Sight-Resighting Open Population

[sea-shepherd]

Dear all,

I'm struggeling a bit in finding the correct method to analyze the data I have collected.
I'm running a sight-resighting study where I can identify animals by its distinct marks. I was able to collect more than 700 sighting/resighting events in the course of the last 4 years.
For the moment I'd like to use the data just to come up with a estimate in population (super-population) size. No other question should be answered at this stage.
I have recordings of marked (known) and unmarked (unknown) animals; there is a constant in-and-out of new and old animals a closed population model therefore is not applicable. I was reading through chapter 18 of the MARK handbook but I'm not sure if this would be the correct method to analyze the date.
Could anybody out there please point me into the right direction?

Harry

[dhewitt]

You're on the right track, but there are a few critical issues you need to resolve. All of them are addressed in Ch 18 to some degree, and each needs careful thought.

For starters:

- Over what period (interval) do you wish to estimate (super)population size? Practically, which sightings/resightings are you going to use? If the answer is all of them over all 4 years, you might try to articulate if/why that number is necessary or useful. This will bring out details of the life history of your species (demographic closure?) and will help us understand what you're doing and why.

- Can you organize sightings and resightings into shorter, closed periods with the years so that a robust design analysis could be feasible?

[sea-shepherd]

I can break down the data from the entire period down to a single day in nearly every possible interval. I was under the impression that the more data I would have available the more precise the estimate will be.

Over an initial period I was able to identify about 25 individuals which return to the observational site more or less regularly, the others I observed do not carry either marks which makes them easy to be recognized or are just visitors from other sites.

Basically the study should provide a rough guess how big the population at that site could be and how big the super population around the island might be.

Harry

[sea-shepherd]

Typically my data shows data for each day with a number of known individuals which I was able to identify and a number of individuals unknown.

All 700 entries carry those two numbers resulting into a total number of animals observed. The question which troubles me is, is it possible to include the unknown individuals into some sort of statistical program to come up wtih something sensable?

[bmcclintock]

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

[sea-shepherd]

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