Robust design models - temp trap v's permanent trap response

[cathrumm]

Hi

RE: models for robust design, specifically setting up PIMs to reflect the temporary trap response and permanent trap response models

I’m analysing a data set of a 5 year mark-recapture study on an endangered species of wallaby, the brush-tailed rock-wallaby, in NSW, Australia. The wallabies at two colonies were trapped twice a year, for between 5-7 sessions each period. I’m approaching each colony separately at present. The data set for colony 1 is 9 periods where each period has 5 sessions except for the 2nd period which has 7 sessions. (colony 2 has only 8 periods (as very first had no captures at all), with period 1 having 6 sessions otherwise 5 sessions each period).

I’m analysing the recapture only data first. Wallaby numbers are small (less than 20) and capture probabilities are small. I want to make sure I’ve sorted the Robust design for recapture before I proceeded with the additional information on resightings under the Barker and Barker/Kendall extensions. Unfortunately the next workshop closest, in NZ, has been booked up for some time. I’ve hit a block point and have been going round in circles and would appreciate some help getting through it so I can proceed!

I have been setting up PIMS so as to apply the models as described in Kendall et al 1995, within models that reflect Random, Markovian and No emigration in both situations where S and g are time dependent and/or constant. My question relates specifically to setting up PIMs to reflect the temporary trap response and permanent trap response models. Clearly I am misunderstanding something!!

I think my confusion lies in what the PIMs look like when I introduce a trap response between periods. From the literature I understand this to be called a permanent trap response, where the trap response in Period 1 is maintained throughout the other periods. To reflect this I have set my values for c1, c2, c3 ...c(i) (whether they be time dependent or constant within periods) to be equal. Having done this, Model b/b (ie trap response between/within periods) looks exactly same as Model o/b(null between periods/trap response within period); as Model b/tb looks like Model o/tb.

I just accepted this to be correct but got into uncertainty when I proceeded with what to do Model tb/b and Model tb/tb. When I continue with the same approach: for Model tb/b I set PIM values where c1= c2= c3 ...c(i) (even though the p(i) have a time response between periods), and for Model tb/tb where c1j = c2j c3j ....etc. But when I went to check this against the diagrams in Fig 1 and 2 in Kendall et al 1995, it seemed to not be right (because the c(ij) are already constrained in the way they say to adjust, and hence the c(ij) in my Model tb/tb looks the same as what the would be in Model b/tb). My understanding from the diagram is that for Model tb/tb the c(ij) would differ for each period - and in which case my Model tb/tb looks exactly like my Model t/tb.

Is my original understanding about how to reflect trap response between periods wrong? If all models come from setting constraints on either the Model t/tb and Model tb/tb then I thought I better clarify where I’m going wrong and what exactly the PIMS of these two models look like (i.e. as I set them up in MARK).

Does the answer rest in something to do with the design matrices which Kendall (in the Program MARK notes) refers to for establishing a relationship between p(ij) and c(ij) where there is both time and trap response within a period (which is something I am still to get my head around).

I plan to then take model with lowest AIC, and also then test with LRTs between nested models (and if different results indicate different effects then to go with the most parsimonious test). (although I’m confused by Help file saying that all closed models can be tested under Robust data type, but the Kendall paper says that can do Models with Mt and Mb within period (and presumably Mo models to test if these effects present in first place) otherwise calculate ad hoc.)

Any help would be much appreciated.
Thanks,
Cath Rummery