Trap dependence in CJS models

[Bryan Hamilton]

Hello,

I’m working with a snake species that may have a lower capture probability once it has been captured and marked. In the literature its been referred to as “spook factor” or “intimidation effect”. Similar to trap shy individuals in a closed capture framework, snakes avoid recapture. Snakes are captured at different ages and released. Their recapture probability would be relatively low the year after capture, then increases in subsequent years.

I want to model p with an open capture model, with a parameter representing this “capture shyness”. I think I have the time since marking (TSM) model figured out. Its just an age model (or an Age model), with the following PIMS.

Code: Select all

p(~age)
     1981 1982 1983 1984 1985 1986
1980    2    3    4    5    6    7
1981         2    3    4    5    6
1982              2    3    4    5
1983                   2    3    4
1984                        2    3
1985                             2


This allows p to vary as a function of time since capture. But I understand that as individuals are captured and released at different ages, the age model is not appropriate.

Can someone offer me any advice on modeling trap dependence?

Thank you.

[Morten Frederiksen]

Hello Brian,

I don't use RMark, but I'll try to address the general issue.

Trap dependence (either trap happiness or trap shyness) is a very common phenomenon in CMR data, there are all sorts of biological and methodological reasons. If you're talking about a behavioral reaction to first capture, it is simply a TSM model you're after. Since this is essentially an age model, you'll need to split your individuals into groups based on their age at first capture to keep track of both age and TSM effects on p. You should then be able to come up with an additive model including both factors.

On the other hand, if your species reacts in a similar way each time it's captured,what you want is a 'time since last capture' model. There are several ways to achieve this. The 'classical' way is to split the encounter histories at each capture and thus create a series of dummy individuals to replace the real individuals. U-CARE includes a utility to do this. You can then use a two-age class TSM model to include immediate trap-dependence, but you lose track of real age of your individuals. This approach is described in the book chapter by Roger Pradel, which you should read in any case:

Pradel R (1993). Flexibility in survival analysis from recapture data: handling trap-dependence. In: Lebreton J-D, North PM (eds) Marked individuals in the study of bird population. Birkhäuser Verlag, Basel, pp. 29-37.

Alternatively, you can use a multi-state approach (again this covers immediate trap-dependence). Here you include a dummy state (coded e.g. 2) which is never observed. You can then fix the nominal p to 1 for the observable state, and 0 for the non-observable state. The actual p is then modeled as the transition probability between the two states. Doing it this way retains age information, and it is simple to set up a model with both age and trap effects on p.

A third approach involves time-varying individual covariates, which show for each occasion the number of years since last capture. I haven't tried this, but it should be useful if you expect trap effects to last more than one year (or whatever your time interval is).

However you do it, the model with trap effects is only fully identifiable if the trap effect is additive to age and/or time effects (as explained in Pradel 1993).

Good luck!

Morten

[jlaake]

Thanks Morten for that very clear explanation. As Moten noted, the TSM model only includes the effect for the initial capture and handling. It is the time since initial release in CJS. To model a continuing effect if animals are always caught and handled to "recapture", you can split capture histories but that is a bit of a pain. It is not necessary if you use a time varying individual covariate which Morten also explained. The covariate value would be reset each time the animal was caught. For example, with a capture history of 100101 the time varying covariate values for RMark would be v2=0,v3=1,v4=2,v5=0,v6=1 assuming your times start at 1 and your time intervals are all 1(If that is not the case then the suffixes for v would be changed. See time varying individual covariates in the workshop notes.) v2 would be for p2, v3 for p3, etc. Then you could use ~v as the model to include a linear (on the link scale) trap effect over time. The intercept would be the probability of being caught at an occasion given the animal was caught at the previous occasion.

If you also had an age effect then ~v+Age provides an additive model with a linear trap and Age effect. Then the intercept is the the probability an animal of Age=0 was caught at an occasion given it was caught at the previous occasion. If you use ~v+age then the intercept is the value for whatever is the first level with the age factor variable.

To model a single time step effect on p, v is defined by shifting the capture history values to the right for the covariate. Using the sample above you would define v as v2=1,v3=0,v4=0,v5=1,v6=0. Note that now the intercept would be the probability the animal was caught given that it was not caught the previous occasion. If you wanted to keep the same intercept definition just change v to be 1- capture history value (v2=0,v3=1,v4=1,v5=0,v6=1).

--jeff

[gwhite]

There are also 2 functions built into MARK to make determining the previous capture time easy:

5. PriorCapL, PriorCapD functions.

These functions allow you to determine whether an animal was previously captured on the specified occasions. For example, priorcapl(i,j) will return the value of 0 if the animal was not previously captured on occasions i, i + 1, i + 2, ..., j, and 1 if the animal was captured during this set of occasions. Priorcapl(i,i) is valid -- again returning 0 if the animal was not captured on occasion i, and 1 if it was captured. Priorcapd(i,j) is equivalent but tests whether an animal was detected in the D part of the LD pair of the encounter history.

[jlaake]

Very nice feature but don't try to make that work in RMark. It will not. --jeff

[Bryan Hamilton]

Thanks to everyone for the advice. I still don't fully understand how an age model differs from a TSM model, even though I'm marking animals at different ages. If I don't think the response varies by age, an age model seems appropriate to model trap response. I'm not sure what I'm missing here?

Another question. I notice that some authors find the model with the best fit for p, then those parameters to model Phi. That would greatly reduce the complexity of the model set and should produce more robust estimates of survival. Any thoughts on that as a strategy? I've heard p described as "nusiance parameter" something you want to use to get the best estimate of Phi. But then I see a lot of papers that build their a priori model set with various combinations of Phi and p.

I'm working through the trap dependence example in Appendix C of the Mark Book (p. 76). I've broke the "create.td" function up so I can follow what's happening. It creates time dependent dummy variables of "1"s and "0'"s based on whether the individual was captured in a given sampling period. I'm still trying understand the real parameters for that example. I'll probably have more questions later but as I understand the results, the capture probability following release is generally lower than the other times. Then it increases. This would suggest trap avoidance?

Thanks again.

[jlaake]

Thanks to everyone for the advice. I still don't fully understand how an age model differs from a TSM model, even though I'm marking animals at different ages. If I don't think the response varies by age, an age model seems appropriate to model trap response. I'm not sure what I'm missing here?

I'm not sure what you are missing either. If you think age of the animal affects its capture probability or survival then you should create groups in your data and assign an initial age for each group. There are examples of this in the documentation. If you do that then the age variable in the design data is group-specific and it will NOT be time since initial marking. However, you can create a new design data field and call it TSM and give it the value of Age - initial.age. Then you can use a model ~Age+TSM or ~age+TSM.

If you don't think age affects capture probability or survival, don't assign initial ages and age and Age are factor and numeric versions of TSM.

The create.td function creates the time varying individual covariates that I mentioned in a previous email.

Please keep your posts to a single thread and put posts in the relevant sub-forums. Your question about model fitting approaches is not relevant to the RMark sub-forum.

--jeff