Ralston et al.: A meta-analytic approach to quantifying scientific uncertainty in stock assessments 
223 
Table 1 (continued) 
Stock group 
Species 
Year 
Author! s) 1 
Koundfish 
Pacific whiting ( Merluccius productus ) 
2004 
Helser et al. 
(continued) 
2005 
Helser et al. 
2006 
Helser et al. 
2007 
Helser and Martell 
2008 
Helser et al. 
2009 
Hamel and Stewart 
lingcod ( Ophiodon elongatus ) 
2000 
Jagielo et al. 
2003 
Jagielo et al. 
2005 
Jagielo and Wallace 
2009 
Hamel et al. 
sablefish ( Anoplopoma fimbria) 
1992 
Methot 
1994 
Methot et al. 
1997 
Crone et al. 
1998 
Methot et al. 
2001 
Schirripa and Methot 
2005 
Schirripa and Colbert 
2007 
Schirripa 
Flatfish 
Dover sole ( Microstomus pacificus) 
1997 
Brodziak 
2001 
Sampson and Wood 
2005 
Sampson 
petrale sole ( Eopsetta jordani ) 
1999 
Sampson and Lee 
2005 
Lai et al. 
2009 
Haltuch and Hicks 
Coastal pelagic 
Pacific mackerel ( Scomber japonicus) 
2004 
Hill and Crone 
2005 
Hill and Crone 
2007 
Dorval et al. 
2009 
Crone et al. 
Pacific sardine ( Sardinops sagax) 
2004 
Conser et al. 
2007 
Hill et al. 
2009 
Hill et al. 
1 Individuals should contact the PFMC (John.DeVore@noaa.gov) for copies of specific assessment documents 
or visit “http://www.pcouncil.org/ 
groundfish/stock-assessments/” or “http://www.pcouncil.org/coastal-pelagic-species/stock-assessment-and-fishery-evaluation-safe-documents/”. 
Pooled results 
Figure 5 shows the unweighted, pooled distributions of 
residuals for the four groupings of stocks. The distribu- 
tion for rockfish is close to normal, whereas those for 
roundfish and flatfish exhibit some non-normal features. 
For example, the distribution for coastal pelagic species 
exhibits a tail to the left. However, the pooled estimates 
of a are all rather similar, regardless of the method used 
to aggregate the data (Table 3). Although to some degree 
the point estimates of <7 differ among groups, the sample 
sizes are also rather small. To explore whether the data 
provide support for treating each group separately, esti- 
mates of a 2 were fitted by using a linear mixed model 
with group as a random effect. That analysis provided no 
support for stratification by group; the point estimate of 
the between-group variance was essentially zero (<1(F 5 ). 
Given the lack of support for among-group variation 
in cr, we combined the data over all stocks. In this 
instance, because the need to treat each species as a 
replicate is not required, method 2 (simple pooling of 
all residuals) is most justified. Aggregating the devia- 
tions over all stocks (Fig. 6) led to a point estimate of 
a- 0.358. If the residuals are assumed to be indepen- 
dent, an approximate 95% confidence interval for the 
statistic is 0.342<er<0.374. 
Discussion 
We evaluated three approaches for quantifying scientific 
uncertainty in the groundfish and coastal pelagic stock 
assessments that have been conducted over the last 20 
years for the PFMC. We conclude that measurement of 
log-scale variability as deviations from the mean is a 
suitable analytical approach for measuring uncertainty 
in biomass estimates. Moreover, a comparison of stock- 
and group-specific estimates indicated that a single 
value of a=0.36, which is equivalent to a CV of 37% 
on the arithmetic scale, is a reasonable lower-bound 
