Darrochs method. is a method for estimating the size of a population using multiple

Chapter 14, Problem 74

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Darrochs method. is a method for estimating the size of a population using multiple (more than two) captures. For example, suppose that there are four captures of sizes n1, n2, n3, and n4, respectively, and let M be the total number of distinct individuals caught in the four captures (i.e., an individual that is captured in more than one capture is counted only once). Darrochs method gives the estimate for N as the unique solution of the equation 11 - M N 2 = 11 - n1 N 211 - n2 N 211 - n3 N 211 - n4 N 2. (a) Suppose that we are estimating the size of a population of fish in a pond using four separate captures. The sizes of the captures are n1 = 30, n2 = 15, n3 = 22, and n4 = 45. The number of distinct fish caught is M = 75. Estimate the size of the population using Darrochs formula. (b) Show that with just two captures Darrochs method gives the same answer as the capture-recapture method.