Violating the closure assumption in a robust design model

questions concerning analysis/theory using program MARK

Violating the closure assumption in a robust design model

Postby GDistiller » Thu May 30, 2019 8:14 am

Hi, I am hoping to get some clarity on a widely used reference related to the consequences of violating closure in a robust design model. Section 15.5 in the Mark manual discusses the assumptions of the RD model and says:

"If movement in and out of the study area is completely random during the period, then the estimator for p∗i remains unbiased." and the 1999 Kendall paper is referenced.

I've read the Kendall paper and have some doubts whether this is true. Figure 1 in the paper shows two scenarios and in a) movement into and out of the study area happens throughout the secondary occasions. Kendall says "In this case, the probability of being in the study area is at best confounded with capture probability" and then in the discussion he says "...although completely random emigration does not introduce bias to estimators for parameters associated with the superpopulation, the probability of temporary emigration is confounded with capture probability if it occurs at the same temporal scale as sampling."

If capture probability is confounded with temporary emigration how can p* be unbiased? I'm trying to resolve this apparent contradiction, especially since I know Kendall wrote the RD chapter in the Mark manual and so is unlikely to have gotten the reference wrong. Also, it seems to me that scenario a) in the paper is the more general situation whereas b) applies to quite specific situations.

Many thanks

Greg
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Re: Violating the closure assumption in a robust design mode

Postby Bill Kendall » Fri May 31, 2019 1:07 am

Greg,
Thanks for pointing out the need for some clarification in the Mark book. The passage you point out should have been phrased to something like "If movement in and out of the study area is completely random during the period, then FOR ESTIMATING THE SIZE OF THE SUPERPOPULATION,the estimator for p∗i remains unbiased."


Actually, I also need to make similar clarifications for the ingress only and egress only versions of that. These changes would make the chapter consistent with the paper.
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Re: Violating the closure assumption in a robust design mode

Postby GDistiller » Fri May 31, 2019 5:27 am

Hi Bill and thanks so much for the quick response. Just to double check that I understand things properly, is the bottom line that:
a) if there is random movement violating the closure, the estimates for N are unbiased although they then estimate the superpopulation rather than the local population.
b) And capture probability and temporary emigration are confounded.

If b) is correct, can one say anything about the capture probability and temporary emigration estimates or is the nature of the confounding unpredictable?

Many thanks

Greg
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Re: Violating the closure assumption in a robust design mode

Postby Bill Kendall » Fri May 31, 2019 1:43 pm

Yes, your points a and b are correct. Just to clarify, the superpopulation is the set of individuals associated with the study area for that primary period but not necessarily available at each sampling occasion (e.g., for a colony some may be making foraging trips on a given occasion). When this is a completely random process then capture probability becomes redefined as effective capture probability (availablility*detection), and p* is derived from these.

In terms of separating within-season detection from availability processes (e.g., temporary emigration), the situation is analagous to modeling unobservable states across primary periods. If you have a tertiary level of sampling (e.g., double observers at each sampling occasion), you could model the process flexibly (as in Kendall et al. 1997 and others). Without that extra level of sampling you could still attempt to model it, but less flexibly (as in Schaub et al. 2004 and Kendall and Nichols 2002). This type of work has been done on the occupancy side. Hines et al. modeled availability and detection of tiger sign along trails. Larissa Bailey's student Chinchani et al. (Conservation Biology) did a similar thing, but using two observers per sampling occasion.
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Re: Violating the closure assumption in a robust design mode

Postby cooch » Fri May 31, 2019 2:02 pm

Bill Kendall wrote:Yes, your points a and b are correct. Just to clarify, the superpopulation is the set of individuals associated with the study area for that primary period but not necessarily available at each sampling occasion (e.g., for a colony some may be making foraging trips on a given occasion). When this is a completely random process then capture probability becomes redefined as effective capture probability (availablility*detection), and p* is derived from these.


There are strong parallels (equivalences?) with this concept of the 'superpopulation', and the derived parameters in the POPAN model(s) -- chapter 12 in the MARK book.
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Re: Violating the closure assumption in a robust design mode

Postby murray.efford » Sat Jun 01, 2019 5:21 am

Evan - to me your meaning is obscure. The superpopulation for the robust design is a thing "the target population of interest" (some members of which may be unavailable at sampling) whereas I doubt that can ever be said for the POPAN model.
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Re: Violating the closure assumption in a robust design mode

Postby GDistiller » Tue Jun 04, 2019 6:43 am

Hi Bill
I just wanted to say thanks again for the replies and the clarification. I am supervising a student that fitted RD models to a dataset that is very sparse and so I don't think we are going to try and model the availability process. I just wanted some guidance on whether one can say much about the estimates of p, c and gamma because the secondary periods run for several months and so closure is likely to have been violated. The model produces a fairly high p, a very low c (time constant), and a very high gamma of like 0.95. But if detectability is confounded with availability then it seems as if we shouldn't read too much into these estimates.

Thanks again.

Greg
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Re: Violating the closure assumption in a robust design mode

Postby cooch » Fri Jun 07, 2019 6:08 pm

Bill Kendall wrote:Yes, your points a and b are correct. Just to clarify, the superpopulation is the set of individuals associated with the study area for that primary period but not necessarily available at each sampling occasion (e.g., for a colony some may be making foraging trips on a given occasion). When this is a completely random process then capture probability becomes redefined as effective capture probability (availablility*detection), and p* is derived from these...


Updated text for this section of Chapter 15 now online.
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