ones it should be possible to score them (again focusing on toads first time captured on occsion 3) as 0011xx. They were indeed captured on day 3 and, techically also on day 4. They were part of the population on both day 3 and 4. However, there was no real surprise they were captured, so to speak, on day 4. But this should be possible to account for. On the recapture PIM one could make sure that all recapture rates on the occasion after first capture carries the same code number. On the "fix parameter" screen one sets this parameter, by force, to 1. On the PIM, first time captures and other recaptures should probably carry a day specific parameter (becasue weather much influences capture rate) (but this is not part of teh present problem).

Any ideas about this suggestion?

[Natterjack]

Hi again,

I had the same problems JonL mentioned in 1. However, I tried to run a POPAN analysis - first with the encounter histories as described in a) and then I modified them as explained in c). The results were almost identical.
Still, there seems to be something wrong: We are interested in the population size, which is given by the model. There are different types of "N" which are mentioned in the manual, but I don't understand their biological meaning. The estimated parameter "N" obviously just gives the number of individuals we marked - not very helpful. Then, there is one derived parameter "N-hat" for each sampling occasion. If this is meant to be the number of individuals present at that occasion, how come the number is sometimes bigger than "N*-hat", which is supposed to be the super-population parameter/the total number of individuals in the population?

And then, I have another question: I'd like to use a JS model which includes the number of individuals that were seen at a sampling occasion but neither caught nor marked. The original JS model seems to include those numbers but it is not available in MARK. Is there another way?

Thanks in advance!