Chapter 9.B, Problem 49E

Wildlife Management. A common technique for estimating populations of birds or fish is to tag and release individual animals in two different outings. This procedure is called catch and release. If the wildlife remain in the sampling area and are randomly caught, a fraction of the animals tagged during the first outing are likely to be caught again during the second outing. Based on the number tagged and the fraction caught twice, the total number of animals in the area can be estimated. a. Consider a case in which 200 fish are lagged and released during the first outing. During a second outing in the same area, 200 fish are again caught and released, of which one- hall ate already tagged. Estimate N, the total number of fish In the entire sampling area. Explain your reasoning. b. Consider a case in which 200 fish ate tagged and released during the lira outing. During a second outing in the same area, 200 fish ate again caught and released, of which one- fourth are already tagged. Estimate N the total number of fish to the entire sampling area Explain your reasoning. c. Generalize your results hum parts (a) and (b) by letting p be the fraction of tagged fish that are caught during the second outing. Find a formula for the function N = f(p) that relates the total number of fish, N, to the fraction lagged during the second outing, p. d. Graph the function obtained in part (c). What is the domain? Explain. e. Suppose that 15% of the fish in the second sample are tagged. Use the formula hum part (c) to estimate the total number of fish in the sampling area. Confirm your result on your graph. f. Locate a real study in which catch and release methods were used. Report on the specific details of the study and how closely it followed the theory outlined in this problem.