Practice question

Using the Lincoln–Petersen relationship, the marked fraction in the population is equated to the marked fraction in the recapture sample: M/N ≈ R/C. Solving gives N ≈ MC/R, where M is the initial marked release, C is the total second capture, and R is the number of marked recaptures. Substituting M = 100, C = 150, and R = 25 yields N = 100 × 150/25 = 600 fish. The logic is also intuitive: one-sixth of the second catch is marked, so the original 100 marked fish are inferred to constitute one-sixth of the population. Reliable estimation requires a closed population between occasions, durable and harmless marks, complete mixing, correct mark recognition, and equal capture probabilities for marked and unmarked individuals. If marked fish avoid traps or lose marks, recaptures decline and estimated N becomes too large. For small samples, the Chapman correction is preferable, but the unadjusted estimator produces the stated value exactly from these data.