General analysis and use of survival estimates

[mldavis13]

Dear All,

I have used the MARK book and RHelp resources to teach myself MARK and RMARK gradually over the past two years and have become stuck on a few different but interrelated points. Thank you for your time and for any insight you can provide!

1) I have mark-recapture data of known-ID roe deer at my study site. They are box-trapped over a ~4 month period each winter. I have data on about ~650 individuals over about 22 years. Note, I do not have specific capture occasions within winters so each winter is one event. So far, I have used RMark to estimate survival rates (Phi) of age-sex groups in the populations using what I believe are basic CJS models (stated in the output file). I have included some covariates (such as capture effort for p). I have then used the number of individuals captured and the estimate of p for a given winter to produce an estimate of abundance (N) for that year (i.e. N = counted individuals/p). Is this generally a valid use of the program?
2) I have run GOF tests on my processed data using program Release (called via R). Is this appropriate and sufficient for publication? Or is there more I should do within RMark? - I haven't seen the reference to c-hat as much in RMark as I did in Mark. . .
3) My understanding is that the methods described do assume population closure among events (years). Is this correct? Do I need to worry about closure within a given winter?
4) I’ve looked into trap happy/shy parameterizations but most of what I find seems to imply that this requires treatment of the population as if it were closed, so is not possible with my data. Is this correct?
5) I have semi-independent data on mortality rates of marked individuals. I have run binomial models of survival using these data (based on number of deaths and sample size each year) in order to test for climatic drivers. Is it possible for me run such models using the Phi estimates output by RMark? How would I calculate my sample size for a given occasion? Is it as obvious as using the number captured on that occasion?
6) Finally, over various analyses I have tested covariates for both p and Phi (with the ultimate goal of estimating population size). Interestingly, I have noticed that when I include a covariate for Phi it doesn’t appear to affect the estimates of p produced. This surprised me because I thought that the estimation of p and Phi was semi-simultaneous and that one would impact the other. Am I missing something? I feel certain I am getting confused somewhere.

[bacollier]

Dear All,

I have used the MARK book and RHelp resources to teach myself MARK and RMARK gradually over the past two years and have become stuck on a few different but interrelated points. Thank you for your time and for any insight you can provide!

1) I have mark-recapture data of known-ID roe deer at my study site. They are box-trapped over a ~4 month period each winter. I have data on about ~650 individuals over about 22 years. Note, I do not have specific capture occasions within winters so each winter is one event. So far, I have used RMark to estimate survival rates (Phi) of age-sex groups in the populations using what I believe are basic CJS models (stated in the output file). I have included some covariates (such as capture effort for p). I have then used the number of individuals captured and the estimate of p for a given winter to produce an estimate of abundance (N) for that year (i.e. N = counted individuals/p). Is this generally a valid use of the program?

You should know whether you are using a CJS or not as in RMark you have to define what MARK model you are using in the process.data(model="") statement. Did you type CJS in there? If not, I think CJS is the default model in MARK which is why it says that.

On your 'generally valid' question, I don't think the approach you are using is commonly used under a standard CJS model as the focus under CJS is usually Phi and p. Rather, if estimates of annual abundance are of interest, most folks use (since you have an open population) either a Jolly-Seber (POPAN perhaps) approach, or one of the various robust design approaches. But, with your only considering 1 sampling occasion in winter, neither of those will probably work.

2) I have run GOF tests on my processed data using program Release (called via R). Is this appropriate and sufficient for publication? Or is there more I should do within RMark? - I haven't seen the reference to c-hat as much in RMark as I did in Mark. . .

Remember that RMark is merely a front end for running MARK analysis in R, MARK is still what is being used in the background, so your c-hat is from MARK, not RMark.

3) My understanding is that the methods described do assume population closure among events (years). Is this correct? Do I need to worry about closure within a given winter?

Yes you need to worry about it as it is likely that your population is not closed across 'years' although if the only time you are trapping is winter then you might have closure in that period but you are not, as far as I can tell estimating any winter-specific parameters. Using a different approach than a CJS may alleviate some of the assumptions you are concerned about (e.g., RD designs allow for both open and closed periods, etc).

4) I’ve looked into trap happy/shy parameterizations but most of what I find seems to imply that this requires treatment of the population as if it were closed, so is not possible with my data. Is this correct?

You could code trap happy or tray shy responses to capture, but since your sampling occasion is 1 time per year, I doubt that you will see any annual responses in trap happy/shyness, but that is just a guess as happy/shy is usually shown in studies with much shorter intervals between capture than yours are (yours are annual if I understand correctly).

5) I have semi-independent data on mortality rates of marked individuals. I have run binomial models of survival using these data (based on number of deaths and sample size each year) in order to test for climatic drivers. Is it possible for me run such models using the Phi estimates output by RMark? How would I calculate my sample size for a given occasion? Is it as obvious as using the number captured on that occasion?

Perhaps, is the data known fate (e.g., from transmittered individuals) or just based on your capture data? You are able to incorporate climatic data into your models for Phi if you wanted too (see the section in the MARKBOOK on Linear Models)

6) Finally, over various analyses I have tested covariates for both p and Phi (with the ultimate goal of estimating population size). Interestingly, I have noticed that when I include a covariate for Phi it doesn’t appear to affect the estimates of p produced. This surprised me because I thought that the estimation of p and Phi was semi-simultaneous and that one would impact the other. Am I missing something? I feel certain I am getting confused somewhere.

Its plausible that no significant changes are found. However, if your interest is in population size, then I am fairly sure a standard CJS model is not what you want. You probably need to read MARKBOOK chapters 13-15 if abundance is your interest as CJS is not commonly used for abundance modeling.

[jlaake]

To continue on Bret's comments.

Median c-hat cannot be run from RMark. You need to export the global model (export.MARK) and then import into MARK and run median c-hat from there.

CJS can be used to estimate N in the fashion that you mention but it is ad-hoc and not fully efficient because CJS models don't use the initial capture event as "data". If you are interested in abundance I would do as Bret suggested. I and others have used that approach to estimate N with polar bears when covariates other than temporal ones (eg effort for p) are used.

--jeff

[mldavis13]

Hello both,

Thank you for your detailed comments!

Regarding CJS I am sure that CJS models are what I am running (this is the default and what MARK says in the output) - I thought given the flexibility of the CJS framework this is where I should start. I (perhaps mistakenly) thought my data were a fairly straightforward case. I'm rather unsure about a lot of this, as I have only the book to guide me.

Jeff - it was actually the Taylor et al. 2002 polar bear article that I was looking at to support my estimates of abundance. I used the "pop.est" function in RMark (based on n and p as described previously) and then calculated lognormal CI's around the estimates as suggested in that article. I understand that I am loosing a year in the process, but did I misinterpret this paper? Is there something wrong with the way I have described using the method given my data type?

I will look further into POPAN, I am very unfamiliar with this framework and have had trouble working through the material I have read on it. Is there a source I should be looking to other than the MARK book?

Thanks again,
Miranda

[murray.efford]

Given your interest in abundance, it is worth thinking of creative ways to use the within-year data. What is possible depends on the trapping scheme: Where was the trapping done? Was effort spread across multiple trap sites in each year, and recorded consistently? Were there within-year recaptures of individuals at different trap sites? It is possible in principle to estimate population size and density from the spatial 'footprints' of animals without separate within-year samples (e.g. Ecology (2009) 90:2676-2682) , and I'm curious whether that theory applies here.
Murray

[mldavis13]

I am interested in both the survival and abundance estimates available from MARK which I guess is why I am getting confused about the closure assumptions. I understand that the population is not closed between occasions (if there weren't deaths then how would the estimate of survival fit in?), but thought this was not a problem as long as each sampling occasion was over a short enough period to assume closure for that period (in my case a winter). Just to keep the threads straight I'm going to respond to the other suggestions by name:

Bret - you suggested JS(Popan) approaches but simultaneously say that they probably wouldn't work with my data type. I am looking more thoroughly at chapters 13-15 of MARK now but, if the methods listed there aren't appropriate given my data, do you have any suggestions on what else to look into?

Jeff - I notice that you mentioned that you used the ad hoc method discussed to "estimate N with polar bears when covariates other than temporal ones (eg effort for p) are used." (Taylor et al. 2002 I believe) Is there a reason why temporal variables (such as effort or climate metrics) would be a problem in this case?

Murray - Thanks for the suggestions. As for the sampling scheme, I have one site where the number was consistent across years and another where it was variable (ranging ~7 -14 locations) among years. In the latter case I have been trying to use the number of trap locations as covariate of capture probability (a rough index for one aspect of trapping effort). There are within year recaptures of individuals but I don't know if the "recapture rate/probability" would be high enough for a within year approach - I rather doubt it. I will look into the article you recommended, but perhaps given my spotty records of capture effort this might be difficult to apply. Any thoughts?

Thank you all again for the advice!

[murray.efford]

I was mystified, too, by Brett's POPAN comment. It would seem that JS(POPAN) estimates can at least be calculated. The problem to me is in the interpretation. If your deer are not restricted to a habitat island that you fully sample then you have a problem with the definition of the target population, especially in a multi-year study with possible between-year movement. Any N estimated across years will relate to an unknown and inflated catchment area. This is resolved by fitting a spatial capture-recapture model as I suggested.

Following your 'Murray' subthread...
So long as you know where and when traps were set and animals were caught (I'm not clear if it's the records that were spotty or the effort!), the software can handle varying trap locations and effort. Fewer than 10-20 recaptures per year would be a problem, but with so many years there is scope for multi-year models that take advantage of (more or less) constant per-trap detection parameters (while allowing the number of traps to vary). If you want to follow up on this, I suggest using the Density | secr forum.

[jlaake]

Jeff - it was actually the Taylor et al. 2002 polar bear article that I was looking at to support my estimates of abundance. I used the "pop.est" function in RMark (based on n and p as described previously) and then calculated lognormal CI's around the estimates as suggested in that article. I understand that I am loosing a year in the process, but did I misinterpret this paper? Is there something wrong with the way I have described using the method given my data type?

You didn't misinterpret the paper or explain incorrectly. But you do lose more than just a single year estimate. You lose information and precision using CJS approach unless you use the fully time dependent JS. In that case, from what I understand the CJS and JS estimates are equivalent. However, if you constrain parameters (e.g. Phi(.)) then the JS model abundance estimates should be more precise than the CJS estimates although I've not explored it or seen any paper on the issue. There is a paper by Judy Zeh on bowheads that makes the point relative to survival and presumably the same will be the case for abundance. However, if you have individual covariates then you are forced into using CJS approach (see below).

Jeff - I notice that you mentioned that you used the ad hoc method discussed to "estimate N with polar bears when covariates other than temporal ones (eg effort for p) are used." (Taylor et al. 2002 I believe) Is there a reason why temporal variables (such as effort or climate metrics) would be a problem in this case?

I should have written this better. It says "when covariates other than temporal ones". It is individual covariates that are the problem because you need to know the value of the covariate for all animals, seen and unseen. Temporal covariates are fine.

I hope this is more clear.
--jeff

[bacollier]

I was mystified, too, by Brett's POPAN comment. It would seem that JS(POPAN) estimates can at least be calculated. The problem to me is in the interpretation. If your deer are not restricted to a habitat island that you fully sample then you have a problem with the definition of the target population, especially in a multi-year study with possible between-year movement. Any N estimated across years will relate to an unknown and inflated catchment area. This is resolved by fitting a spatial capture-recapture model as I suggested.

Sorry to be so mysterious (which I guess is better than being wrong )

All I meant imply was that abundance estimation with CR models using data collected over time typically rely on one of the various JS methods or RD designs. Given the way the data were collected, Murray is right that one could fit a model such as POPAN and estimate period-specific N, but the interpretation would be difficult at best. Murray's solution is much better if the data he described are available and abundance during the winter is the objective.

Bret

[mldavis13]

Okay, thanks all, this is helping a lot.

I've asked my collaborators, about coordinates for the trap stations. I believe that I have the dates and locations of all captures available to me. I also believe that both the number and locations of trap stations has changed over the years, although the overall study area (the area encompassed by the trap stations) has remained the same (in size and geographic location) - according to my collaborators.

Unfortunately, the data pertaining to the number of nights the traps were set is non-existent for one site, so an important component of trap effort is missing.

Does this mean that the spatial footprint approach is not possible? Given the missing data, does this mean that the best I may be able to do is the POPAN (if that is even possible) method or the ad-hoc method with the CJS models as I have already done? Despite the short-comings of the data set, I want to learn as much as I can from it while limiting my interpretation as appropriate.

Miranda