Seeking advice on multistate model structure

[AdamC]

Hi there,
I am relatively new to mark-recapture analysis and so I feel I have just enough knowledge to be dangerous. With that in mind I thought it would be a good idea to run my current model past the much more knowledgeable folks here on the forum.

We have a population spread across 8 habitat patches and we're investigating the overall patterns of connectedness across these 8 patches. I've run a multistate model with patch as the state variable to get estimates of transitions between the individual patches. This runs fine and more or less tells the story we've been seeing on the ground for the last 15 years.

Now to drill down a bit deeper: how is patch connectedness related to animal age (Juvenile, Subadult, Adult). I can visualize a multistate model with the Patch*Age interaction as the state variable but that has 24 states, far far too many transitions/parameters to be reasonable. Furthermore we're not necessarily interested in comparisons at the individual patch level (i.e. We care less about a PatchA->PatchB transition than we do about a SomePatch->AnyOtherPatch, i.e. a dispersal event) so such a complicated models seems like overkill. Now onto the model:

The model has seven states outlined below:

1: All animals are given this state for the first capture and transition out during their first transition period. Animals in "1" state can transition into any of the other 6 classes. This state is necessary because all other states have memory of the previous capture, which is impossible to know at the first capture.

Fidelity States: If the animal is recaptured in the same patch as it was found in at the previous capture it enters a "fidelity" class. There are three age-based fidelity classes: Jf, Sf, Af

Dispersal States: If the animal is recaptured in a different patch as it was found in at the previous capture it enters a "dispersal" class. There are three age-based dispersal classes: Jd, Sd, Ad

To demonstrate by example:
Patch_ch: AA00BCAA
Age_ch: JJ00SAAA
Fidelity_ch: 1-Jf-0-0-Sd-Ad-Ad-Af

Is it reasonable to build the state variable with memory of the previous state like this? It lets us ask whether movement last year can predict movement in the coming year and whether that varies by age class. The model runs great and has interesting results but I can't shake the feeling that it violates some critical assumption that I have yet to encounter. So here I am seeking reassurance/correction/castigation/citations/etc.. Thanks!

[Eurycea]

I don't have an answer for you and I'm no expert,but one thing you might try is a further simplification.

For example, for your last two encounters, you have:

AA patch
AA size class

but you infer a transition from Ad to Af, which seems like it's a transition out of dispersal mode by virtue of not having dispersed? I'm having trouble wrapping my head around it.

If you are interested in dispersal vs. not, it makes more sense in my mind to code transitions between patches as going from one state to another, with two possible states. Using your example, i would code this as:

Aj Aj 0 0 Bs Aa Ba Ba

With the big letters indicating patches and little letters indicating size class. Thus any transition from A to B OR from B to A indicates a dispersal event. I think from that framework it would be simple enough to modify the PIMS or PIM chart in MARK to test for equal or different transition rates (dispersal) between size classes. You might note that A to B and B to A transitions are measuring the same thing, and to account for that in your PIM structure.

[AdamC]

Thanks Eurycea. I appreciate your comments and I am currently mulling them over. I definitely see how your model helps to simplify the comparison of the frequency of patch-transitions within the three age classes. At the same time it discards information that my model provides. I have to dig a little deeper and decide if that additional information is meaningful and important for our analyses. Once my wrap my head around it a bit better, I'll add another post here with my conclusions. If anyone else has additional perspectives I'd love to hear them.

[AdamC]

Update:
I thought I would post a comparison of the model I proposed and the model Eurycea proposed. Both have advantages and disadvantages. Eurycea's model better gets at the question of patch transition frequency and the effects of age. I didn't fix any transitions to be equal since this is just a preliminary look and I wasn't sure that assumption was true. All animals start in "A" and so 100% of animals that change patches make the A->B transition. So then, animals that make the B->A transition have already demonstrated a propensity to move and consequently might have a higher transition probability? (Note: I set "A-Juv" as the subtraction state and didn't calculate its probability, that's why it's missing from the plot)



My model is a bit different. Each state (except "1" or "First Capture") has a built in memory of whether that animal changed patches from the previous interval. So then the transition probabilities show whether previous dispersers are more or less likely to disperse again. And whether animals showing fidelity in the last transition period are more or less likely to show fidelity again.



So again, different models answering different questions. Any other comments or contributions would be greatly appreciated.