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Fishery Bulletin 95(2), 1997 
serted between and engaged behind the ptery- 
giophores of the dorsal fin. Fork length, tag number, 
and the geographical position and date of release 
were recorded for each fish. Only fish judged to be in 
viable condition were tagged. 
Wetherall (1982) reviewed literature on analyti- 
cal methods for estimating tag-shedding rates. For 
mathematical convenience, tag shedding is usually 
described by tag-retention models. Following 
Wetherall (1982) and common practice, we assume 
that the retention rate of a tag of type i through the 
mid-point of the yth recovery period is 
retij = p,e ~ L,tj , (1) 
where p ; 
i 
i 
t; 
retention rate during initial brief time 
after tagging for tag type i; 
instantaneous tag shedding rate for tag 
type i; 
1 for anterior tag; 
2 for posterior tag; and 
time at liberty at midpoint of jth recov- 
ery period. 
The probability that a recovered tag-bearing fish has 
only tag type 2 during the jth recovery period is 
_ J l] (l-J 2] ) 
2] 
The probability that a recovered tag-bearing fish has 
both tags is 
(1 J XJ ) ( 1 J 2J ) 
We assumed that the proportions of tag recoveries 
among recovery type followed a multinomial distri- 
bution. After terms not affected by the parameter 
estimates were dropped, the log likelihood of the ob- 
served recoveries is 
T 
£ = X [ r !> ln ' ( J 2j- ) + r 2 j In ( J xj ) + (r K , + r 3j .) In ( 1 - J u ) 
7=1 
+A +r 3 j)ln(l-J 2j )-{r lj +r 2j +r 3j )\na-J lj J 3j j\; 
We used a weighted linear regression approach, 
as suggested by Wetherall (1982) for multiple re- 
leases, for an exploratory analysis of the data. The 
results indicated that p ; did not vary with tag type, 
but that L did. The regression approach assumed 
that the error terms were independent and normally 
distibuted. We believed that these assumptions may 
not be valid and that it would be more appropriate 
to use a maximum-likelihood procedure for the analy- 
sis. We also decided to assume that p is independent 
of tag type. Because the linear regression approach 
was used only for an exploratory analysis of the data, 
we neither describe it nor present the results from 
using it in this paper. 
We developed a new model and used maximum- 
likelihood principles to estimate the parameters, fol- 
lowing the suggestions of Wetherall (1982). We com- 
bined recoveries from the three release periods and 
estimated confidence bounds for the parameters ( p,L v 
and L 2 ) by bootstrapping ( Efron and Tibshirani, 1993 ). 
The probability that a tag of type i is shed by the 
jth recovery period is 
J,j = 1- pe L,tj . (2) 
Then the probability that a recovered tag-bearing fish 
has only tag type 1 during the jth recovery period is 
p _ j) 
1J '-"'.A, 
where T = number of recovery periods; 
when i = 1 or 2, 
r t j = number of fish recovered with only a type 
i tag duringyth recovery period; and 
when i =3, 
r = number of fish recovered with both tags. 
We used the NLIN procedure (SAS Institute Inc., 
1990) with the Gauss-Newton method, which re- 
quires derivatives of the log likelihood with respect 
to the parameters, to estimate the parameters of the 
model. The derivatives are 
8J£ 
8p 
XK /{ P ~ eLlt ‘ ) + r 2j /( P - eL ' tj ) + 
7=1 
A + r 2 j +2r 3j )/p- 
(r i; + r 2) +r 3j )( 1/ p- 1 /(div)e L ' +L2)tj )], 
jr = Xhi A /eL ' tj ~ p) ~ {r ^ + r 37 Xj - 
° ^i 7=1 
(r t 7 + r 2j + r 3j )tj e~ L ' tj (pe ^ - 1)/ div J, 
T 
= S[ r nA /(e ^ - P ] - (r 2 7 “ r 37 )f 7 - 
2 7=1 
A +r 2 J +r 3j'> t j e L ‘‘ J (P e L> ‘ J ~ 
