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.