170 



Abstract.— Fish and other animals are 

 often tagged to estimate their abun- 

 dance as well as rates of growth, fish- 

 ing mortality, natural mortality, and 

 movement. Results of these studies are 

 biased if tags are not retained perma- 

 nently and if tag loss is not taken into 

 account. In this paper, we develop a 

 simple tag shedding model to account 

 for the effects of time at liberty, sex, and 

 other factors and use one of its special 

 cases to estimate the instantaneous tag 

 shedding rate from data based on two 

 double-tagging experiments on the 

 school shark. Galeorhinus galeus, and 

 gummy shark, Mustelus antarcticus, off 

 southern Australia. For either species, 

 tag shedding rate could vary with tag 

 type, position of tag on fish, and sex of 

 fish, but not with length at release or 

 time at liberty. The shedding rate of 

 Petersen disc fin tags was well above 

 SO'i'f/yr. Dart tags were shed at a higher 

 rate (41%/yr for school shark; 6.3'7f/yr 

 for gummy shark) than either "Roto" or 

 "Jumbo" fin tags (S'/r/yr for school 

 shark; 6'7f/yr for gummy shark). For 

 either species of shark, the shedding 

 rate of dart tags anchored in the basal 

 cartilage of the dorsal fin was about 

 half that of dart tags anchored in the 

 dorsal musculature. 



Estimation of instantaneous rates of 

 tag shedding for school shark, 

 Galeorhinus galeus, and 

 gummy shark, Mustelus antarcticus, 

 by conditional likelihood 



Yongshun Xiao 



CSIRO Divis)on of Marine Research 



GPO Box 1538, Hobart, Tasmania 7001, Australia 



Present address: South Australian Aquatic Sciences Centre 



SARDI, 2 Hamra Avenue, West Beach, South Australia 5024, Australia 

 E-mail address xiaoyongshun@pi.sa.gov.au 



Lauren P. Brown 



Terence I. Walker 



Marine and Freshwater Resources Institute 



PO Box 114, Queenscliff, Victona 3225, Australia 



Andre E. Punt 



CSIRO Division of Marine Research 



GPO Box 1538, Hobart, Tasmania 7001, Australia 



Manuscript accepted 19 March 1998. 

 Fish, Bull. 97:170-184 (1999). 



Tags are markers placed on or in 

 animals to identify an individual. 

 Animals are tagged to estimate 

 their abundance as well as rates of 

 growth, fishing mortality, natural 

 mortality, and movement. In many 

 studies, a tagged animal is assumed 

 to retain its tag permanently. This 

 assumption, however, is not valid 

 for certain types of tags. Conse- 

 quently, many attempts have been 

 made to estimate tag shedding rates 

 (e,g. Davis and Reid, 1982; Francis, 

 1989; Faragher and Gordon, 1992; 

 Treble et al,, 1993; Hampton, 1996; 

 Xiao, 1996a). 



Tag shedding models are of three 

 main tjqjes; all are based on Bever- 

 ton and Holt's (1957, p, 205, equa- 

 tions 14,32-14.37) model for a 

 double-tagging experiment. Some 

 models are conditional on the num- 

 ber of recaptured fish with a single 

 tag, as well as the number of recap- 

 tured fish with both tags as a func- 



tion of time at liberty, and use the 

 least squares method (GuUand, 

 1955, 1963; Chapman, 1961; Paulik, 

 1963; Chapman et al., 1965; Bayliff 

 and Mobrand, 1972; Russell, 1980; 

 Kirkwood, 1981; Alt et al., 1985) or 

 more generally the maximum like- 

 lihood method (Robson and Regier, 

 1966; Seber, 1973; Seber and Felton, 

 1981; Wetherall, 1982; Kremers, 

 1988; Fabrizio et al,, 1996) for esti- 

 mation of parameters. Other mod- 

 els are conditional on the number 

 of recaptured fish retaining at least 

 one tag as a function of time at lib- 

 erty and on the exact times at lib- 

 erty (Wetherall, 1982). Use of these 

 types of models in data analysis re- 

 quires grouping recaptured fish by 

 time at liberty because of an insuf- 

 ficient number of recaptures for a 

 particular (exact) time at liberty, 

 especially in small-scale tagging 

 experiments. Still other models are 

 conditional only on the exact times 



