N hat = number of captures

[Bryan Hamilton]

I've been working through the transition from MARK to RMark with some small mammal data. I'm using a closed capture framework to estimate small mammal abundance on trapping grids. My estimates of Nhat are often equal to the number of animals I capture. I'm using the Otis model set and all the models give similar estimates of abundance. In some cases my standard errors are zero or approaching zero.

1. Do the estimates of abundance include the animals captured? I've worked through an example where they added the captures to the MARK estimate of Nhat. This was model averaging example and its not explained why this was done.

2. How common is the situation where abundance estimates are nearly equal to the number of animals captured? This is basically telling me that the capture probability is one. If this is correct, I could use the raw numbers of animals captured as my estimate of abundance.

Thank you.

[cooch]

I've been working through the transition from MARK to RMark with some small mammal data. I'm using a closed capture framework to estimate small mammal abundance on trapping grids. My estimates of Nhat are often equal to the number of animals I capture. I'm using the Otis model set and all the models give similar estimates of abundance. In some cases my standard errors are zero or approaching zero.

Then you're doing something wrong (or your data are lousy -- meaning, relatively few individuals encountered more than once). Are you getting more reasonable answers from MARK, or is the problem what you're generating in RMark?

1. Do the estimates of abundance include the animals captured? I've worked through an example where they added the captures to the MARK estimate of Nhat. This was model averaging example and its not explained why this was done.

Yes. N = M(t+1) + f(0). M(t+1) are number of individuals seen at least once (a count), while f(0) is the estimated number of individuals missed. For technical reasons, the likelihood for closed population abundance estimators is parameterized in terms of f(0), while N is then returned as a derived estimate (i.e., as the sum of M(t+1) and the estimate for f(0)).

If you're reading Chapter 14 of the MARK book, this is explained in several places...

2. How common is the situation where abundance estimates are nearly equal to the number of animals captured? This is basically telling me that the capture probability is one. If this is correct, I could use the raw numbers of animals captured as my estimate of abundance.

Also explained. From Chapter 14, section 14.3.1

...unless a constraint is placed on the last p, then the estimated abundance N will simply be M(t+1.)
Thus, it is diagnostic to check to see whether N= M(t+1), and if so, to see if the last pi estimate equals M(t+1). If they are, then you've forgotten to constrain p.

[cooch]

I've been working through the transition from MARK to RMark with some small mammal data. I'm using a closed capture framework to estimate small mammal abundance on trapping grids...

Cue Murray or one of the other SECR cartel for pointing out that if you're using a trapping grid, and having ordinates encounter data (which you no doubt do), you should probably have a long look at SECR and equivalent approaches to abundance estimation.

[Bryan Hamilton]

Thank you. I'll re-read chapter 14 (Chapter 15 in my old hard copy manual).

Great, another R package to learn....Thanks for the advice I will take a look.

I think my recapture rates are OK, here is a summary:

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0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
  10    8    5   12    3    3    6   10    6    3    7    8    5    9   29

I had the same issues when I was using MARK

[cooch]

Thank you. I'll re-read chapter 14 (Chapter 15 in my old hard copy manual).

Great, another R package to learn....Thanks for the advice I will take a look.

Only a suggestion, given the sort of data you probably have. There is the R package, and the older, somewhat less-complete (but still very useful) windows program called DENSITY. See the sub-forum on secr/DENSITY.

I think my recapture rates are OK, here is a summary:

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0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
  10    8    5   12    3    3    6   10    6    3    7    8    5    9   29

I had the same issues when I was using MARK

If this is the correct translation of your data into an .inp file:

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0001   10;
0010    8;
0011    5;
0100    12;
0101   3;
0110   3;
0111   6;
1000   10;
1001    6;
1010   3;
1011   7;
1100   8;
1101   5;
1110   9;
1111  29;


then you must be doing something wrong. I had no trouble generating reasonable estimates of p, or abundance, using these encounter frequency data.

Using a Huggins form, with and without individual random effects, I ran the standard 3 starting models ({p(t)=c(t)}, {p(.)=c(.)}, and {p(.),c(.)}). Here is the output of model averaging, with random effects:

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                     Derived Parameter N Population Size 1
Model                                     Weight    Estimate      Standard Error
---------------------------------------- -------   -------------- --------------
{sigma,p(.)=c(.)}                        0.63493   205.2092227    57.4924234
{sigma,p(.),c(.)}                        0.30867   187.5560239    46.7803327
{sigma,p(t)=c(t)}                        0.05640   205.3005257    57.6356810
---------------------------------------- -------   -------------- --------------
Weighted Average                                   199.7653724    54.1940098
Unconditional SE                                                  55.0280748       


and without random effects:

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                     Derived Parameter N Population Size 1
Model                                     Weight    Estimate      Standard Error
---------------------------------------- -------   -------------- --------------
{sigma=0,p(.)=c(.)}                      0.66785   128.3618669    2.3566863
{sigma=0,p(.),c(.)}                      0.27816   129.2458210    3.2348226
{sigma=0,p(t)=c(t)}                      0.05399   128.3318308    2.3478517
---------------------------------------- -------   -------------- --------------
Weighted Average                                   128.6061302    2.6004759
Unconditional SE                                                  2.6599399         


Note that models with random effects (sigma>0) were better supported in the data than were the models without random effects (sigma=0), which I suppose isn't surprising with trapping grids likely to introduce individual heterogeneity in capture probabilities.

Point here isn't to tell you which of the two estimates are 'correct', merely that your data are sufficient to get reasonable estimates -- with sensible SE's and the like. If you're not generating the same estimates of N for ({p(t)=c(t)}, {p(.)=c(.)}, and {p(.),c(.)}), then you might want to check how you've set things up.

[Bryan Hamilton]

I had 124 captures and the model estimates with random effects are 128. Those are pretty much equivalent. The standard errors are small too, around 2.At least close enough, I feel like I could use the raw abundance data.

Without the random effects, the model estimates are more variable. Do you know what the RMark code is for the Huggins model with random effects? I can't find that anywhere. Something to the effect of:

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model="HugFullHet

I probably am doing something wrong. I'll keep reading. And stop whining about more R packages.

Thank you again for your help.

[cooch]

I had 124 captures and the model estimates with random effects are 128. Those are pretty much equivalent. The standard errors are small too, around 2.At least close enough, I feel like I could use the raw abundance data.

Nope -- RE is 199, non-RE is 128 (ignore the title you see -- I generated the latter by fixing sigma=0, but that doesn't update the title for the RE data type). No reason you would have known that. I'll edit my post.

[Bryan Hamilton]

Is it possible to implement the Huggins model with random effects in RMark? I'm not sure what the model code is.

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model="XXXX"

[jlaake]

All of the models supported in RMark are listed in MarkModels.pdf that accompanies RMark and is stored in the RMark subdirectory of your R library directory. Also you can open MARK and look at Help/Data Types. I'm familiar with Huggins models with heterogeneity but not random effects but Gary is always adding new models.

--jeff

[Bryan Hamilton]

Thanks for posting the pdf. I've been looking for this for some time.

"Huggins' p and c with Random Effects" is the last MARK option under "Close Captures" and does not seem to be implemented in RMark.

I'd like to thank Evan and Jeff for responding. I don't think we always appreciate how lucky we are to have you two on this forum.