Population estimates from small data sets?

[jaxzwolf]

Hello,

I've been doing some work for an undergraduate thesis. I completed a capture-recapture study last summer and now I'm working to obtain population estimates from the data. The issue I've been encountering is that my data sets are very small. Because of time and budget constraints, I was only able to trap two areas for each of two treatments (four sites total). For one of the two treatments, I had no recaptures.

I realize this is a serious problem, but I was wondering if there is any way at all that I could obtain population estimates from this data set, even by hand? I've been able to get a few estimates using CAPTURE, but from what I've read these are unlikely to be very accurate.

I hope this is the appropriate place to ask this question, but no one I've been in contact with thus far has had any familiarity with obtaining population estimates from capture-recapture data. I would really appreciate any and all advice, and please let me know if more particular details about the study are needed.

[cooch]

Hello,

I've been doing some work for an undergraduate thesis. I completed a capture-recapture study last summer and now I'm working to obtain population estimates from the data. The issue I've been encountering is that my data sets are very small. Because of time and budget constraints, I was only able to trap two areas for each of two treatments (four sites total). For one of the two treatments, I had no recaptures.

I realize this is a serious problem, but I was wondering if there is any way at all that I could obtain population estimates from this data set, even by hand? I've been able to get a few estimates using CAPTURE, but from what I've read these are unlikely to be very accurate.

I hope this is the appropriate place to ask this question, but no one I've been in contact with thus far has had any familiarity with obtaining population estimates from capture-recapture data. I would really appreciate any and all advice, and please let me know if more particular details about the study are needed.

Well, to a fair degree, this is the right place to ask such questions. You mention trapping two areas for two treatments (4 sites total) - how many trapping occasions per location/treatment? Presumably (hopefully) at least 3, because without at least three is will be significant limits to what you're going to be able to do. Obviously, lack of recaptures is problematic (fatal) for the one location, but start with telling us how many sampling occasions per site/treatment.

[jaxzwolf]

I trapped four sites total, two for treatment A and two for treatment B. Each site had 45 traps and was trapped for 10 consecutive days, for a total of 450 trap-days/site. There were no recaptures for either of the sites in treatment B.

I hope I'm assuming correctly that by occassions you mean days spent trapping at each site? If so, there would have been 10 trapping occassions/site.

[cooch]

I trapped four sites total, two for treatment A and two for treatment B. Each site had 45 traps and was trapped for 10 consecutive days, for a total of 450 trap-days/site. There were no recaptures for either of the sites in treatment B.

I hope I'm assuming correctly that by occassions you mean days spent trapping at each site? If so, there would have been 10 trapping occasions/site.

Correct.

Alas, with no recaptures in treatment B, there are clear limits to what you can do. There are some games you could play assuming that encounter after first capture is 0, encounter effort is constant over sampling occasions, and treating the whole thing like a removal study, but that might be stretching it. If you're inclined, have a look at the Zippin estimator (as one approach) - see the recent book on 'Wildlife Demography' by Skalski, Ryding and Millspaugh. I think there is also some text on this in the 'big book' by Williams, Nichols & Conroy.

[murray.efford]

You could take this in a different direction: pool estimates of detection probability across treatments (given you have a fair number of recaptures in the other treatment). That won't wash if you have reason to think the probability differs between treatments, but with sparse data I'm guessing you don't. As you refer to 'trapping' (of small mammals?) I'm also guessing this is a problem calling for spatially explicit capture-recapture (see www.otago.ac.nz/density for references). Routine spatially-induced heterogeneity (due to the varying locations of home ranges in relation to traps) makes a real mess of Zippin estimates, so I wouldn't waste time on them. You can fit SECR models with the software 'Density'. Treat each site as a 'session' and use a 'between-session' ML SECR model to get site-specific densities while fitting a constant detection function across sites. Confidence limits will be wide, but please don't blame the analysis!

[cooch]

You could take this in a different direction: pool estimates of detection probability across treatments (given you have a fair number of recaptures in the other treatment). That won't wash if you have reason to think the probability differs between treatments, but with sparse data I'm guessing you don't.

Except that no recaptures in one treatment pretty well implies that recaptures differ between treatments, wouldn't you think?

I was suggesting a Zippin (or similar) estimate for the problem treatment, and then whatever technique might serve well for the other where there were recaptures. With no recaptures at all in one treatment, trying to find a single approach that works for both seems rather pointless.

[murray.efford]

I beg to differ: there may be no recaptures purely by chance, especially if the treatment has lowered density (we have very little to go on in the original post). Also: different methods for different treatments will give misleading results if the methods differ in bias, as they often do. Better to apply one method that works.

[jaxzwolf]

If you're inclined, have a look at the Zippin estimator (as one approach) - see the recent book on 'Wildlife Demography' by Skalski, Ryding and Millspaugh. I think there is also some text on this in the 'big book' by Williams, Nichols & Conroy.

Thank you for your advice, cooch. The Zippin estimator was one that I was able to obtain population estimates from using CAPTURE.

You could take this in a different direction: pool estimates of detection probability across treatments (given you have a fair number of recaptures in the other treatment)....You can fit SECR models with the software 'Density'. Treat each site as a 'session' and use a 'between-session' ML SECR model to get site-specific densities while fitting a constant detection function across sites.

Hi murray. I'm sorry if my original post wasn't detailed enough. I was trapping small mammals (tree squirrels). The two sites in the first treatment (A) were of intact, dense forest, whereas the two sites in the second treatment (B- the treatment for which I obtained no recaptures) were areas that have recently undergone restoration/mechanical thinning and removal of trees. I have reason to believe that squirrel denisty for treatment B would be much lower than for treatment A.

Treat each site as a 'session' and use a 'between-session' ML SECR model

I also apologize if I'm being slow, but this is my first time dealing with population analyses. SECR = spatially-explicit capture-recapture? To what does "ML" refer?

[murray.efford]

Thanks for the extra info - I do think it helps.
Yes, SECR stands for spatially explicit capture-recapture. ML stands for maximum likelihood (see a stats book); 'ML SECR' is a specific option in Density.

[jaxzwolf]

Hi murray,

I installed Density and input my capture-recapture data with each site as a different session. I then asked the program to "Read data," selected 'ML SCER' under "ANALYSIS GROUPS" and under the options checked "use between-session model." However, after making these changes and asking the program to "GO all," I receive the error "No valid data for intial values."

Am I doing something wrong? Would you be able to tell just from what I've described? I can be more specific, if you need.

Thanks~