## Estimate N with given p and c

questions concerning analysis/theory using program MARK

### Estimate N with given p and c

I am trying to estimate population sizes for 4 hedgehog populations in one city. All four locations were sampled within a month for 8 nights. I was recommended to use a Huggins model for closed populations.
As two of the populations seem to have very low hedgehog densities, I estimated detection probabilities by combining all four data sets and using a Mo model with p and c being the same values.

Now I would like to get N estimates for the four populations individually using my averaged value for p and c (being the same). I guess this must be the easiest part of the analysis, but I cannot figure out how to do this in MARK. If I run the model with fixed p and c values, I don't get derived estimates. Can anyone help me? Thank you very much in advance.
Ataucher

Posts: 4
Joined: Thu Aug 10, 2017 10:08 am

### Re: Estimate N with given p and c

I am trying to estimate population sizes for 4 hedgehog populations in one city. All four locations were sampled within a month for 8 nights. I was recommended to use a Huggins model for closed populations.
As two of the populations seem to have very low hedgehog densities, I estimated detection probabilities by combining all four data sets and using a Mo model with p and c being the same values.

Now I would like to get N estimates for the four populations individually using my averaged value for p and c (being the same). I guess this must be the easiest part of the analysis, but I cannot figure out how to do this in MARK. If I run the model with fixed p and c values, I don't get derived estimates. Can anyone help me? Thank you very much in advance.

It's difficult to know exactly what you did given the limited details you provided, but you shouldn't need to fix p or c. If you haven't already, you should stratify your data into four groups (i.e., 4 sites). Then simply make all sites share the same intercept so that p=c and is constant among sites. You might also want to consider alternative models where there are 2 or 3 p parameters in a model and let AICc sort it out rather than enforcing constant p among all sites without assessing if this is a reasonable thing to do.

In the two p parameter model scenario, you could constrain one p to represent the two high density populations and constrain the other p to represent the two low population densities (i.e., 2 intercepts). In the 3 p parameter scenario, you could constrain p to be constant between the two low density populations and each of the high density populations could have their own estimate of p (i.e., 3 intercepts). I hope this helps!

Cheers,
Eric
ehileman

Posts: 35
Joined: Sat Nov 26, 2011 6:40 pm
Location: USGS, Fort Collins Science Center, Yigo, Guam

### Re: Estimate N with given p and c

Hi Eric

Thank you very much for your quick response. Unfortunately, I am a bit lost in how to implement your suggestion as I am still very new to MARK.
Maybe I can try to explain a bit better what I did:
I used the "Closed Capture Data Type, Huggins'p and c" with my data file, which contains the encounter history and group identity for each captured individual (I will attach it at the bottom). Then I set the encounter occasions to 8 and the attribute groups to 1 (not sure if that's right, but it won't run with 4).
Then I just ran all 'Pre-defined Models' and chose the 'Model Averaging' to get the Real Estimates.
I thought I could then just use the averaged p and c values to estimate N for the 4 sites.

Then simply make all sites share the same intercept so that p=c and is constant among sites...In the two p parameter model scenario, you could constrain one p to represent the two high density populations and constrain the other p to represent the two low population densities (i.e., 2 intercepts). In the 3 p parameter scenario, you could constrain p to be constant between the two low density populations and each of the high density populations could have their own estimate of p (i.e., 3 intercepts).
This sounds great, could you tell me how I do this in MARK? I found ways to constrain p and c values in the POPAN models but not in the closed capture models.

Thank you very much for your help.
Cheers,
Anouk

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Ataucher

Posts: 4
Joined: Thu Aug 10, 2017 10:08 am

### Re: Estimate N with given p and c

Then I set the encounter occasions to 8 and the attribute groups to 1 (not sure if that's right, but it won't run with 4).

Hi Anouk,

Your data are not formatted properly. You should be coding sites as groups (i.e., factors). You currently have it coded as a covariate (incorrectly, I should add--you are missing the 1 prior to the covariate). To code it as four groups, it should look like this: 00101100 1 0 0 0; In this example, the capture history would be from an individual from Site 1. An individual from Site 2 with an identical capture history would look like this: 00101100 0 1 0 0; Following this idea through, Site 3 would look like this: 00101100 0 0 1 0; and Site 4 would look like this: 00101100 0 0 0 1;

I suggest you read or reread chapter 2 on data formatting in the book. Constraining models is explained in chapter 6, but you'll likely need to read chapter 3-5 to understand chapter 6. If you haven't already, you should also read chapter 14 (Closed population capture-recapture models). Running models via the 'Pre-defined Models' option is ill advised if you don't have a thorough understanding of the models and their structure. If you read the above chapters and go through all of the examples Evan and Gary provided, you should have no problem figuring this out for yourself.

Good luck!

Eric
ehileman

Posts: 35
Joined: Sat Nov 26, 2011 6:40 pm
Location: USGS, Fort Collins Science Center, Yigo, Guam

### Re: Estimate N with given p and c

Hi Eric
Thank you very much for the correction on the formatting! I will happily read the other chapters (chapter 14 I have already read multiple times ).
Thanks a lot for the help and pointing me in the right direction!
Cheers,
Anouk
Ataucher

Posts: 4
Joined: Thu Aug 10, 2017 10:08 am

### Re: Estimate N with given p and c

Thanks a lot for the help and pointing me in the right direction!

My pleasure. Happy to help!

Cheers,

Eric
ehileman

Posts: 35
Joined: Sat Nov 26, 2011 6:40 pm
Location: USGS, Fort Collins Science Center, Yigo, Guam