Lenarz and Shaw: Estimates of tag loss from double-tagged Anoplopoma fimbria 
295 
Figure 1 
Estimated distribution function of initial tag-retention rate, p , for sable- 
fish from a 2,000 replicate bootstrap. Intersections of the vertical lines 
with the distribution function mark the estimated 90% confidence band. 
1 7 * L-it . Ijnpt . ( Li b Z/o ) t . 
where dw - e J + e J - pe . 
We employed Mathematica (Wolfram, 1991) as an 
aid in deriving the derivatives. 
We programmed a parametric bootstrap with 2,000 
replicates in SAS to estimate confidence limits and 
bias. Since the bias estimates were very low, we used 
the uncorrected percentile method to estimate 90% 
confidence limits (Efron and Tibshirani, 1993). 
Results 
The SWFSC double tagged 229 fish during its egg- 
production survey cruise in early 1987. These fish 
were caught by bottom trawl and represented what 
was left over after needs for extensive biological 
samples were satisfied. The AFSC double tagged 
10,316 fish during its sablefish abundance-indexing 
surveys in the fall of 1986, 1987, and 1988. The fish 
were caught by fish traps and represented a signifi- 
cant portion of the catches by the AFSC. There were 
five recoveries of trawl-caught fish and 1,552 recov- 
eries of trap-caught fish through the end of March 
1995. Because there was an insufficient number of 
recoveries from trawl-caught fish to allow for exami- 
nation of recoveries by release gear types, we com- 
bined trawl and trap releases of tagged sablefish. We 
used recoveries of tag-bearing fish that were at lib- 
erty for no more than six years so that each release 
would have the same number of full years at liberty. 
Recoveries of tag-bearing fish were summarized by 
year of release and years at liberty (Table 1). 
Bootstrap estimates of the averages and medians 
of the parameters, p and L , were very close to the 
maximum-likelihood estimates, indicating that the 
estimation procedure was unbiased (Table 2). The 
bootstrap-estimated distribution functions indicated 
that the density functions were unimodal, smooth, 
and symmetrical (Figs. 1 and 2). The 90% confidence 
band for p does not overlap with 1 (Fig. 1), indicat- 
ing that although initial shedding is low, it is greater 
than 0. The 90% confidence bands for L 1 and L 9 do 
not overlap (Fig. 2), indicating that the instantaneous 
shedding rate is greater for posterior tags than for 
anterior tags. The model provided an excellent fit to 
the observed pattern of tag recoveries (Fig. 3). 
Discussion 
The double-tagging experiment with sablefish re- 
vealed that both immediate ( 1-p) and long-term in- 
stantaneous (L • ) tag loss rates were low and that long- 
term loss rates were higher for the posterior tagging 
position. The model fitted the recovery data very well, 
indicating that loss rates did not change with time 
at liberty during the first six years. Loss rates may 
have been higher for tags from the first release year 
because the ratio of single to double tag recoveries 
was higher than that during the other years (Table 
1). Since tags and tagging procedures were identical 
in all three years, we assumed that any differences 
in loss rates were random. 
Fishermen may have occasionally reported only 
one tag from recaptures of fish bearing two tags 
(Laurs et al., 1976; Wetherall, 1982). A reward was 
given for each tag returned to encourage complete re- 
porting of tags, and single tags were checked to deter- 
mine if the other tag of the pair had been reported at 
