Chapter 14, Problem 73E

One of the problems with the capture-recapture method is that in some animal populations there are individuals that are trap-happy (easy to trap) and others that are more cagey and hard to trap. Too many trap-happy individuals can skew the data (see Exercise 62 ). A removal method is a method for estimating the N-value of a population that takes into account the existence of trap-happy individuals by trapping them and removing them. In the first “capture,” individuals from the general population are trapped, counted, and removed from the habitat so that they can't be trapped again. In the “recapture,” individuals from the remaining population (those that had not been trapped before) are trapped and counted. The number of individuals trapped in the capture can be denoted by $pN$, where $p$ denotes the fraction of the population trapped and N is the size of the population. The number of individuals left after the removal is $\left(1-p\right)N$. If we assume that the number of individuals trapped in each capture represents the same fraction of the population, then the number of individuals trapped in the recapture should be $p\left(1-p\right)N$. From the two equations $\left(pN=\text{number of individuals trapped in the capture}\right)$; $\left(p\left(1-p\right)N=\text{number of individuals trapped in the recapture}\right)$ we can solve for N and get an estimate of the population. Suppose 250 individuals are trapped in the capture stage and removed from the population, and 150 individuals are trapped in the recapture stage. Estimate the size of the population.