Xiao et al.: Instantaneous rate of tag shedding for Galeorhinus ga/eus and Mustelus antarcticus 



171 



at liberty ( Kirkwood and Walker, 1984; Hampton and 

 Kirkwood, 1989; Hearn et al., 1991; Xiao, 1996a). 

 These models 1) use the exact times at liberty in 

 model fitting, 2) use probabilities of tag retention 

 directly rather than using the often statistically un- 

 desirable ratios as the dependent variable in regres- 

 sion analysis, 3) apply to both small (but see below) 

 and large numbers of recaptures, and 4) yield esti- 

 mates of tag shedding rates independent of instan- 

 taneous fishing mortality, natural mortality, and 

 mortalities due to all other causes. Almost all previ- 

 ous tag shedding models have considered only the 

 effects of fish time at liberty on shedding rates, ig- 

 noring effects of other equally or potentially more 

 important factors, such as fish sex and size. 



School shark Galeorhinus galeus (Linnaeus) and 

 gummy shark Mustelus antarcticus (sensu Last and 

 Stevens, 1994) are major species in the Australian 

 southern shark fishery — a commercial fishery that 

 extends from Western Australia through South Aus- 

 tralia to Bass Strait and Tasmania in the east and 

 that has an annual landed value of $A15.6 million 

 (Walker et al., 1996). Two tagging studies were un- 

 dertaken to study the growth (Moulton et al., 1992), 

 natural mortality (Grant etal., 1979), and local move- 

 ments of these two species within Bass Strait and 

 off eastern Tasmania (T L Walker, Marine and Fresh- 

 water Resources Institute, PO Box 114, Queenscliff, 

 Vic 3225 Australia, unpubl. data ). These studies sug- 

 gest that school shark are highly migratory, compared 

 with gummy shark, but they provide little quantita- 

 tive information about their rates of movements be- 

 yond these areas, where most sharks were tagged 

 and released. Also, fishing effort was too poorly docu- 

 mented at the time of Grant et al.'s (1979) tagging 

 program ( 1940s and 1950s) to be adequate for quan- 

 tifying the rates of movement for these two species. 

 Finally, predominant use of gill nets with large mesh 

 sizes (8 inches) off the southern coast of Western 

 Australia and off South Australia at the time of T.L 

 Walker's tagging study (1970s) led to a low level of 

 fishing effort and a small number of recaptures. Such 

 a lack of quantitative information on rates of move- 

 ment hampered stock assessment. Consequently, a 

 large-scale tagging experiment was designed (Xiao, 

 1996b) and implemented to fill in this gap. In that 

 study, thousands of individuals were released; each 

 individual was tagged with an easily attachable and 

 highly visible external tag (a Roto tag or a dart tag), 

 the shedding rate of which was to be determined 

 through an accompanying double-tagging experiment 

 (see below). 



In this paper, we develop a simple tag shedding 

 model to account for the effects offish sex, size, and 

 factors other than time at liberty and use a special 



case to estimate the instantaneous tag shedding rate 

 for the two species of sharks. 



Materials and methods 



Tagging experiments 



Two double-tagging experiments were performed on 

 G. galeus andM. antarcticus. In the first experiment 

 (Olsen, 1953; Walker, 1989; Table 1), a total of 2597 

 school and 363 gummy sharks with a respective to- 

 tal length range of 31-164 (85 ±43, «=2586) cm and 

 32-179 (102 ±24, n=362) cm were captured by long- 

 line hooks, measured to the nearest centimeter, tagged 

 with an internal and external tag, and released in in- 

 shore waters off Victoria, South Australia, and Tas- 

 mania, Australia, fi-om 22 May 1949 to 10 July 1954. 

 Internal tags were either 50 mm long and 23 mm wide 

 (J-tag), or 50 mm long and 22 mm wide (L-tag), or 

 35 mm long and 10 mm wide (S-tag) and were inserted 

 into the body cavity through an incision on the left flank 

 parallel to the muscles in the lower half of the body 

 immediately below the posterior half of the first dorsal 

 fin. External tags were a white ( W-tag) or gray Petersen 

 disc (G-tag); both were 16 mm in diameter and 1 mm 

 thick and were placed in the midcentral part of the 

 first dorsal fin. Of those released, 417 school and 20 

 gummy sharks were recaptured within 42.5 years. 

 Their respective total length at recapture ranged from 

 43 to 175 ( 127 ±35, /!=267 ) cm and from 83 to 152 ( 125 

 ±19, n = 12) cm; their respective times at liberty ranged 

 from 31 to 15,510 (2761 ±2758, n=417) d, and from 52 

 to 3900 (1771 ±1159, n=20) d. 



In the second double-tagging experiment (Table 2), 

 as part of a major tagging experiment (see above), 

 291 school and 731 gummy sharks with a respective 

 total length range of 38-168 (134 ±17, n=291) cm 

 and 40-176 (108 ±20, n=729) cm were captured in 

 gill nets, measured to the nearest millimeter, tagged 

 with two external tags (a Roto tag and a dart tag) 

 either in the lower half or basal cartilage of the first 

 dorsal fin, and released off southern Australia, from 

 15 December 1993 to 24 April 1996. Two types of Roto 

 tags were used: either a 45-mm-long and 18-mm-wide 

 Jumbo (Roto) tag, or a 36-mm-long and 9-mm-wide 

 Roto tag (Daltons of New South Wales, AustraHa). 

 The dart tag was 95 mm long and 2 mm in diameter 

 (HallprintofSouth Australia, Australia). As of 1 May 

 1997, 48 school and 207 gummy sharks were recap- 

 tured. Their respective total length at recapture 

 ranged from 85 to 179 (135 ±18, n=38) cm and from 

 66 to 167 (115±17,n=150)cm; their respective times 

 at liberty ranged from 31 to 633 (269 ±163, n=48) d, 

 and from 1 to 1138 (275 ±244, a!=207) d. 



