In this video, we're going to talk about the mark and recapture calculations and assumptions. Recall that we ended the last lesson video introducing this equation that you can see right here, which allows us to estimate the total population size after the mark and recapture method. Recall from that last lesson video that m is equal to the number of marked individuals in the first capture, which was 5, and n is equal to the unknown total population size, which we're trying to calculate. This is going to be equal to r, which is the number of marked individuals in the second capture, which was just 1, over c, the total size of the second capture, which was 5. All we need to do is use our algebra skills to solve for the variable n, which we can do in several different ways, but what we're going to do here is take the reciprocal of both sides of the equation.

Literally just flip these ratios around so that we have n5 is equal to 51, and of course, 51 is just 5. To isolate the variable n, all we need to do is multiply both sides of the equation by 5, and what we get when we do that is n=25. That is the total population size in the scenario from our last lesson video. Now, over here on the right, what we have are mark and recapture method assumptions, which must be maintained in order for this mark and recapture method to work appropriately. There are three assumptions.

The first assumption is that the marked individuals must fully mix between captures. The second assumption is that marked and unmarked individuals are equally as likely to be captured. This means that the behavior of those marked individuals did not change and they didn't devise a way to avoid being captured a second time. Third, the population size must be stable during the sampling, which means that there's no significant births, deaths, immigration, or emigration, or if they do happen that they balance each other out. This concludes this video, and I'll see you all in our next one where we'll be able to practice these concepts.