How Many Fish are in the Pond?

◆ THE CAPTURE-RECAPTURE ◆ ESTIMATE THE “capture-recapture method” or “Petersen’s method”, as it is sometimes referred to by fishery biologists, is a simple method of estimating the size of an animal or human population. A number of applications to the estimation of animal population size are given in Seber (1982). Lock and Moore in Gordon and Gordon (1992) note that the capturerecapture method is “at the heart of proposals to adjust for undercount in the U.S. Census” (c.f. the November 1994 issue of Statistical Science). McKeganey (1993) describes its application to estimating the number of prostitutes in Glasgow in an attempt to monitor the spread of HIV. A description of the method now follows. For concreteness, suppose we are interested in estimating the number of fish, N, in a pond. We begin by capturing a sample of size c of the fish, tagging them, and then returning them to the pond. After allowing some time for mixing, a second recaptured sample of size r is taken from all the fish in the pond and the number t of them which are tagged is recorded. An estimate of the number of fish in the pond is