Problem using MSCRD with unobservable and dead states

[Billy.Requena]

Hello MARK users,

I'm trying to implement a Multi-Strata Closed Robust Design (MSCRD) model, but since I’m a new user of MARK, I’m not confident I’m doing it in the right way.
I have collected data on an arachnid species over a year (12 primary occasions), 3 or 4 days every month (secondary occasions), in a total of 46 sample occasions and 850 encounter histories. I classified individuals as females (state 1), non-reproductive males (state 2) and reproductive males (state 3). The main goal of my study is interpret Survival of all states and transitions between reproductive states of males throughout the study period.
In order to improve the quality of apparent survival rate estimate, I created two additional states: unobservable females (state 4) and unobservable males (state 5), both with fixed recapture rates (p=0).
Furthermore, I created other 3 states: dead female (state6), dead non-reproductive male (state7) and dead reproductive male (state , all with fixed recapture rates (p=0), as well as transition rates to any other state (all transitions fixed to ZERO).

Under such framework, I’ve made some constraints that I’m not sure if they are correct and I expose them below:

A) Transitions between any female category to any male category (and vice-versa) fixed at ZERO

B) Live females can only: stay as observable females (given they are alive), move to unobservable areas (given they are alive) or die. For males, they can: stay at the same reproductive state (given they are alive), move to another reproductive state (given they are alive), move to unobservable areas (given they are alive) or die. To avoid confusion effects, I fixed all survival parameters at 1 and interpreted transitions from live individuals to dead individuals as mortality rates estimates. At the same time, I interpreted transitions from observable states to unobservable states as temporary emigration rate estimates. Is that correct?

C) Assuming the mortality risk inside the area I’ve sampled is the same as at the surrounding area, transitions between observable individuals to dead individuals are equal to transitions between unobservable individuals to dead individuals (e.g. Psi 1 to 6 = Psi 4 to 6; Psi 2 to 7 = Psi 5 to 7)

Given now I have a model with 8 states, a bunch of transitions between each pair of them, several primary and secondary occasions, I’m using a co-variate to estimate the time effect and reduce the number of parameters.

Well, I’d like to know if I am in the right direction and f there is no bizarre mistake I’m making.
Thank you all

Gustavo Requena
PhD student - Laboratory of Arthropod Behavior and Evolution
Universidade de São Paulo - Brazil
http://ecologia.ib.usp.br/opilio/gustavo.html

[claudiapenaloza]

Hello Billy,

You've come up with very cool and advanced design, which is great (!) but there are a couple of things that might make it more simple (and ultimately identifiable, i.e., MARK will actually calculate what you want and not explode in your face

1) You don't really need the dead states unless you are recovering marked individuals in those states. Your usual "S" parameter will take care of deaths... you don't need to account for it as an extra state, again, unless you have data from that state.
2) You will probably need two unobservable male states... one for each reproductive state. They will be able to switch from, for example: obs.rep -> unobs.rep -> obs.non.rep, but not between unobservable states.

Otherwise, all your constraints were right... I recommend building it again without the dead states and re-evaluating to see which transitions will be allowed and which won't (I don't think that will be a problem for you, because your logic was right with the more complicated model)

You should end up with the following states:
1) Observable Female
2) Observable Male Reproductive
3) Observable Male Non-reproductive
4) Unobservable F
5) Unobservable M Rep
6) Unobservable M Non-rep

I recommend you take a look at the following papers for further background into how to set this up (if you don't have access to them, email me claudiapenaloza@gmail.com):
- Bailey et al. 2010 (Ecology, 91(6), 2010, pp. 1598–1604)
- Hunter, C.M. and H. Caswell. 2009. Rank and redundancy of multistate mark-recapture models
for seabird populations with unobservable states. Modeling Demographic Processes in
Marked Populations. D. Thomson, E.G. Cooch, and M.J. Conroy (editors). Ecological
and Environmental Statistics 3:797-825.

[Billy.Requena]

Dear Claudia,

Thanks for your help and sorry about my late reply.
In fact, the original sequence of 'structures' I have used to my data was:

1) A structure comprising only females, caring males and non-caring males, with the correspondent transitions. However, apparent survival estimates looked like strange and I built a new structure paying attention on unobservable states

2) So, I added two new states - unobservable females and unobservable non-caring males. I did not include unobservable caring males because they only reproduce and care for the offspring inside the area I've sampled. Therefore, if male individuals are unobservable, they HAVE to be in the non-reproductive state and that's the reason I just include ONE unobservable state for males. However, I obtained the same 'strange' apparent survival estimates. And that was the reason I built the bizarre structure I reported here.

3) A model including also de dead females and males states. However, all my friends that know MARK better than me and you had troubles to buy the last structure.

I said 'strange' apparent survival estimates because the best model selected to the data included three different estimates for survival, dependent on the group: female, caring male and non-caring male. However, one of them was estimated as 0.998, another as 0.995 and the last one as 0.992. Besides the incredibly high values, they do not look like so different. But thinking better about the system, individuals of the species studied (an arachnid) can live as adults more than two years and all values were estimated for an interval no longer than 30 days. Furthermore, although the best model considered three different estimates for survival (the delta AICc for the second selected model is more than 9), the magnitude of the effect seems to be not so strong and my decision was interpret this cautionsly. What do you think?

Thanks again

Billy

[claudiapenaloza]

Hello Billy,
Let me apologize for the delay, I had written you a lengthy response last week only to have the server boot me off and erase my work… urgent things got in the way of following up immediately after. Now for a shorter, though I hope still useful version of my first response.

1) If you are pretty sure your arachnids leave and return to the study area between your sampling sessions, you NEED the unobservable states, so good move there to have included them.
2) If you are sure the reproductive males do not leave the study area, then there is no need to have an unobservable state for them, well done again.
3) The problem with the dead states is that, unless you have data from that state (i.e., recoveries), the model is already "taking care" of your deaths when it calculates survival. Besides, transitions between states are "given that the individual survived"… if you think of this in the case of transitioning to a dead state it doesn't make sense because the individual did not survive if it died, i.e., transitioned to a dead state (see page 388 , or Chapter 10, page 28, of the Gentle Introduction, http://www.phidot.org/software/mark/docs/book/). So, no, do not include the dead states unless you have recovery data… in which case, we would need to talk again.
4) So you are calculating daily/weekly/monthly survival during one year for an organism that can live for two years… as you say, it is not unusual to get such high survival in that case. The differences you see between states may be the "beginning" of larger differences that you can't determine unless you have several years of data (>one generation time). Do the females "protect" the reproductive males? Feed them? Provide a "home"? Just curious if there may be a biological reason for the difference between reproductive and non-reproductive male survival.

I would say your highest ranked model is telling you something about real differences in survival between states. Whether or not the difference is small, there seems to be a difference. How are the CI's and SE's for the survival estimates?

Cool stuff! Keep at it.
Hope to hear from you again.
Cheers,
Claudia

p.s.: just to make things clear… when you use a Robust Design, you are actually calculating "Survival" (S), not "apparent survival" (Phi).

[egc]

Hello Billy,
Let me apologize for the delay, I had written you a lengthy response last week only to have the server boot me off and erase my work…

Unrelated to the post (thanks Claudia for giving this thread so much attention), but wanted to point out that the forum does have a 'session timeout' feature -- mostly for security reasons (long technical backstory which is not of general interest). At present, this 'timeout' is set to 25 minutes -- meaning for 'lengthy' replies, I suppose there is some chance that your session will timeout before you hit the submit button.

I'm going to leave this set as is for now -- if it becomes a problem, I'll make a change. The average 'reply/session' time is 3-4 minutes, so I'd assumed that (generally) a 25 minute timeout period should be sufficient,

Apologies to anyone else who might run into this. I suppose if you know you're going to take a while to post, you can edit/create the answer 'offline', and copy and paste.

[Billy.Requena]

Hello Claudia,

Thanks for your help and advice and sorry for my late reply, but I faced some troubles with models I'm building and it has driven me crazy in the last weeks.
For suggestions of some other people, I changed from the Multi State Robust Design models to Multi State Closed Populations models. The reason was that there is no reason to investigate if the probability of first capture in each primary sampling occasion (p) is different of the probability of recapture in subsequent sampling occasions within the same primary occasion (c) because we used the active searching method. Furthermore, we was not interested in any estimate of abundance of individuals (N).
What I'm doing now is pooling the capture-recapture data obtained during the sampling days of same month to generate a single sampling occasion per month, and reducing the estimates of parameters we are not interested now.
Making the long story short, in this system female approach males, they copulate and females leave the eggs under males' protection in a small territory. We are interested in the survival consequences of parental behavior to males. Females just abandon males with the eggs and don't come back to provide food or any help to them. They have really specific oviposition sites at the vegetation at the margin of forest streams and caring males are pretty philopatric, then we are really convinced that if males temporarily emigrates the sampled area, they were not in the parental state.
The problem I'm facing now is an overdispersed problem. Several females and some non-caring males were just captured once during the entire study period, and the observed c-hat is higher than 6.5. I don't know exactly how to proceed now and even the bootstrap procedure to estimate median c-hat is kinda weird.
Any suggestion will certainly be helpful
Thanks again

Billy

[claudiapenaloza]

Quick answer...
If you are SURE you have temporary emigration from the sampling area for any one of your states (if I'm not mistaken, the non-caring males and females) you should NOT drop the Robust Design.
You do not need to estimate "p" and "c" separately, just choose the "Huggin's Closed Capture" model in MARK (MARK/New File/Closed Robust Design Multi-state/Huggin's Closed Captures) and then make p=c in the PIMs.
If you don't use the Robust Design and your states do exhibit temporary emigration, your parameter estimates will be biased (could be highly biased depending on temp emigration behavior).

I'm sorry I can't help you with the c-hat problem...