Method for estimating number of fish in my Aquarium Context: I have an aquarium (50 Liters) with lots of fishes from the same specie (Guppy) and i have noticed that recently their number as grown exponentially due to their reproductive cycle. I would like to estimate their number.
Problem: It's not possible for me to count them individually, and i cannot dry the aquarium due to the fact that the newborns are translucid and have sizes bellow 4 milimeters, it would be an impossible task to distinguish them from the grains of smalls rocks in my aquarium.
Pre-Condition: Due to the fact that newborns stay relatively close to the ground and as they grow they will occupy (swim) in places increasingly closer to the surface level, we can consider that the fishes are uniformly distributed in the aquarium. Fish Tank
Possible method: Take a cup of water (for example 150 milliliters) consistently from the same place of the aquarium, and count the number of fishes from inside the cup. By repeating this method multiple time i could in theory estimate the total number of fishes in my aquarium.
Question: Is this a good method? Are there any big flaws in my lines of thinking? Could you think of a better, more pratical method?
Thanks in advance for your help :)
 A: You can try the capture-recapture method which uses the expectation of the hyper-geometric distribution.
A: Given your assumption that the fish are evenly distributed this is a reasonable method.
You have assumed that each level of the tank has fish of a given age and that the fish are laterally evenly distributed.  Maybe the fish avoid the walls and you sample in the corner, getting a much lower than average density of fish.
Your assumption of equal distribution is not reasonable because you are sampling the old fish and if the population grows exponentially there are many more young fish.  If the fish are stratified by age the lower levels will be denser with fish than the surface.  If you have observations over a span of time you will be able to estimate the rate of exponential growth.  If you know how the age of the fish changes with level in the tank you can estimate the increase in density as you go lower and use that to estimate the total population.
It would be much better to sample the water with a random distribution in space.  That would eliminate some of the systemic bias in the last two paragraphs.  If you believe that the age distribution is tied to the level you sample at, you can use your observations to find the function between level and density.  That can improve your estimate of the total population.
Even distribution is an easy assumption to make.  It makes a number of things easier.  It is hard to defend because many things can make the distribution uneven.  If you take samples from various places you collect data that can support or deny the even distribution assumption.
A: Why not take a photograph or video and count them using that?
