This paper investigates the influence of mixing of fish, and the uneven distribution of tag placements and recapture effort, on bias in the Petersen estimator of population size. It does so by constructing a spatial 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 1 000 m contour. The uneven distribution of fish was simulated by adjusting an average movement rate downwards when fish entered a high-density box (as indicated by high CPUE) and upwards in a low-density box, so that they tended to be retained in high-density boxes. The model allows simulation of releases by box over multiple 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’, it is meant that either tagging or fishing effort was in direct proportion to density (CPUE). When both tagging and fishing effort were non-ideal, e.g. when fishing effort was
concentrated away from tag concentrations, or overly concentrated in them, the Petersen estimator either overestimated or underestimated (respectively) the true population size. When run on the real tag–release data, and using average CPUE from 2002 to 2004 and recapture effort in 2003 and 2004, the model indicated that the Petersen estimator produced an underestimate of true population size. Although this paper does not advocate using the
magnitude of the estimated bias to correct the tagging estimate of exploitable population size made for Subarea 48.3, it is concluded that the particular distribution of tag releases and recapture effort at South Georgia is likely to lead to an underestimate of the true population size rather than an overestimate of it.