Pradel f0

questions concerning analysis/theory using program MARK

Pradel f0

Postby sixtystrat » Mon Feb 06, 2017 12:03 pm

I am using a Pradel Robust Design model and cannot find any documentation on the parameter f0. What is f0 and how does it relate to lambda and phi? Thanks!
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Re: Pradel f0

Postby jlaake » Mon Feb 06, 2017 12:12 pm

f0 is the number not caught. The estimate of abundance is M+f0 where M is number caught during study. Look at closed capture models for derivation of this concept.
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Re: Pradel f0

Postby gwhite » Mon Feb 06, 2017 12:12 pm

f0 is the number animals captured zero times, i.e., f0 = N = M(t+1) for each of the primary sessions. Same f0 as all the closed models.
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Re: Pradel f0

Postby sixtystrat » Mon Feb 06, 2017 1:38 pm

Okay thanks. I don't remember that parameter being in past versions of the Pradel model. Why the change? The reason I am asking is that I want to constrain both lambda and phi as time invariant but don't want to run into problems since the 2 are correlated (forcing phi to conform with the estimated lambda). Does keeping f0 time independent help account for such effects?
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Re: Pradel f0

Postby gwhite » Mon Feb 06, 2017 1:46 pm

Leave f0 varying across primary periods -- otherwise you get a non-sense model. f0 is different than the f parameters of the Pradel model. If you make phi and lambda time-invariant, then f is also time invariant. But these constraints have nothing to do with f0.

f0 was put into the closed-captures models several years (maybe 3?) ago because too many people that should have known better were constraining the N parameter equal across primary periods, thinking that they were forcing equal estimates of population size. However, what was really happening was that they were forcing the number of animals not captured to be equal across primary periods, which is a non-sense model. So, I changed the parameter name to make it clear that you are really estimating f0, and then getting N as a derived parameter.

Again, f0 is a different parameter than f of the Pradel and Link-Barker models.
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Re: Pradel f0

Postby sixtystrat » Mon Feb 06, 2017 1:52 pm

Thanks Gary. Yes, I remember that about the old Pradel models, have to keep N time independent. Showing my age I guess...
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Re: Pradel f0

Postby sixtystrat » Mon Feb 06, 2017 2:09 pm

So I guess my question is, can I constrain both phi and lambda (with f0 time independent) and expect to get accurate estimates of both? The mark book seems to suggest this is a no-no but I was wondering if this had changed with the new parameterization. Thanks.
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Re: Pradel f0

Postby gwhite » Mon Feb 06, 2017 3:45 pm

What you shouldn't do is have a time-varying phi and a constant or trend model on lambda, because you are forcing the f values to meet the constraint of lambda = phi + f. If you have the same constraint on both phi and lambda, then the model would be valid (in that f would now have the same constraint).
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Re: Pradel f0

Postby cooch » Mon Feb 06, 2017 6:54 pm

gwhite wrote:What you shouldn't do is have a time-varying phi and a constant or trend model on lambda, because you are forcing the f values to meet the constraint of lambda = phi + f. If you have the same constraint on both phi and lambda, then the model would be valid (in that f would now have the same constraint).


All of which is discussed in Chapter 13 -- see section 13.4.1 This issue invariable comes down to the desire to look at trend (specifically) in $\lambda$. Ths issue (and pros and cons thereto) is discussed in Chapter 13, and also Appendix D, where a random effects approach to Pradel models is discussed.

Folks that haven't looked at the 'Pradel chapter' in a while might want to do a quick read through the current version. Fair bit of new stuff has been added over the past 12 months or so.
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Re: Pradel f0

Postby cooch » Mon Feb 06, 2017 7:10 pm

As Gary, and Jeff Laake have already noted, $f_0$ is simply the estimated number not caught. Abundance $\hat{N}$ is in fact estimated as the sum of individual encountered at least once (historically, $M_{t+1}$) plus the number estimated to have been misseed ($f_0). So, $\hat{N}=M_{t+1}+\hat{f}_0$. Note that $M_{t+1}$ is a count, not an estimate, and represents the minimum estimate of abundance. See section 14.2.1 in Chapter 14 for some of the basic bckground.

gwhite wrote:f0 was put into the closed-captures models several years (maybe 3?) ago


August, 2013 -- immediately following the second 'advanced MARK workshop'...

because too many people that should have known better


Larissa Bailey and I, who fessed up at some point during said workshop...

were constraining the N parameter equal across primary periods, thinking that they were forcing equal estimates of population size.


which Gary pointed out was sort of silly. But, we blamed him for letting MARK permitting us to be silly, so, ultimately, it was entirely Gary's fault. ;-)

However, what was really happening was that they were forcing the number of animals not captured to be equal across primary periods, which is a non-sense model. So, I changed the parameter name to make it clear that you are really estimating f0, and then getting N as a derived parameter.


which is discussed in Chapter 14.
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