Constraining the final p in removal models

[JGerb]

Hi,

I am working with three-pass removal data from brook trout streams in the Upper Peninsula of MI. I used the closed captures model and built the models {N,p(t),c(.)}, {M,p(.),c(.)} and fixed c=0 as it states in the manual. However, the time dependent model is invalid because of the lack of estimability for the final p. How should I constrain the final p? I can not constrain it to c because it is fixed at 0. Can I constrain the final p to the second p and if so how?

Thanks in advance,
Joseph, a confused grad. student

[cooch]

Hi,

I am working with three-pass removal data from brook trout streams in the Upper Peninsula of MI. I used the closed captures model and built the models {N,p(t),c(.)}, {M,p(.),c(.)} and fixed c=0 as it states in the manual. However, the time dependent model is invalid because of the lack of estimability for the final p. How should I constrain the final p? I can not constrain it to c because it is fixed at 0. Can I constrain the final p to the second p and if so how?

Thanks in advance,
Joseph, a confused grad. student

Actually, model {N,p(t),c=0) is not invalid - the only real estimate that is 'invalid' is the terminal estimate for p. The estimate for N (which is what you're after) should be unbiased. So, simply ignore the final time-specific estimate for p - if I recall correctly, it simply gets estimated at 1. Alternatively, constrain p(t) to be some function of an external covariate that you think actually explains time variation. One that is commonly used (again, as I recall - I don't "do fish", but have vague recollections of some papers) is to use a trend model, since you might imagine that each successive pass leaves a selected group of fish which might have different p that other fish.

If some of the real fish-squeezers have differing opinions, then I'm sure they'll chime in.

[cooch]

Actually, model {N,p(t),c=0) is not invalid - the only real estimate that is 'invalid' is the terminal estimate for p. The estimate for N (which is what you're after) should be unbiased.

Actually, in thinking about it for longer than 30 seconds, the estimate of N is probably biased from {N,p(t),c=0). So, you can either fix p(3)=p(2) (for such a simple model, its easiest to do this in the PIMs directly - see chapter 4 if all this is new to you), or use the 'constraint' or 'trend' models, as suggested in my first response.

[mcmelnychuk]

If you have some measure of sampling effort that varies among capture occasions, you could use that as a linear constraint for p. This could include a measure of gear quantity (number of traps, length or area of gillnet, anglers etc.) or soak/angling time, or a combination of these. Whatever you think might reasonably affect p (and whatever you've recorded in your field notebook!). The relationship could potentially be spurious with few capture occasions, though, so you should also try the constant p or trend p models like Evan suggested.

[JGerb]

Thanks guys, I will try to constrain p to a measure of sampling effort (i.e. minutes electrofished) or fix p(3)=p(2) and see what model fits the data best.

[cooch]

Thanks guys, I will try to constrain p to a measure of sampling effort (i.e. minutes electrofished) or fix p(3)=p(2) and see what model fits the data best.

Actually, you fit a series of plausible candidate models, then use model averaging. This is discussed at length - first in Chapter 4, then (in terms of mechanics) again in Chapter 14.

[JGerb]

If you have some measure of sampling effort that varies among capture occasions, you could use that as a linear constraint for p. This could include a measure of gear quantity (number of traps, length or area of gillnet, anglers etc.) or soak/angling time, or a combination of these. Whatever you think might reasonably affect p (and whatever you've recorded in your field notebook!). The relationship could potentially be spurious with few capture occasions, though, so you should also try the constant p or trend p models like Evan suggested.

I built a model constraining p to a unit of sampling effort (i.e. minutes electrofished) for each pass. The amount of sampling effort generally decreased over each successive pass. I also built a trend model with a descending p for each successive pass (due to less sampling effort). In these models the real estimates of p increased over each pass even though less sampling effort was put forth catching these fish. This seems odd, it trended p opposite of what I expected. Is this the result of a smaller pool of fish left in the sampling area? The estimate of N equaled the total number of fish captured over the three passes, which also seems odd. I should note my data are fairly sparse (an example of the number of fish caught on each successive pass: 14, 8, 3).

[mcmelnychuk]

Assuming that p should be positively related with sampling effort (minutes electrofished), I agree that it's strange that in the trend model you're seeing p increase over sampling occasions when minutes electrofished is actually decreasing over sampling occasions. A couple things that might help to consider (?):
1) Could there be cumulative effects of electrofishing? For the fish that got zapped on the first pass but didn't rise to the surface, could they be more susceptible to rising to the surface after the second pass zapping, compared to fish that didn't get zapped on the first pass? That could explain the increase in p over sampling occasions
2) In the model where you constrain p to be a function of minutes electrofished, does p also decrease over sampling occasions (similar to the trend model), as you would expect? If so, does it seem reasonable to go with this model?
3) When you plot minutes electrofished by sampling occasion, does the relationship appear fairly linear (you said it generally decreased)? Using a linear trend model forces it to be just that, but if the relationship is actually non-linear there could be some issues with the linear trend model.
4) In some removal models, people throw out the first sampling occasion because that's when all the dumb fish are generally caught, and they use the remaining sampling occasions to extrapolate to N. I'm not sure how this would fit in with closed capture models, and it might not be possible with only 3 sampling occasions.
5) Yes, the strange estimates could be related to sparse data, especially if you're estimating that you've caught all fish in the stream after 3 passes.
Cheers, Mike