Investigation of bias in the mark–recapture estimate of toothfish population size at South Georgia

This paper investigates the influence of mixing of fish, and the uneven distribution of tag placements and recapture effort, on bias in the Petersen estimate. It does so by constructing a linear model of the South Georgia toothfish fishery, simulating fish movements within this system and overlaying various combinations of tagging and recapture effort to investigate bias. The fishable grounds around South Georgia were divided into 77 very small scale boxes lying along the 1000m contour. The uneven distribution of animals was simulated by adjusting an average movement rate downwards when animals encountered a high CPUE box and upwards in a low CPUE box so that they were retained in high CPUE boxes. The model incorporates the facility for releases by box over a number of years.
The model performed as expected with test situations. It produced a near-perfect estimate of stock size when there was an ideal distribution of tags and/or fishing effort; by ideal we mean that either tagging or fishing effort was in direct proportion to CPUE. When both tagging and fishing effort were non-ideal, eg when effort was concentrated away from tag concentrations, or overly concentrated in them, the Petersen estimator either over-estimated or underestimated (respectively) the true population size. When run on the real tag release data, and using CPUE from 2002-2004 and recapture effort in 2003 and 2004, the model indicated that the Petersen equation produced an under-estimate of true population size. Although we do not advocate using the magnitude of the estimated bias to correct the tagging estimate made last year for 48.3, we do conclude that the particular distribution of tag releases and recapture effort at South Georgia is likely to lead to an under-estimate of the true population size rather than an over-estimate of it.