model selection for a sea turtle nesting population

[mcazabon]

I am working with tagging data from a leatherback nesting population, and trying to choose a model in MARK to estimate abundance, but am having trouble deciding between closed and open models.
I would appreciate any help you can give me to help me choose the most appropriate model for my data.

I have 4 months of data. On average, each turtle nests 6 times, once every 9 days. So throughout the sampling period turtles come and go. Turtles encountered early on for example would not be expected to be available for encounters towards the end of the season etc.
I have found a couple of other studies with similar datasets which used closed capture models, assuming that within one nesting season the population is closed. However, my concern is that the probability of capture varies with time for each turtle.
Of the studies I have found, one used multiple years of data with the Open robust design multi-strata model which fit well since turtles do not generally nest in successive years (the primary sampling sessions) but skip years.
But i only want to work with one years data. The other study i found used the Darroch Mt model where capture probabilities vary by time or trapping occasion.
Does this approach fully take into consideration the fact that turtles would not be encountered throughout the whole season? I have read that this model assumes each animal has the same capture probability on any given sampling occasion. That concerns me - I don't think that is an accurate assumption in this case - depending on how many times a turtle has nested, the capture probability would be different from other turtles. If a turtle has already nested 6 times, it is very unlikely to be encountered again, but if a turtle has only nested once, then it has a much higher chance of encounter.
Also, in this approach they divided the population into cohorts based on the 9 day cycle, but my data does not fit this closely enough. (frequency of nesting varies too widely). So would it be appropriate to divide the season into consecutive sampling sessions of 9 days instead? (So each number in the encounter history would represent whether or not an individual was encountered in that 9 day sampling period.) Will that type of data still fit this model appropriately?

SO
Are closed capture models best for my dataset?
Is the Mt model suitable?
Will dividing the season into consecutive 9day sampling sessions be appropriate for the Mt or any other model?
are there any alternatives you recommend?

Thanks!!!

[murray.efford]

I don't know there's a simple answer... It might help to know some more details. Were the data collected daily? Do you think all turtles that came ashore were detected? Maybe you could consider an open population model with fixed population size and 'age' dependent detection where animals are assigned age zero on first encounter.

[Bill Kendall]

I have run into this with hawksbills and leatherbacks. Your situation certainly calls for an open model. As you suggest, if expected nesting frequency is 9 days, divide the season into 9-day sampling periods (i.e., pool everything within those nine days). The idea is to have a separate sampling period for every time an individual lays a nest, to track her nesting history through the season. Because there is variability, for some females you will have two encounters per sampling period and then a gap, and for others you will have her in periods 3 and 5, even though those were consecutive nests. However, the same thing can occur if you make the interval longer or shorter. If you check out Chapter 15, especially 15.8, and most especially 15.8.8, you'll see I discuss this problem, and briefly consider how to "trick" the MS open robust design module into analyzing just one year of data. Of course if you did not want the probability of departure to be a function of how long the turtle had been nesting, you could just use the POPAN feature, which would include abundance as a parameter. However, the open robust design feature will give you abundance as a derived parameter while permitting departure to depend on time since arrival.

On a final note, I don't know about your population of leatherbacks, but my understanding is that they are not faithful to a given beach. If they are not using your study area faithfully, and if that within season movement process is Markovian, you will have some lack of fit.

I'd be curious to learn how it works out for you.

[murray.efford]

The population of interest is presumably the superpopulation of females that breed at some time during the season... Does a non-POPAN approach address this, Bill?

[Bill Kendall]

Murray,
The model I am talking about is still a POPAN like model, with the exception of the way departure probability is modeled. In fact by restricting the phi's to vary only by time, you get the POPAN model. Therefore the derived abundance estimate is the "superpopulation", which is the number of turtles that nest that season. The likelihood for this piece is (I believe) equivalent to your paper with Shirley Pledger in the last Euring proceedings, except at least in her talk she included an added feature of an option to include heterogeneity through mixtures.

[murray.efford]

Bill
Thanks for the clarification, and for your very clear writeup in the book (I should have read this first). The possible equivalence with Shirley's 'unknown time since arrival' models is new to us and worth following up.
Murray

[mcazabon]

Thanks so much for your advice! Especially to Bill!
I will try the open robust design as you suggested. This sounds more appropriate than the POPAN i think.

Bill, you also mentioned "Because there is variability, for some females you will have two encounters per sampling period" (when dividing the season into sampling sessions)
I certainly have encountered this, but have chosen to stick with 9 days and I only count one encounter in the encounter history when there are more than one in any sampling session.
Another contributor to this, is that sometimes we have turtles that crawl on the beach without nesting and sometimes they are inaccurately recorded as having nested when a nest was never confirmed.
Because we miss so many nesting events, when there is a gap I assume this is because we did not encounter the turtle, not that it was a longer than usual nesting interval.


To answer some of the questions that were raised:

"Were the data collected daily?"
Yes, data was collected daily, but data collection start late in the nesting season, fairly close to the peak of nesting activity. Also, data collection was restricted in most locations to the hours of 8pm to 1am - not all night.

"Do you think all turtles that came ashore were detected?"
I am certain that we miss a lot of turtles. This is supported by the fact that although each turtle would be expected to nest about 6 times within a season, the majority of the turtles we record are only observed once for the season.

"I don't know about your population of leatherbacks, but my understanding is that they are not faithful to a given beach"
My data actually includes that collected from patrols across 6 beaches, and a total of about 23km coastline, across 2 islands. (Trinidad and Tobago, WI). While leatherbacks show lower nest site fidelity than other species, they still stay within a range on the scale of kms. I believe that through our coverage of beaches we dont miss much because of movement. This year, of about 3800 turtles we recorded, about 200 were encountered on more than one beach. We also get few reports of our turtles from nearby beaches on the continent (Suriname, Fr. Guiana etc).


Thanks again for your feedback! I intend to give the open robust design model a shot, and will let you know how it goes!

Michelle