"Quasi Lincoln-Petersen" with multiple occasions

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"Quasi Lincoln-Petersen" with multiple occasions

Postby stshroye » Fri May 26, 2023 5:21 pm

In my natural resources agency, it is common for biologists to estimate population sizes of fish in lakes using what I'll call a Quasi L-P study design. They capture and batch mark as many fish of a given species as reasonably possible over multiple days, wait a week or so for marked and unmarked fish to mix, then go back and capture both marked and unmarked fish during the recapture period, which may include 10 or more daily capture occasions. With single batch marks there is no way to tell if unmarked fish are caught multiple times during the recapture period. Therefore, both marked and unmarked fish are counted each time they are caught, so n2 and/or m2 may be greater than they would be if each fish were only counted once. To me, this is similar to the roe deer example (3.9) in Seber (1982). Rather than using the estimation methods in Example 3.9, however, our biologists typically use the Chapman modification of the Lincoln-Petersen estimator and calculate confidence intervals using the Poisson distribution as described in Ricker (1975).

Until talking with a couple of our biologists this week I had assumed that they were only counting fish once during the recapture period, since I thought that was the "correct" thing to do. Some biologists intentionally count fish more than once even if they are individually identifiable. If numbers of fish caught more than once are enough to matter, I think multiple captures could exacerbate potential effects of trap response or individual heterogeneity; on the other hand, if they result in increasing m2, then precision of N-hat will increase (but perhaps only due to pseudoreplication).

Should I be advising people to use secondary batch marks during the recapture period and only count individual fish once? Or are their methods perfectly fine? Thanks.
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Re: "Quasi Lincoln-Petersen" with multiple occasions

Postby gwhite » Fri May 26, 2023 10:38 pm

An efficient estimator using the daily captures is the joint hypergeometric maximum likelihood estimator. See White and Garrott, page 260, for an example comparing a number of ways to combine the daily Lincoln-Petersen estimates. White, G. C. and R. A. Garrott (1990). Analysis of wildlife radio-tracking data. San Diego, Academic Press.

Gary
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Re: "Quasi Lincoln-Petersen" with multiple occasions

Postby stshroye » Tue May 30, 2023 11:48 am

gwhite wrote:An efficient estimator using the daily captures is the joint hypergeometric maximum likelihood estimator. See White and Garrott, page 260, for an example comparing a number of ways to combine the daily Lincoln-Petersen estimates. White, G. C. and R. A. Garrott (1990). Analysis of wildlife radio-tracking data. San Diego, Academic Press.

Gary


Thanks, Gary. I will look into your suggestion for my own research. However, most of our fisheries managers are unlikely to do anything beyond simple Lincoln-Petersen calculations in Excel. If they are going to stick with the old-school estimators circa Ricker (1975) and Seber (1982), is there anything blatantly wrong with their methods as described above?

Steve
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Re: "Quasi Lincoln-Petersen" with multiple occasions

Postby gwhite » Tue May 30, 2023 2:40 pm

White and Garrot provide a table comparing alternatives to the MLE full hypergeometric estimator, so you can get an idea of the bias and loss of precision by using alternatives.

Gary
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Re: "Quasi Lincoln-Petersen" with multiple occasions

Postby stshroye » Wed Jul 12, 2023 6:01 pm

gwhite wrote:White and Garrot provide a table comparing alternatives to the MLE full hypergeometric estimator, so you can get an idea of the bias and loss of precision by using alternatives.

Gary


I finally obtained a copy of White and Garrot (1990) through interlibrary loan. It is informative, but none of the examples in Table 10.4 reflect exactly what I am asking about. If people were actually doing the arithmetic mean method, I would be satisfied. However, instead of calculating a separate Lincoln-Petersen estimate for each multiple recapture occasion and then taking the average, they are simply totaling all the n(i) and m(i) and calculating a single estimate. There often are not enough recaptures on an individual occasion for a legitimate estimate (< 3), but "a few" of the same fish may be counted as recaptures on different occasions. Would this method be more biased and less precise than the arithmetic mean method? And should people try to count recaptures only once? Thanks.
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