Huggins and the Closed 2-event expt.

[Owen]

Situation: Closed 2-event mark-recapture experiment -fish abundance.

I believe one can use measured fish length in a Huggins model to account for a length effect on probaility of capture. The simplest model would be that the length effect on probability of capture is linear and is the same for both events.

My question is : Can you allow the length effect to be different between the 2 events in this Huggins context? (Are there enough independent bits of information to allow you to do that?). I have a number of 2-event expts. to analyze, and the model where I've allowed the length effect to vary by event always floats to the top of the AIC league table (the other models: 1) Length effect constrained to be the constant over events and 2) No length effect at all ). The result makes me a little suspicious.

Thanks for any input.

[gwhite]

The question is, what do you use for a length for the occasions that you did not capture the animal? The Huggins model assumes a closed population, so it is hard to imagine that the animal could change in length very much. You have to have a length for ALL occasions, not just the one where the animal was captured, because in the closed captures model, zeros mean the animal was available but just not captured.

Gary

[Owen]

Thanks for the rapid response. We assume that the length of the fish does not changee between events. To put my quesiton in another way, is it legitimate to run the Huggins closed captures analysis for a two-event experiment with TWO length covariates (2 columns representing covariates in the design matrix), one pertaining to each event (i.e. a different effect of length on probability of capture in each event). Thanks again for any input.

[gwhite]

Certainly, as long as you have lengths for the zeros in the 01 and 10 encounter histories. I don't see how that can be the case given you didn't capture the fish on these occasions, but...

Just don't leave a zero in the design matrix -- because that zero will be used as the length.

Gary

[Owen]

Thanks again. So the following design matrix wouldn’t work?

Beta1 Beta2 Beta3 Beta4
1:P 1 Length 0 0
2:P 0 0 1 Length

It seems that this sort of arrangement is presented in Cooch’s book (section 11.3, bottom of page 11-15 for the phi parameters, except he has 2 covariates per time interval ). Is there an arrangement that would work if this doesn’t?

Something I’m not clear about in your answer is that I do have lengths for the 0’s in the 01’s (and 10’s) as I assume the lengths are constant between events and I’ve measured the length in the second (or first) event. Very much appreciate your advice. I'll hit the books again if I don't get it this time!

[gwhite]

This design matrix will work fine as long as you have a legitimate value of length for each occasion for all fish. I just didn't understand how you could have a differnt length value for each fish on each occasion. However, you are using the same length covariate (as specified in the design matrix) on both occasions, but just assuming different relationships for p1 and p2. Could be.

Gary

[Owen]

Yes, your last statement is my intention. Thank you very much for all the help.