Maloney and Sigler: Age-specific movement patterns of Anoplopoma fimbria 
307 
Availability to the fishery by age 
Sablefish move progressively deeper with age, and as 
they do so, become available to the main commercial 
fishery (longline), which operates primarily on the con- 
tinental slope. The fraction of the total population avail- 
able by age to the commercial fishery was estimated by 
the following method. The initial number of tagged fish 
released in year t of age a is N' at . A fraction of the tags, 
Z = 0.048 (Lenarz and Shaw, 1997), are immediately lost 
or the fish die from tagging, such that a short time after 
tagging, some smaller number of tagged fish survive, 
N at = (1 - l)N' at . 
The year following tagging, the number of tagged fish 
is 
N a+U+ 1 = exp (-(M + Xs a F t + H)), 
where M = 0.1 (Sigler, 1999; Hanselman et al., 2006) 
is the instantaneous rate of natural mortal- 
ity; 
A = a calibration parameter (Heifetz and Fujioka, 
1991) to account for bias in assumed values 
for the instantaneous rates of annual fishing 
mortality (F t ); 
s a = availability (selectivity) to the commercial 
fishery; and 
H = 0.03 (Lenarz and Shaw, 1997) is the instan- 
taneous rate of tag shedding. 
The F t values were estimated independently in the 
Alaska sablefish stock assessment (Hanselman et al., 
2006). The fishery captures a number of the tagged 
fish, C at , where 
C at = Xs a F t HM + Xs a F t +H) 
(l-exv(-(M + 7is a F t + H)))N at 
The relationship between availability and age was rep- 
resented by the exponential-logistic function (Thompson, 
1994; Sigler, 1999) 
s a = l/(l-y)((l-y)/y) 7 
exp ( /fy(a - a)) / (l + exp ( /f( a - a ))) . 
The exponential-logistic function is flexible, allowing 
both asymptotic availability when availability increases 
with age to an asymptote, and dome-shaped availability 
when availability increases with age to a maximum and 
then decreases for older fish. The exponential-logistic 
function automatically scales maximum availability to 
1.0 and reduces to asymptotic availability as the param- 
eter y approaches zero. When y = 0, the parameter a is 
the age of 50% availability and the slope of the curve 
equals (4 (5 at a = a. W’hen y > 0, then a and /3 lose bio- 
logical meaning because a no longer represents the age 
at 50% availability, and y is a parameter that allows 
availability to decrease (and form the “dome-shape”) 
for older ages The fishery switched from open access 
to individual fishing quotas (IFQ) in 1995. This switch 
has been shown to affect availability of the fish to the 
fishery (Sigler and Lunsford, 2001). Thus, we estimated 
availability parameters, a, and y, as well as the fishing 
mortality calibration parameter, A, separately for each 
time period (1984-94, 1995-2005). We assumed that the 
estimated availability curves represent the commercial 
longline fishery because most tags (93%) were recovered 
by longline or other fixed gear types. 
Not all tagged fish caught in the sablefish fishery 
are reported (Heifetz and Maloney, 2001). The number 
of tags reported, R, is related to the number of tagged 
fish caught, C at , where R at - w t C at and w t is the report- 
ing rate. Heifetz and Maloney (2001) estimated annual 
reporting rates for 1980-98 and subsequent reporting 
rates were estimated of 0.43 for 1999-2001 and 0.52 for 
2002-05, which we applied in our analysis. 
The model parameters (a, (i, y, and A for 1984-94 
and 1995-2005) were estimated by maximum likeli- 
hood. The observed number of tag recoveries in any 
year-cohort grouping was small (mean of 6, range of 0 
to 27); therefore the expected number of tag recoveries, 
Q , could be approximated by the Poisson distribution 
(Hilborn, 1990). The negative log-likelihood (-log,L) for 
all observed recoveries was 
-log, L(Q at \R at ) 
= X „ X , ' ( ' Qat - R °* loge ( 1 3* ) + log, ' ( ■ R at ! )), 
which was minimized to find the most likely set of 
parameter estimates. We examined model fit using devi- 
ance (McCullagh and Nelder, 1983), which for any obser- 
vation of tag recoveries is 
devianceia, t) = - 2 { log, L( Q at \R at ) - log, L( R at \ R at J 
(Heifetz and Fujioka, 1991). We applied the likeli- 
hood ratio test for nested models (Hilborn and Mangel, 
1997) to determine whether model fit was significantly 
improved by assuming separate parameter sets for the 
open access and IFQ fisheries. We estimated the 95% 
confidence intervals of the parameters from their likeli- 
hood profiles (Hilborn and Mangel, 1997). 
Density-dependent effect on migration 
Migration may be affected by abundance if sablefish 
tend to disperse when abundant. We tested for a den- 
sity-dependent effect by examining whether recovery 
patterns by area were influenced by cohort abundance 
(recruitment strength). Recruitment strength is esti- 
mated through age-structured population modeling 
(Hanselman et al., 2006) and is expressed as the number 
of fish at age 2 (in millions). We tested by linear regres- 
sion whether more recoveries occurred in western areas 
for stronger year classes, hypothesizing that more mem- 
