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Hi, I've added tsm within a POPAN model to account for transience. This is based on guidance from various other posts in here (I don't have the links to hand).

When I check the output of the phi~ tsm+time model it is exactly the same as the phi~time model without tsm, which makes me think I've done something wrong. This worked fine for the CJS, and I've seen a couple of papers that have used a similar method for POPAN.

Could someone please advise how I could correctly add tsm to the square PIMS in a POPAN?

Code: Select all

# add time-since-marking (as a two-age class) to ddl
capt.ddl$Phi$tsm = 1
capt.ddl$Phi$tsm[capt.ddl$Phi$age==0] = 0

#run for phi
Phi.time.tsm=list(formula=~time+tsm)

Output for Phi~tsm+time:

    2014     2015      2016      2017      2018
 0.6931365 0.862137 0.5720489 0.8306271 0.6485813

Output for Phi~time:
     2014      2015    2016      2017      2018
 0.6931331 0.8621404 0.57205 0.8306223 0.6485844



Thanks so much!

Here is what you did using the dipper data and hopefully it is obvious that you can't fit a time+tsm model because the time model fits a separate parameter for each time.

Code: Select all

> library(RMark)
> data(dipper)
> dp=process.data(dipper,model="POPAN")
> ddl=make.design.data(dp)
> ddl$Phi$tsm = 1
> ddl$Phi$tsm[ddl$Phi$age==0] = 0
> ddl$Phi
  par.index model.index group age time Age Time tsm
1         1           1     1   0    1   0    0   0
2         2           2     1   1    2   1    1   1
3         3           3     1   2    3   2    2   1
4         4           4     1   3    4   3    3   1
5         5           5     1   4    5   4    4   1
6         6           6     1   5    6   5    5   1


Technically you wouldn't have been fitting a TSM model. What you were proposing was a model where survival of previously marked (seen) animals was different in the intervals after the first one following their initial sighting. Not even certain why that would be the case. You could do that with a time-varying individual covariate but to be honest I'm not certain how that would be handled in MARK. It would have to know that the variable is 0 for unmarked animals in the likelihood and I'm not sure that would be the case.

POPAN is a Jolly-Seber type model and is not the same as CJS models. It is using the estimated Phi and p from the marked animals to model initial sighting of unmarked animals. For example, let's say that an animal entered the population prior to the beginning of the study but wasn't seen until the third occasion (001....). That means it had to survive two intervals Phi_1*Phi_2 and not be detected first two occasions but then be detected on third (1-p_1)*(1-p_2)*p_3. The values of Phi and p come from the marked animals. That is why p_1 is not estimable because there are no marked animals prior to the first occasion. See the problem?