In the book The Math of Life & Death, Kit Yates estimates the population of snails in his yard with his son using the mark recapture method. I understand the math behind it, but I can't wrap my head around the intuitive understanding behind it.
Why is it assumed that the proportion of the marked individuals that are caught is equal to the proportion of the total population that is marked? (according to wikipedia and the Lincoln–Petersen estimator)
You start with a population of unmarked individuals and take a sample of which some are marked. It is assumed that the marked individuals randomly distribute throughout the population. This is key. If they are truly randomly distributed throughout the population, then when you take the second sample, the proportion marked in the sample should be the same as the proportion marked in the population. This assumption is the basis of the equation for estimating the unknown population size. If m is the number of marked individuals in the second sample of n total sampled and M is the total number that were marked originally and N is the unknown population size then m/n = M/N (the assumption). You rearrange the equation and solve for N. I hope that makes sense. There is an excellent, more in-depth description at https://derekogle.com/NCNRS349/modules/MarkRecap/BKG
