174 
Fishery Bulletin 99(1 ) 
C obs _ 77 * D 
j —^ABC^J- 
The model stock was divided into two subcomponents under 
the refuge management system: one for refugia and the 
other for harvestable areas. Stock within refugia was based 
on the proportion of Gulf-wide biomass in refugia, a, using 
the spatial distribution of the historical catches to represent 
the spatial distribution of the actual exploitable biomass. 
Under the refuge management system, target or observed 
catches were fixed to the level of ABC under the current 
management system minus the average annual discards: 
C? = a-d)F ABC B J , 
where d = the average annual discard rate for shortraker 
and rougheye rockfish. 
Gulf-wide recruitment was allocated into refugia and non- 
refugia areas by using 
2(77 
log 
Q 
Q 
2(7 ? 
log 
M Y[ 
, M nnor)\ 
2o: 
[ 
r a )\ 
log 
A 
prior / J 
+u-<W 2 - 
Priors are listed as follows: 
Survey catchability coefficient, Q Q ~N( 1, 0.6 2 ) 
Natural mortality, M M ~ M0.03, 0.2 2 ) for 
shortraker rockfish 
M ~N( 0.025, 0.2 2 ) for 
rougheye rockfish 
S-R shape parameter, A A ~ N(0.889, 0.2 2 ) 
Catch information weighting A ~ Unz(0.001, 0.999) 
factor, A 
RJ 1 = aR, and R n fi nref = (1 -a)R r 
Impacts of harvest refugia on other fisheries 
Initial biomass for the projection years in refugia and non- 
refugia, where j = 1 , can also be separated at the beginning 
of 1997 as 
zuj = «b , =1 
B r ‘°" ref = (l-a)B i=v 
For, j = 2, 
B'j cf = ( 1 + p)s 0 B','\ ~ ps ■ 0 s l _. 2 aB,_ 2 + R'f - p(os 0 R r ;\ 
B"°" ref = (1 + p)s hl B""" M - ps ) _ 1 s / _ 2 (l- a)B _ 2 + 
Rilduref _ p (0g ^Rnomvf ^ 
Establishing no-take zones obviously affects other fish- 
eries in the zones. Main species in the harvest refugia 
include Pacific ocean perch ( Sebastes alutus), shortspine 
thornyhead ( Sebastolobus alascanus), northern rockfish 
( Sebastes polyspinis), dusky rockfish ( Sebastes ciliatus), 
sablefish ( Anoplopoma fimbria), and rex sole (G/yptoceph- 
alus zachirus), as well as shortraker and rougheye rock- 
fish. To examine the impacts of harvest refugia on other 
fisheries, the effects of depth constraints on refuge areas 
were considered. The reduction rates of “hot spot” catches 
by using different depth constraints were compared for 
each species. 
Results 
where F ( = 0 in refuge. 
And for j > 3, 
B'fi = ( 1 + p)s„B' l '\ ~ P s lB'fi 2 + R r f - p(os H R r ;\ 
B""" rcl =(1+p)s,_ 1 B;T / - PSj-iSj-iB'iT 1 + 
R7"" vr ~ 1 R"T'. 
All fishing mortalities were estimated by using the New- 
ton-Raphson method (Taylor and Mann, 1983). 
According to Bayes theorem, posterior log-likelihood is the 
sum of prior and experimental log-likelihood, logL(0|X) = 
logL( 9) + logL(X | 9). Therefore, posterior values of the oth- 
er parameters were evaluated by minimizing the total 
negative log-likelihood: 
Fixed exploitation-rate strategy 
Under an U F for ABC” fishing mortality (F=0.023), the 
ending biomass of shortraker rockfish would increase by 
about 800 metric tons (t) in twenty years, but the stock 
would decrease by over 7000 t if current fishing intensity 
(actual F=0.063) were continued (Table 2). Rougheye rock- 
fish declined under both U F for ABC” and “actual F" 
fishing scenarios (either F=0.025 or F=0.015) by about 
5000-12,000 t. Although the actual fishing mortality was 
much lower than the fishing intensity for the recom- 
mended ABC, rougheye stocks still declined. 
Annual recruits of shortraker and rougheye rockfish 
ranged from about 1% to 3% of annual biomass based on 
the recruitment scenario, with a Beverton and Holt shape 
parameter A=0. 889. For both scenarios of “F for ABC” and 
“actual F” fishing conditions, similar recruitment trends 
occurred in both species. Because the age at recruitment 
was assumed to be 30 (Nelson, 1986), future recruitment 
was not affected by the future fishing mortality schedule 
during the projection years. Recruitment strength varied 
