Time intervals

[brouwerl]

I am analyzing a time dependent model with 2 ages classes of birds. These birds are usually ringed as a nestling in July, however, in some years I also have nestlings from January. In these years I have two occasions, thus time intervals of half a year. My time intervals therefore look like this:

1 0.5 0.5 0.5 0.5 0.5 1 1 1 1

If I want to run a model with 2 age classes for survival, one for the first year and one for the remaining years, will Mark take into account that the firs year for some individuals are two time intervals and for others just one?
I did the analysis with and without these January nestlings and they look quite comparable. Hopefully someone can help me with this.

Thanks,
Lyanne Brouwer

[jhines]

You can tell MARK which survival rates to apply with the parameter index matrices (PIMs). Capture-histories would be broken into two groups: 1) first captured as young, and 2) first captured as adult. The survival PIM for young should have different numbers on the diagonal (and the 2nd diagonal for years with 2 capture events) than the adult PIMs. For example, here's how a age*time survival model would be parameterized:

adult survival pim

1 2 3 4 5 6 7 8 9 10
2 3 4 5 6 7 8 9 10
3 4 5 6 7 8 9 10
4 5 6 7 8 9 10
5 6 7 8 9 10
6 7 8 9 10
7 8 9 10
8 9 10
9 10
10

young survival pim

11 2 3 4 5 6 7 8 9 10
12 13 4 5 6 7 8 9 10
14 15 5 6 7 8 9 10
16 17 6 7 8 9 10
18 19 7 8 9 10
20 21 8 9 10
22 8 9 10
23 9 10
24 10
25

Jim Hines

[brouwerl]

Yes, maybe my question was not clear enough. In this data set all birds are ringed as nestling. The normal time interval is one year (July till July next year), in two years however, I have resightings and new captures of nestlings in January as well (tropical bird with a small breeding peak in rainy season). If I then make a two age classes model, the first time interval for some individuals will be half a year and for others a year.
However, I adjusted the time intervals. (1 0.5 0.5 0.5 0.5 1 1 1 1 1)
Will these estimates be ok then?
I can't make two groups as the data set for those January birds will be too small. The only other thing I can think of is analyzing them as if they were a subadult in July, however, the nestlings that died before July won't be taken into account then.

Lyanne Brouwer

[jhines]

The intervals will be the same for both young and adults, but it sounds like the capture/resighting probability for adults in Jan is zero. Since you only band and release young, the PIM's would look something like this:

survival:

1 11 12 13 14 15 16 17 18 19
2 3 13 14 15 16 17 18 19
3 4 14 15 16 17 18 19
4 5 15 16 17 18 19
5 15 16 17 18 19
6 16 17 18 19
7 17 18 19
8 18 19
9 19
10

recapture:
20 0 21 0 22 23 24 25 26 27
28 21 0 22 23 24 25 26 27
21 0 22 23 24 25 26 27
29 22 23 24 25 26 27
22 23 24 25 26 27
23 24 25 26 27
24 25 26 27
25 26 27
26 27
27

Parameters 1-10 are young survival rates, 11-19 are adult survival rates. Parameters 28-29 are young recapture probabilities, and 20-27 are adult recapture probabilities. I put zeros in the recapture PIM matrix to emphasize the fact that the recapture probability for that cohort and occasion will be zero. In MARK, you would NOT put a zero in the pim, but use another parameter number (30) and fix it to zero. So, the recapture PIM would be:

recapture:
20 30 21 30 22 23 24 25 26 27
28 21 30 22 23 24 25 26 27
21 30 22 23 24 25 26 27
29 22 23 24 25 26 27
22 23 24 25 26 27
23 24 25 26 27
24 25 26 27
25 26 27
26 27
27

I haven't thought very hard about what parameters are estimable, but in this general model, I know that you would have to fix the last survival or recapture PIM (19 or 27). I suspect that you might have to fix some of the early survival or recapture parameters also (make constant over the first 4 occasions).