I would use mark-and-recapture, the Lincoln-Petersen method (see Pollock et al. 1990 or Krebs 1999). The logic is simple: If the system is closed enough, when you capture, mark and release a first (large) sample, the proportion of marked fish to total fish caught in a second sample (giving time for fish to "mix") is roughly the same proportion between the number of fish caught in the first sample to the total population.
Dear Mohamed thank you for your reply, it is 4.0 cubic kilometers (3,200,000 acre·ft) with Semi-intensive culture. No we do not know the number of initial fries released. Some researchers have suggested CPUE.
This is a very interesting question. Counting the quantity of fish in a big reservoir is difficult. The problem are the reservoir is big, fishes will swim randomly and fishes are not evenly distribute in the reservoir.
One method I can think of is using sonar to count fish.
You use a boat crossing the reservoir from one side to the other (select the path with maximum distance) and count (or estimate) the number of fish using sonar.
You divide the number of fish you found by the area of water you counted and get the density of fish in the reservoir. Then you multiply density by the area of the reservoir and you can have a rough idea about total quantity of fish in a reservoir.
You will have to develop a sampling design to estimate fish abundances. Use fishing gears with low selectivity ( or several fishing gears to sample fishes at different habitats in the reservoir), and that provide an estimate of density (for example: bottom trawling, hoop nets, cast nets, beach seine, etc.). Once you have an estimate of the number of individuals per area (m2, km2, ...) for every species and the total area of the reservoir, you may estimate the total number of fishes. You may have to refine your sampling design as not all fishes occur in all habitats of the reservoir, but I believe that this is the best approach to get your estimates.
I would use mark-and-recapture, the Lincoln-Petersen method (see Pollock et al. 1990 or Krebs 1999). The logic is simple: If the system is closed enough, when you capture, mark and release a first (large) sample, the proportion of marked fish to total fish caught in a second sample (giving time for fish to "mix") is roughly the same proportion between the number of fish caught in the first sample to the total population.
CPUE gives relative abundance rather than absolute. Moreover, the CPUE estimates are highly prone to bias if they are not standardized in spatial and temporal scales. I would rather support the suggestions by Cassiano and Juan for this problem. However, you have to make sure the system is close (or complete the estimation in a short period of time) because the final abundance estimates can be affected by, releasing more fries, natural immigration, fishing or emigration.
The chances of any fish encountering the net is always random . CPUE may be one of the method to estimate abundance . But it is not absolute . The chances of any fish caught by the net is same . The net operated should have a wide coverage and covering all the area and all the hours of day and night considering that diurnal migration is very common in fish .
Thank you very much to all you doctors especially to Juan, Stanley, Chakraborty , Deepak and others for adding your commendable answers to my question. I got the Idea from your comments and it would now be easy for me to do this work.
Juan has it. Mark/recapture (assuming no violations of the model) will be your most robust method that is feasible. Look into using technologies such as PIT tags to mark the fish, which can give you info on induvidual growth rates, movements between sampling sites (informs how well mixed the population and marked fish are), and other useful info. For a 12mm PIT tag we tag fish no smaller than 65mm. Tags are ~$1.50-2.00 USD.
I agree with the above, mark/recapture. And pit tags would give great additionally info (as stated above), however, if you are dealing with thousands upon thousands of fish, you might have to pit tag a lot of fish to make better inferences to the population level.