Xiao et al.: Instantaneous rate of tag shedding for Galeorhmus galeus and Mustelus antarcticus 



179 



were too limited from the second experiment (Table 

 2) to estimate two or more parameters. We estimated 

 PgiA) only, which can, however, be scaled to p^<A) or 

 li2(A) given Ld) and t(i). For tag B (Petersen discs or 

 dart tags), all seven nested models of A(i,B,t(i>> were 

 fitted, where possible, to data from each tagging ex- 

 periment. The final and most parsimonious model 

 was decided by the x^ statistic ( Seber and Wild, 1989, 

 p. 196-197). All parameters were estimated by mini- 

 mizing -log(L) by using the simplex algorithm by a 

 FORTRAN 77 program (available on request). 



Results 



Maximization of Equation 4 for both sets of tagging 

 data yielded estimates of shedding rate for various 

 (independent) combinations offish sex, tag type, and 

 tag position, and their (asymptotic) standard errors 

 (Tables 3 and 4). If a tag was retained in all recap- 

 tured fish, we assumed that its shedding rate was 

 zero in order to estimate other parameters of the 

 model. Because shedding rates must be nonnegative, 

 the assumption of zero shedding rate will lead to an 

 underestimate of the parameter concerned and in- 

 troduce a positive bias into the estimates of other 

 parameters. The extent of such bias could be assessed 



by simulation studies but is beyond the scope of this 

 work. 



Fish length at release or time at liberty, or both, 

 entered certain final models for X(i,B,t(i)), only when 

 the number of fish recaptured was small. By con- 

 trast, whenever there were many fish recaptures (e.g. 

 rows 14-15 and 20-21, Table 1), neither factor en- 

 tered the final model. Therefore, we conclude that 

 fish length at release or time at liberty, or both, did 

 not significantly affect tag shedding rates; and their 

 inclusion in certain models was a result of too few 

 recaptures. 



Fish sex affected tag shedding rates of Petersen discs 

 for some combinations of tag type and tag position. For 

 a combination of a 50-mm-long and 23-mm-wide inter- 

 nal tag (J-tag) with a white Petersen disc (external) 

 tag (W-tag) (rows 1-3, Table 3), Mi,B,t(i))^0.37l8 

 (±0.1089)/yr if data are pooled for both sexes of school 

 shark, with a -log-likelihood of 9.4439. For the sex- 

 specific model, A(/,fi,^r/))=0.2829 (±0.1104 )/yr for males; 

 Mi,BMi»=:0.58l6 (±0.2946 )/yr for females, with a (male 

 and female) combined -log-likelihood of 8.7841 

 (=5.4509-h3.3332). The increase in value of the -log- 

 likelihood function for an extra parameter is, in this 

 case, negligible (x-io2507=2x(9-4439-8.7841)=1.3196), 

 suggesting no statistically significant differences in tag 

 shedding rates between sexes for white Petersen discs. 



