When you want to know the population size of a species, you can use the tag-recapture method to do so. This method is also called the mark-recapture method. This method only works in local populations, you will have to measure several populations separately to asses the total number of individuals on larger scales, like on the scale of the country or state.
Requirements for tag-recapture method
You can only apply this method for animals under the following conditions:
Individuals in the population are randomly distributed
Individuals in the population should (be allowed to) move freely
The tag does not influence the survival or behavior of the individual
The tag does not make it more likely the individual will be recaptured
There is no migration to or from the population
There is no mortality in the time between marking and recapturing
Of course some of these conditions are hard to meet, but it is important to keep these influences as low as possible and to be aware of how they affect your measurements.
How it works
You will go out into a population and capture individuals of the species. The best method is to use life traps instead of manual capture. Do not mark nests or other clusters as these individuals are not randomly distributed.
Mark the captured individuals. This can be done with paint, a ring, a tag or collar. Make sure the method is suitable for the species. Count how many you have tagged.
Come back to do the same capturing on a different day. This can be after a few days or a few weeks. If you wait longer the results will become more and more unreliable because of migration and mortality.
Count how many individuals are captured. Also count how many of the captured individuals are tagged.
Do the math (see below).
How to do the math
The formula to calculate the total amount of individuals in the population is according to the Lincoln–Petersen method:
N = (M*C) / R
N = Total number of individuals in the population M = Number of individuals that are marked the first time C = Total number of individuals captured the second time (marked and unmarked combined) R = Number of marked individuals captured the second time (the only ones that are recaptured)
Lets say you capture 50 individuals the first capture and again 50 in the second time you capture them. The first 50 will all receive a mark, but in the second capture you only find 10 marked individuals. The formula becomes:
N = (50*50) / 10 = 250
This means there are probably 250 individuals of this species in the population.
What if you find none marked back? Then you should mark more individuals. Maybe the population is much larger than you estimated. You should also double check if the marking itself does not harm or influence the animals. Maybe you caused the marked individuals to die or migrate away.
If you only mark very few individuals or if you only recapture very few individuals the estimate becomes less accurate. If you cannot increase your captured amount, you can use a different formula called the Chapman estimator (not discussed here).
Less invasive methods
Instead of tagging or marking an individual, you can also use DNA techniques or physical characteristics to determined the identity of the captured individuals. For example with killer whales the markings on their tails are used to determine if the individual has been seen before.
Little personal side-note
This method always fascinates me because you can use it outside of biology too. In that case you do not tag your individuals, but you memorize them. For example you memorize some people in a fair or lecture hall. After some time and reshuffling you can check how many of the memorized people you see again. If it is a huge crowd, you will not see many. If its a small crowd you do. I never use math on it, but you will get a rough estimate. Even when online shopping I use it. If you are in a webstore and you click to get a random new item on your screen, the number if times you will get the same item again says something about how many different items in total are available. Forget about using the formula for this, it’s just nice to see that you can use a biological way of thinking on more than just biology.