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Fishery Bulletin 97(1), 1999 



tagged fish have higher shedding rates than others, 

 because tags that are less securely attached are shed 

 earlier. The proportion of less securely attached tags 

 decreases with increasing time at liberty. This will 

 yield an apparent decrease in tag shedding rate with 

 time at liberty. A similar argument applies when tag 

 shedding rates vary among individuals. The lack 

 of a trend may indicate negligible tag losses ft-om im- 

 proper attachment, insignificant individual variability 

 in tag shedding rate, or insufficient data (see below). 



Estimates of tag shedding rates in Tables 3 and 4 

 must be used cautiously because only those that are 

 based on many recaptures are reliable, whereas those 

 that are based on few recaptures are unreliable. For 

 example, the estimates of tag shedding rates for a 

 combination of a 50-mm-long and 22-mm-wide in- 

 ternal tag (L-tag) with a white Petersen disc (W-tag, 

 external) (rows 4-6, Table 3) were based on only 11 

 recaptures (rows 11 and 12, Table 1), only one of 

 which had retained both tags (row 11, Table 1), and 

 hence are unreliable. No estimates could even be 

 obtained for a combination of a 35-mm-long and 10- 

 mm-wide (S-tag) internal tag with a white Petersen 

 disc (W-tag, external) (rows 11-14, Table 3), despite 

 seven recaptures, none of which had retained both 

 tags (rows 16-18. Table 1). Similarly, no estimates 

 could be obtained, for any tag combinations, from 

 data on gummy sharks from the first double-tagging 

 experiment, despite 20 recaptures, none of which had 

 retained both tags (rows 1-8, Table 1). Equally un- 

 reliable estimates of tag shedding rates could also 

 result from pooling of information while ignoring 

 differences in its sources. For example, estimates 

 from pooling all three internal tags (i.e. J-tag, L-tag 

 and S-tag) (rows 54-65, Table 3) should be treated 

 cautiously because of sexual differences inferred 

 above. By contrast, for both sexes of school sharks, 

 the estimates of shedding rates of gray Petersen discs 

 are reliable for its combination with a 50-mm-long 

 and 22-mm-wide internal tag (L-tag) (rows 9 and 10, 

 Table 3) or with a 35-mm-long and 10-mm-wide (S- 

 tag) internal tag (rows 17 and 18, Table 3) because 

 information from many fish recaptures was used in 

 their estimation. Much less reliable estimates were 

 obtained for dart tags on gummy sharks (rows 5, 6, 

 9, and 10, Table 4 ). Although rather high in all cases, 

 all these shedding rates are actually underestimated, 

 as will be shown and published elsewhere. 



Although we have examined only the effects of tag 

 type, sex, length at release, and time at liberty on 

 tag shedding, many other factors, such as tagging 

 operator (Hampton, 1996), can also affect tag shed- 

 ding rate. However, hundreds or even thousands of 

 fish need to be recaptured (many more need to be 

 released) to estimate effects of tagging operators re- 



liably. Such a great demand of data is well expected 

 of Equation 1 or 2, which is a compartmental model. 

 The solution of a compartmental model can be given 

 by a linear combination of exponentials and is known 

 to yield bad ill-conditioning (Seber and Wild, 1989, 

 p. 118-119). Indeed, for some compartmental mod- 

 els, no amount of data is sufficient for identifjdng 

 model parameters. Similarly, the "best" model of all 

 possible models of a general model is identifiable only 

 by a sufficient volume of data. As mentioned above, 

 fish length at release or time at liberty, or both, en- 

 tered certain "best" models for X(i,B,t(i)), when the 

 number of fish recaptured was small, but did not, 

 when there were many fish recaptures. This finding 

 suggests that fewer data than sufficient cannot iden- 

 tify the "best" model. To detect and address problems 

 with parameter and model identifiability for a par- 

 ticular general model ( e.g. Equation 1 or 2 ), one might 

 generate as large a set of data as necessary, for ex- 

 ample, by duplicating each record of an existing set 

 of data from a double-tagging experiment a neces- 

 sary number of times, analyse it, and design one's 

 tagging experiment accordingly (e.g. to determine the 

 number offish to be released and the expected num- 

 ber offish to be recaptured). 



Results of our study have major implications for 

 future double-tagging experiments for estimating 

 instantaneous tag shedding rate and for analysis of 

 tagging data. Because estimation of a single para- 

 meter requires many fish recaptures and hence in- 

 curs considerable financial resources, use of an eas- 

 ily detected and permanent tag eliminates a need 

 for considering tag loss and is preferred in any tag- 

 ging experiment. However, with a commercially or 

 recreationally harvested species, problems of tag re- 

 porting remain. Use of two readily detectable, identi- 

 cal tags with a moderate shedding rate in a double- 

 tagging experiment reduces the number of parameters 

 to be estimated by one half A moderate shedding rate 

 is necessary because too low a shedding rate requires 

 some recaptures after a long time at liberty for reliable 

 estimation of parameters; too high a shedding rate ren- 

 ders the tag useless for some applications. 



Acknowledgments 



We wish to thank Mick Olsen of the CSIRO Division 

 of Fisheries for collecting and making available to 

 us data for the first tagging experiment. We also 

 thank Natalie F. Bridge (Victorian Marine and Fresh- 

 water Resources Institute) for her field work and for 

 managing the data, and Grant West and John D. 

 Stevens (CSIRO Division of Marine Research) for 

 their help with the tagging data and practicalities of 



