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Fishery Bulletin 99(1 ) 
exact dates of recovery are known, as was the case with 
the data from the Maldives. 
Following Kirkwood and Walker (1984), consider an 
originally single tagged fish. Assuming that a is the type-I 
retention probability (1-type-I shedding probability) and 
A is the type-II shedding rate, assumed to be constant for 
short-lived species such as the skipjack tuna, then for an 
originally single tagged fish, the probability of a tag being 
retained at time t is given by 
Q(t) = a exp (-At). (1) 
Suppose that fish are double tagged with identical tags 
and released at time t = 0, and let pft) be the probability 
that the fish is alive and at liberty retaining i (z=0, 1, 2) 
tags at time t. Then, under the assumption that both tags 
are retained after immediate shedding and have indepen- 
dent and identical probabilities, 
p 0 (t) = [1 - Q(t)] 2 
zation routines in AD Model Builder (Otter Research Ltd., 
1996). 
Results 
The numbers of recoveries of originally double tagged fish 
reported as retaining one (indicating left- or the right-side 
tag) or two tags on recapture are shown in Table 1, with 
their times at liberty. 
The maximum likelihood estimate of A was 0.22/yr 
(SE=0.13) and that of a was 0.97 (SE=0.03). If a = 1, the 
maximum likelihood estimate of A was 0.30/yr (SE=0.065/ 
yr). A likelihood ratio test (Cox and Hinkley, 1974) shows 
that the full model does not provide a significantly better 
fit to the data (at 5% level) than its special case (a=l) 
(P=0.146). 
Discussion 
p 1 (t) = 2Q(t)[l-Q(t)} (2) 
p 2 it ) = Q(t) 2 . 
In practice, identifiable recaptures will consist only of fish 
retaining either one tag or two tags. If P' j (t) is the prob- 
ability that an originally double-tagged fish, recaptured at 
time £■, is reported to have retained i tags (1=1, 2), then 
conditional on the retention of at least one tag, the prob- 
ability of capturing a fish retaining two tags at time t is 
P'(t) = 
P 2 (*> 
1-PoU) 
(3) 
and the probability of capturing a fish retaining only one 
tag at time t is 
p;(t) = 
P i<C 
(4) 
Suppose n fish were recaptured in the experiment and 
reported to have retained at least one tag on recapture, 
and that the ith fish was recaptured at time t r Define indi- 
cator variables N 221 = 1, N/ 11 = 0 if two tags were reported 
upon recapture, and N/ 2) = 0, N/" = 1 if only one tag was 
reported upon recapture. 
It follows from Equations 3 and 4 that if all fish suffer 
the same risks of mortality, the log likelihood ( ig) of the 
data conditional on recapture times { t r 1=1, 2, ... , n) is 
given by 
;//(«, A) = N) 2 ' ln[P,'(£, )] + N]" ln[P,'(£ ( )]. (5) 
z=l 
Maximum likelihood estimates of the parameters ( a. A) and 
their asymptotic standard errors were found by maximiz- 
ing ty with respect to them, by using the nonlinear minimi- 
One of the most important assumptions in double-tagging 
experiments and in the model used in our analysis is that 
shedding rates of the first and second tags is the same 
(Hearn et al., 1991 ). A simple way to investigate possible dif- 
ferences in the shedding rates of the first and second tags is 
to examine the number of returns of fish that have retained 
either the first or the second tag and their temporal distri- 
bution. There were seven recoveries of fish reported to have 
retained a single tag, of which four fish retained the left tag 
and three retained the right tag (Table 1 ). Although few, the 
similar numbers of recaptured fish with tags on the left side 
as those on the right side and the temporal distribution of 
these fish (Table 1) show clearly that there is no evidence of 
differences in their shedding rates. 
Another important assumption, but one that might eas- 
ily be violated, and that is difficult to test, relates to the 
way in which double-tagged recoveries were reported. The 
commonassumption( asmadehere )isthatrecoveriesoffish retain- 
ing double tags were always reported as a pair, and never 
as a “single” tag recovery. It is also assumed that the proba- 
bility of reporting fish recovered with single or double tags 
is the same. Hampton (1997) showed that under this as- 
sumption, the reporting probability has no influence on the 
maximum likelihood estimates of a and A. Given the public- 
ity and incentives to return all the recaptured tags (Ander- 
son et al., 1996), and the procedures adopted in tagging, it 
is highly unlikely that these reporting-rate assumptions 
were violated in the Maldives tagging program. 
In their original paper describing the method of analysis 
and application to small data sets, Kirkwood and Walker 
(1984) noted that potential bias arises because the result- 
ing estimates are conditional on the times of recapture; 
a different time sequence of recapture times would result 
in different parameter estimates. Clearly, this potential 
bias arose in our experiment. Ideally, for robust estimation 
of the parameters, one would need a data set with large 
numbers of fish that have shed a tag. This point needs to 
be borne in mind when designing future tagging experi- 
ments for skipjack tuna in the Indian Ocean. 
