Soh et al.: Role of marine reserves in the management of Sebostes borealis and S. aleutianus 
173 
i 
j 
A 
Q 
d 
a 
M 
A 
~'a.3C 
P 
(0 
k 
s 
(Jobs 
Qpred 
S C or F C 
gobs 
B 
B re f 
g non ref 
R 
R re f 
gnonref 
years for the assessment period from 1961 to 
1996; 
years for the future projection period from 
1997 to 2016; 
weighting factor between survey and fishery 
information for the combined catch history { = 
1.0 when using survey data alone, 0.0 when 
using fishery data alone); 
survey gear efficiency; 
average annual discard rate; 
proportion of total biomass in refugia, esti- 
mated by cumulated catch data; 
natural mortality rate; 
recruitment strength in the Beverton and Holt 
model; 
fixed exploitation rate for determining ABC; 
Brody coefficient; 
annual growth rate of a fish in weight, = ; 
age at recruitment; 
survival rate (s- = e~ [Fl+M) )\ 
observed catches for i and predetermined pre- 
dicted catches for j; 
predicted catches based on catch equation; 
reconstructed catches based on survey (S) or 
fishery (F) information; 
biomass index from surveys; 
Gulf-wide total predicted biomass; 
predicted biomass in refugia; 
predicted biomass in nonrefugia; 
Gulf-wide total recruits; 
predicted recruits in refugia; 
predicted recruits in nonrefugia. 
mass level was assumed to be in an equilibrium state. As 
a result, initial biomass and the annual recruitment bio- 
mass to the unexploited stock can be shown as follows: 
B 1 - B 0 = B 
1961 
R 1 = R 19S1 = B 
1 s„ + p ( s„ s 0 ) 
1- p CO s 0 
where survival rate s 0 = e~ M . 
However, biomass in the second year, B 2 , can be defined 
from the SRA model as 
B 2 — B-[9g2 - ( l+p)SjB| pSjSqBq + R 2 p&JSj-ffj, 
where B x = B 0 and survival rate s- = e AFl+M ). 
R t is the recruitment biomass at the stock size B ( and 
is modeled by using a stochastic Beverton and Holt stock- 
recruitment relationship: 
R ; = R,e f ' , e ( - AhCfcr;) for 2 <i<k, and 
R — B, 
B , 
Bn 
1- A 
1-A* 
a. 
e f ' ,f, ~ N(Q,g 2 c ) for i > k, 
where k = the recruitment age (assumed k=30). 
Stock assessment 
Catch histories, based on survey and fishery information, 
were reconstructed for both shortraker and rougheye rod; fish 
(Soh, 1998). Because surrey data were available from 1961 
and fishery data from 1977, survey information was used 
in the construction of catch history for the years 1961-76, 
whereas an information weighting factor (A) was applied to 
combine the two catch histories for the years of 1977-90. 
Since 1991, independent catch data for the shortraker-rough- 
eye roekfish subgroup have been available. As a result, the 
combined catch history, which was used as observed catches 
(C ofcs ) in the model, can be described as follows: 
/~iobs 
^1961 
S C 
^1991 
fiobs 
'“'1976 
s c 
'-'1976 
/^obs 
'“'1977 
^ S Cl 977 +( 1 - A) F C 1977 
, r^obs 
'“'1990 
A s C 1990 + ( 1-A) f C 3990 
obs 
^1991 
F c 
^ 1991 
f^obs 
_ 1996 
F c 
^1996 
13 1 is defined as an initial biomass at the beginning of 
1961 and R 1 is the recruitment in 1961. The pristine bio- 
Since 1963, biomass has been able to be estimated by 
using the SRA model based on the Deriso’s delay-differ- 
ence equation (1980): 
Bj = (1 + p)s,_iB,_i - ps ,-\S i-%B i + 
R t - pws t _ 1 R i j for i > 3. 
Future projection of biomass and recruitment 
The following biomass and recruitment models were 
applied throughout the projection period under the cur- 
rent management system: 
B, = (1 +p)s l _ l B i _ l - ps j^s j_. 2 Bj _2 + Rj - pcos J _ l R ] _ l 
B _ l± 
R = R Jk e' ,f ~ N(0,o 2 ). 
l-Al-Ai 
l B„ ) 
Under the current management system, F ABC was fixed 
during the projection period. Predetermined predicted 
catches (“target catches” or “observed catches”) could then 
be calculated from 
