Robust design N estimate

questions concerning analysis/theory using program MARK

Robust design N estimate

Postby RBoys » Thu Mar 15, 2018 10:09 am

Hi everyone,

I am using the closed robust design conditional likelihood (Huggins model with only p and c) and so N is estimated as a derived parameter. Giving an estimate for each primary occasion. However, because of the data collection, an estimate of N from each primary period doesn't make so much sense. So I want to know if there is a way that I can get a single estimate of N from the whole study period in the Huggins model?

Thank you
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Re: Robust design N estimate

Postby ganghis » Thu Mar 15, 2018 11:31 am

Since the Huggins estimator is a constructive procedure there is no way to enforce a single value for N.

However, you might consider estimating a single value for N in a second step. To do this, you will need to enforce some sort of distribution for the collection of N's. For instance, I think it's most common to assume the sampling distribution of N is lognormal. Maybe something like

N-hat_i ~ lognormal (N, sigma_i^2 + 1/tau)

where N-hat_i is the estimate of N from the ith primary period, N is the single estimate of abundance you want and sigma_i^2 is your estimate of variance. I put in an extra variance component (1/tau) as "additional variation" that can try to soak up extra variation that isn't explained by sigma_i^2 (you may or may not want to estimate tau depending on how compatible your estimates are).

A model like this should be fairly straightforward to implement in JAGS. Maybe put a scale prior (see papers by Bill Link) on N, and a Gamma(1.0,0.01) prior on the precision tau which is pretty flat near the origin.

-Paul
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Re: Robust design N estimate

Postby RBoys » Thu Mar 15, 2018 11:38 am

Hi Paul,

Thank you very much for your reply, but I must admit that it has gone a little over my head!

As the N is not in the model likelihood, it is onky derived, I am not sure that I understand how to enforce the sampling distribution of N to be lognormal?
I am working in Program MARK, do you know if there is a way to do this in MARK?

Thank you very much and sorry for not fully understanding!

Rebecca
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Re: Robust design N estimate

Postby ganghis » Thu Mar 15, 2018 11:40 am

There is no way to do this in MARK
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Re: Robust design N estimate

Postby RBoys » Thu Mar 15, 2018 11:47 am

Hi Paul,

Ok thank you very much for your help one again!
I will have a look into JAGS.

Thanks,

Rebecca
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Re: Robust design N estimate

Postby Bryan Hamilton » Thu Mar 15, 2018 1:30 pm

Learning JAGS for one abundance estimate sounds pretty intimidating to me.....

Another way to get the estimate in MARK would be to use POPAN. This would be outside the robust design framework though so some information would be lost.

Could also divide number of capture by recapture probability.

Jeff Laake, creator of RMark, once recommended a method from a paper to me for abundance estimation:

Taylor, M.K., Laake, J., Cluff, H.D., Ramsay, M., Messier, F., xe and ois (2002) Managing the Risk from Hunting for the Viscount Melville Sound Polar Bear Population. Ursus 13, 185-202.
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Re: Robust design N estimate

Postby RBoys » Thu Mar 15, 2018 1:34 pm

Hi Bryan,

It definitely is, but I also think it's helpful to learn something new, you never know how useful it could be for the future!

However, I must admit that I am on a bit of a tight schedule with this work, so if there are simpler ways to estaimte this it would be very helpful to know about them.

When you say 'Could also divide number of capture by recapture probability', is this the capture probability divided by recapture probability, or do you mean the actual number of captures of individuals divided by recapture probability?

Thank you very much for the paper recommendation, I will have a look at this now!

Rebecca
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Re: Robust design N estimate

Postby Bryan Hamilton » Thu Mar 15, 2018 2:31 pm

Total number of individuals captured (minimum number known alive)/ recapture probability (p)

Hope that helps.
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Re: Robust design N estimate

Postby RBoys » Thu Mar 15, 2018 2:41 pm

Thank you very much Bryan, I will give it a try
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Re: Robust design N estimate

Postby jlaake » Thu Mar 15, 2018 3:00 pm

I think you are missing the point here. In the Robust design, N can change between primary occasions(between sessions), so there is no single N because you are assuming the population is open between sessions. There is an N for each session. No way to get around that. I assume Paul was trying to suggest a way to get an average abundance over the entire study. I'm not sure what Bryan is suggesting because what I think I suggested to him was a way to get an estimate of abundance from a CJS model and not a robust design. The RD is intended to give you an N for each session. CJS is not and is designed for survival estimation but if you assume marked and unmarked have the same capture probability, you can use the recapture probability to get an annual estimate of N. But if you have robust design data, don't go backwards.

Now if you are looking for an average abundance, then you can get the derived N's and their variance-covariance matrix and derive an average abundance over the sessions. Mean N will be sum of the N's divided by the number of sessions(k). Easy enough. Getting the variance is a little tricky but not that hard. Simply sum up all of the values in the vcv matrix for derived parameters and divide by k^2 and then take the sqrt to get the std error of that mean. That only accounts for the sampling variance however. Maybe missing a term here. Thoughts, Paul?

--jeff
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