Models of tag shedding for double tagging as a function of time at liberty and approximate solutions for the single tagging model in CASAL

The model of tag shedding implicit in CASAL is that of Kirkwood and Walker (KW) (1984) which models the annual tag shedding (i.e. loss) rate as a constant for individual tags. The CASAL software applies this model correctly for fish released with a single tag but does not have the facility at present to correctly apply the KW model for fish released with two tags. The solution of Dunn et al. (2005) and Hillary et al. (2006) to apply the square of the individual tag loss annual rate in CASAL over-estimates the correct proportion of fish that have retained at least one tag, and are therefore detectable, as a function of time at liberty. This over-estimation is shown to be significant and the implications for stock assessments of this are discussed.
Models of tag shedding were calibrated using data for a large sample of recaptures of fish released in the Heard and MacDonald Island (HIMI) (Division 58.5.2) Patagonian toothfish fishery that were double (Tbar) tagged fish. These models included the single-parameter KW model and 2 and 3 parameter extensions of this model. A Generalized Additive Model (GAM) was also fitted and is the most flexible in shape. The estimation method accounts for the fact that fish that have shed both tags cannot be detected and therefore do not contribute to the data but in the theory need to be considered. The KW model gave a considerably poorer fit than the other models. It is recommended that CASAL be modified to correctly handle double-tagged releases and at the same
time allow more flexible models of probability of shedding of individual tags. In lieu of this an  improved approximation compared to squaring the rate parameter is given. This approximation could be combined with a sensitivity analysis that varies the KW constant rate parameter in CASAL assessments.