226 
Fishery Bulletin 109(2) 
0.40 
§ 0.30 
t 
o 0.20 
o 
d: o.io 
0.00 
0.60 
0.50 
c 
O 0.40 
O 0.30 
Q. 
O 0.20 
^ 0.10 
0.00 
0.25 
c 0.20 
O 
■E 0.15 
O 
§■ 0.10 
0.05 
0.00 
0.60 
0.50 
C 
.9 0.40 
O 0.30 
CL 
o 0.20 
0.10 
0.00 
0.25 
c 0.20 
O 
‘-E 0.15 
O 
§■ 0.10 
0.05 
0.00 
, mf 
bocaccio 
Sebastes 
paucisipinis 
t=u 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
yellow eye rockfish 
Sebastes 
ruberrimus 
LL 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
cabezon 
Scorpaenichthys 
marmoratus 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
sablefish 
— I Anoplopoma 
fimbria 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
0.25 
0.20 
0.15 
0.05 
0.00 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
Residual 
0.25 
0.20 
0.15 
0.10 
0.05 
0.00 
canary rockfish 
Sebastes 
-d- 
0.50 
0.40 
0.30 
0.20 
0.10 
0.00 
ad 
chilipepper 
Sebastes 
goodei 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
darkblotched 0.40 
Pacific ocean perch 0.40 
widow rockfish 
rockfish 
Sebastes alutus 
Sebastes 
Sebastes 0.30 - 
—1 
0.30 ■ 

entomelas 
crameri 
0.20 - 
0.20 - 
0.10 ■ 
— | 0.10- 
0.00 • 
. , d 
■ 1 ■ . . , 0.00 ■ 
. . . . r 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
0.60 
0.50 
0.40 
0.30 
0.20 
0.10 
0.00 
yellow tall 0.50 
shortspine 
rockfish Q 4Q 

thornyhead 
Sebastes 
Sebastolobus 
fl avid us 0.30 ■ 
alascanus 
0.20 ■ 
0.10 ■ 
. . n-rr 
~l 0.00 • 
=i 
=1 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
0.30 
0.25 -I 
0.20 
0.15 
0.10 
0.05 
0.00 
lingcod 
Ophiodon 
elongatus 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
0.40 i 
0.30 -I 
0.20 
0.10 - 
0.00 
-4=1=4 
Pacific w hiting 
Merluccius 
productus 
0.40 
0.30 
0.20 
0.10 
0.00 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
Dover sole 
Microstomus 
pacificus 
-4=4 
a 
0.40 
0.30 
0.20 
0.10 
0.00 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
petrale sole 
Eopsetta 
jordani 
Jd 
a 
■1 4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1 4 
Residual 
Pacific mackerel 
0.40 
Pacific sardine 
Scomber 
0.30 ■ 
Sardinops 
japonicus 
sag ax 
0.20 ■ 
0.10 ■ 
a 
0.00 ■ 
T T . T n 
=f=l .... 
-1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0 1.4 
Residual 
Figure 3 
Frequency distributions of log-scale biomass deviations for selected groundfish and coastal pelagic species 
in stock assessments conducted for the Pacific Fishery Management Council. Residual deviations were 
calculated from annual means taken from the biomass time series presented in Figure 2 (A and B). 
approach may prove useful for quantifying biomass 
uncertainty if it is applied in other geographical or 
management regions. 
To illustrate how an estimate of log-scale variance 
can be used to form the basis of an ABC control rule, 
we exponentiate a lognormal distribution with a mean 
equal to zero and ct=0.36. Half of the probability den- 
sity is then below a value of 1.00, which represents 
the median of the distribution. One can then select a 
cumulative probability less than 0.50 that maps onto 
a multiplier (=buffer) that can be interpreted as a re- 
duction from the median of the distribution (Fig. 7). 
For example, 40% of the probability density is found 
at values <0.913. If one assumes that the median of 
