Hampton and Kirkwood: Tag shedding by Thunnus maccoyii 



315 



Tag-shedding models 



Various models have been proposed to describe the pro- 

 cess of tag loss (Beverton and Holt 1957 and reviews 

 by Ricker 1975; Wetherall 1982). Tag losses can be 

 classified as type I losses, which effectively reduce the 

 number of tags released (immediate tag shedding, im- 

 mediate tagging mortality, and non-reporting), and 

 type II losses which occur steadily over time (natural 

 mortality, fishing mortality, permanent emigration, 

 and long-term tag shedding). Considering the shedding 

 process only, the simplest model is that proposed by 

 Beverton and Holt (1957) for type II shedding, where 

 the instantaneous rate of shedding (L) is constant over 

 time. In this model, if for a fish originally single-tagged, 

 Q{t) is the probability of the tag being retained at time 

 t after release, then 



Qit) = e-^' 



(1) 



If immediate tag shedding occurs, with a probability 

 1-P of this occurring, then 



Q{t) = p e-^' 



(2) 



In some cases, it may be inappropriate to assume a 

 constant shedding rate. Some tags may deteriorate 



over time, causing their shedding rate to increase 

 (Baglin et al. 1980). Alternatively, some tags may be 

 come more securely fixed over time, e.g., through the 

 gradual laying down of tissue around the tag, causing 

 the shedding rate to decrease (Kirkwood 1981). More 

 generally, Kirkwood (1981) has noted that if individual 

 tags have a different propensity for shedding, then the 

 apparent average shedding rate will decrease with time 

 at liberty, as the tags with the higher shedding rate 

 are lost first. Kirkwood modeled this process by allow- 

 ing the shedding rate to be a gamma-distributed ran- 

 dom variable, rather than a constant; however, his 

 model did not allow for an increasing shedding rate. 

 An alternative approach was adopted by Wetherall 

 (1982), who assumed that the probability of a tag be- 

 ing shed was time-dependent. He proposed a flexible 

 function that allowed either an increasing or decreas- 

 ing shedding rate. 



In this paper, we adopt a time-dependent shedding- 

 rate model that allows the probability of an individual 

 tag being shed to decrease over time in an identical 

 fashion to the average shedding rate of the Kirkwood 

 (1981) model. In this case, we now assume that the rate 

 of shedding at time t after release follows the functional 

 form 



Lit ) = - 



bk 



b + U 



