Help with parameterization for POPAN model.

[brid0030]

I'm running the POPAN model for a resighting study, and I am wondering what is the most appropriate way to parameterize the population size estimate. I have an experimental setup with treatment and control groups, and I am only interested in apparent survival of the marked individuals. As such, I know the population sizes of each treatment group. So N is going to be fixed. My question is whether to use different N parameters for each group (say 21, 23, and 27) or should I use a single N for the sum of the three groups (e.g. 21 + 23 + 27 = 71). My goal is to test how much model fit improves with the incorporation of treatment group labels, sex of the individual, and a body condition covariate. I've generated model sets with a single N estimate and with multiple N estimates. Using multiple Ns greatly improves fit, but I'm not sure that is the appropriate way to go. The effects of the factors and covariates are similar with multiple Ns and a single N, but they make a bit more sense with a single N (i.e. factors that ought to be important have a bigger improvement on model fit). Any advice?

[jlaake]

From what you said it sounds like you want to use a CJS recaptures only if you know the N's and are only interested in survival.

--jeff

[cschwarz@stat.sfu.ca]

As Jeff indicates, if you are interested only in comparing survival rates, then you should be using the CJS and NOT the POPAN models.

At the same time, before bashing your study through CJS (or any other model), you need to consider carefully the experimental design of your study.

For example, you mention that you have 3 groups (control, trt1, trt2), but don't mention how the experiment was set up. For example, if the three treatments are city, suburban, rural with animals marked in each, you have a classic case of a pseudo-replicated study (Hurburt, 1984) and your conclusions are limited. If the 3 groups are 3 treatments applied to individual animals in a randomized fashion, then you are in much better shape in regards to inference.

Carl Schwarz.

[brid0030]

Hey, thanks for the responses, Jeff and Carl.

In my study, the individuals were marked over a longish period of time (like 3 months), but the period that interests me (and the period during which all of the surveying was done) lasted a little over a month. So the encounter history has several individuals with 2 or 3 zeros before their first resighting. But I know they were out there. I chose POPAN because it counts these zeros as "present but unseen" if I fix the birth rate at zero (at least that is my understanding). Also, because this is a resighting study, no new marks enter the population during the survey effort. Wouldn't this violate the expectations of the CJS model?

As you have realized there are some problems with POPAN. Goodness of fit testing is problematic (I actually did this using CJS). And population size becomes a nuisance parameter. I'll play around with CJS and see if I can make it work.

By the way, the constituents of all three treatment groups are in the same population and field site. And they were more-or-less randomly assigned. I think I am OK with regard to pseudoreplication.

[jlaake]

POPAN will not treat them as present and not seen unless you fix all of the pent parameters to be 0 such that all enter prior to first occasion. To be honest I'm very confused about what you are doing. If you know that all are alive prior to the month of interest then you can use a release occasion prior to the month. But if you only know they are alive if they are seen that would not be correct.

What exactly are you doing? Is this a release of marked animals? Why are you only looking at the one month? If it was because your sampling up to that point in time was not complete you could always start with the initial release time and then start sampling occasions at the first survey in the month. That does mean you'll also have to estimate survival to the beginning of that month of interest but I can't see anyway around that.

--jeff

[brid0030]

OK, here's the full story. I did a study of migratory behavior on Dark-eyed Juncos. First, I captured about 85 Dark-eyed Juncos on their wintering grounds in Oklahoma and gave each a unique color band. This took about two months. Then I set up the mist nets again and caught 40 birds (most were recaptures). Of these 40, 20 individuals were held in cages for a week with all the food they could eat and then released. the other 20 birds were held in cages for a week on a food restricted diet before release. All of these release events took place over four days in early March. My research question is whether these feeding treatments affected spring departure.

When the birds were released, I started doing resighting surveys nearly every day (usually at least two surveys per day). Resighting rates were pretty good-- ~60% of birds known to be present. Most birds were seen nearly every day or every other day until they were (presumably) gone (migrated or dead).

So what I have is a bunch of control birds that were banded and released from January to late February plus a bunch of treatment birds that were released in early March. All of the birds show up in the surveys, but some of the control birds were missed in the first few surveys (as you would expect). After about a month, there were no juncos in the area. All had gone North presumably. So I'm trying to model apparent survival to evaluate the effect of treatment group (and I also have some individual covariates to throw in).

I posted about this study earlier, but didn't get much of a response. If you have any advice, Jeff, I'm all ears.

[jlaake]

There is no doubt that this is a CJS design because you are conditioning on the releases and asking what was their apparent survival. But you add a twist with the treatments being a subset of those that are
originally marked. I can see at least 2 ways to handle this. The first and easiest way would be to simply consider the first "resighting" of the control group as their initial release. You are mistaken with what
you said that you can't have new captures in a CJS design. The only down side would be that you would only be able to estimate apparent survival from the time you began your resight survey. However, it seems like you said that all were seen at some point during the resighting surveys and if that is the case then Phi will be 1 for the time period prior to the resighting surveys. If I'm mistaken on that point and you are interested in Phi prior to the resighting survey then I'd use the second approach which would be to use the first marking as the initial release and for those that were "treated" they would be a "loss" on capture and moved to the new group with their new initial release at the time they were released after treatment. For any of the 40 that were not marked originally, they would simply have a release after treatment. Regardless of how you handle it your comparison is only for survival during the period post treatment which would suggest using the first easier approach.

Let me know if you have any further questions.

--jeff

[cschwarz@stat.sfu.ca]

As noted earlier, this is indeed a CJS study.

If you have nearly 100% detectability every day, a known-fate analysis could also be used. You could then compare the kaplan-meier survival curves between the 3 groups starting in early March.

Carl Schwarz

[brid0030]

Thanks guys. It looks like I can make CJS work, and keep things simpler at the same time. Yes, all of the birds showed up in the surveys, so I will just regard the first resight as a "release" for the control birds.

I knew that you could have new captures in a CJS model, but I was (and am) still uncertain about how CJS treats the first few zeros before the initial capture. In theory those zeros could mean the animal was present but not caught or it could mean the animal was not yet born or immigrated. In my study there are no newborns or immigrants, so I was hoping that this knowledge could go into the model somehow. Probably no big deal though.

I don't think I have good enough detectability for a known fate model. It was about 60% each day. I suppose if I had nearly 100% detectability, I wouldn't even use Mark. I would just run simple stats with the last-seen date as the response variable.

Again, thanks for the helpful input.

-Eli

[egc]

I knew that you could have new captures in a CJS model, but I was (and am) still uncertain about how CJS treats the first few zeros before the initial capture. In theory those zeros could mean the animal was present but not caught or it could mean the animal was not yet born or immigrated. In my study there are no newborns or immigrants, so I was hoping that this knowledge could go into the model somehow. Probably no big deal though.

It doesn't. CJS conditions on first encounter only. Preceding zeros contain no information that is used in the likelihood.