bmcclintock wrote:Hi Harry,
Based on your description of the data, it doesn't sound as though the mark-resight models in MARK can provide you with exactly what you're after (if this is indeed site population abundance, N, and site superpopulation abundance, N*, for each time period of interest). As dhewitt pointed out, all of these models require sightings and resightings to be organized into "closed" periods of sampling. More on what "closed" means can be found below and in Chapter 18 of The Book.
When individuals are regularly moving in and out of the site, the immigration-emigration logit-normal model in MARK provides N and N* if the exact number of marked individuals alive and available for sighting is known on each sampling occasion, but it doesn't sound as though you could possibly know this because you're using natural marks.
With an unknown number of marked individuals in the population, the Poisson-log normal model could be used, but this will only provide estimates of N (or only N* when geographic closure is violated).
For both models, demographic closure may be violated through mortality (yielding abundance estimates pertaining to the beginning of the sampling periods of interest), but individual heterogeneity in sighting probabilities should be accounted for in this situation. However, if new individuals enter the superpopulation (via birth or immigration) during the "closed" sampling periods, then the estimators would be biased.
The bottom line: it sounds as though you need an immigration-emigration model for an unknown number of marked individuals, but to my knowledge this hasn't been developed yet. However, it sounds like you could coerce (i.e., torture) the data for use with the Poisson-log normal model in a robust design to get at N (or N*), survival, and temporary emigration from the study area (or from the superpopulation). As always in mark-resight methodology, this is all assuming the marked population is representative of the unmarked population (in terms of sighting probabilities, etc.).
Cheers,
Brett
Thx a lot for your detailed answer, I think you're right - since we only use natural marks we cannot assure that the animals are within the site at the time we do the sampling. From the four years we have 28 animals which constantly return to the sight and will be spotted regularly (at least once within a week). From all the other animals we don't really know where they come from and if our "residents" are just part of a bigger population. The other animals which also show up regularly, but lack clear visual marks to be unmistakably identified, have been recorded by their number only. Like we have recordings of 12 known and 15 unknown animals which were at the observational site summing up to a total of 27 animals. That number is fluctuating by the number of unkowns only. We never spot juveniles; a distincting between immigrant or if others emigranted is difficult. From the isolated nature of the location one could assume that it must be a closed population, but we cannot say for sure, since the species is also well known for long distance migrations, even if they usually return to their home spot.
Anyway - maybe you are right and my request is something for my wishlist for Santa Claus - but maybe some sort of model could be modified to at least get a hint how big the population could be?
I would also love to discuss this in bilateral email or phone conversation but I understand that forum does not support such a function.
Harry