Ralston et al.: A meta-analytic approach to quantifying scientific uncertainty in stock assessments 
229 
It is therefore possible, in theory, to express uncer- 
tainty regarding biomass in a quantitative manner 
by appropriately weighting different states of nature 
presented in groundfish decision tables, which are 
derived through the collective expert opinion of the 
analytical team, the review panel, and the Scientific 
and Statistical Committee. A preliminary analysis 
of this approach has been completed, although a 
comprehensive analysis was not possible because of 
incomplete data in stock assessment documents. In 
particular, statistical weights for all three states 
of nature that are defined in the decision analysis 
(low, base, and high) have not always been explicitly 
expressed. When a characterization of the relative 
probabilities of the various states of nature under 
consideration is lacking, decision tables provide a 
type of risk assessment, but they are inadequate for 
risk management ( sensu Francis and Shotton, 1997). 
Still, in three of the nine cases examined, variances 
from decision tables were greater than a CV=37%. 
We view these preliminary findings as promising 
and recommend that a thorough analysis of statisti- 
cally weighted states of nature be considered as an 
alternative approach to characterization of scientific 
uncertainty in groundfish stock assessments. 
Figure 7 
Relationship between the probability of overfishing (P*) 
and an appropriate buffer between the allowable biologi- 
cal catch (ABC) and the overfishing level (OFL), based on 
varying amounts of uncertainty ( <7=0.36, 0.72, and 1.44) 
assigned to different stock assessment tiers (l=data-rich, 
2 = data-moderate, and 3 = data-poor), respectively. 
Conclusions 
Present and future management approaches 
for setting catch limits 
This analysis was prepared in response to a pressing 
management need that arose from the requirements of 
the reauthorized MSA to implement ACLs by 2011. It is 
revealing to consider the ultimate impact of accounting 
for scientific uncertainty when setting catch limits at 
the PFMC. For all assessed groundfish species Table 4 
provides the ABC and ACL as a percentage of the esti- 
mated F msy harvest level (OFL) as they were adopted 
by the PFMC in June 2010 (see footnote 5). Note that 
groundfish stocks are classified into three tiers based on 
the amount and quality of the information that is avail- 
able for assessment modeling: tier-1 stocks are those for 
which there is data-rich information; tier-2 stocks are 
those for which there is data-moderate information; and 
tier-3 stocks are those for which there is data-poor infor- 
mation. Moreover, there was a consensus that scientific 
uncertainty cannot be lower for stocks that are more 
data limited. Hence, because o=0.36 was derived from 
81 tier-1 stock assessments, the Scientific and Statisti- 
cal Committee recommended, and the PFMC elected to 
adopt, proxy estimates of uncertainty equal to double 
(0.72) and quadruple (1.44) a for tier-2 and tier-3 stocks, 
respectively. This framework then provided a basis for 
separate ABC control rules for each tier. The PFMC 
then elected to adopt a P*=0.45 for all tier-1 stocks 
and, with certain exceptions, P*= 0.40 for tier-2 and 
tier-3 stocks. Hence the scientific uncertainty buffers for 
the Council’s data-rich stocks amounted to setting the 
ABC 4% below the OFL. Similarly, the adjustment for 
tier-2 stocks (<7=0.72 and P*=0.40) was a 17% reduction 
(ABC = 83% of the OFL) (Fig. 7). The differences between 
ACLs and ABCs shown in Table 4 reflect a variety of 
other factors, including 1) requirements for rebuilding 
overfished stocks; 2) harvest control rules for prevent- 
ing stocks from becoming overfished; 3) socioeconomic 
considerations; 4) bycatch concerns for depleted species; 
5) ecological considerations, and other factors. 
Parsing scientific uncertainty in estimates of OFL 
from these other considerations was a particular chal- 
lenge for the PFMC. Before the implementation of the 
new harvest specification framework recommended in 
the revised National Standard Guidelines, which were 
compelled by the reauthorized MSA, scientific and man- 
agement uncertainties were considered jointly in set- 
ting optimum yields below the MSY harvest level. We 
have shown that quantifying scientific uncertainty in 
estimating exploitable biomass across multiple assess- 
ments through meta-analysis is a reasonable first ap- 
proximation for explicitly accounting for uncertainty in 
preventing overfishing. Although all sources of error 
may not be have been considered with this approach, 
it was a helpful first step in the PFMC process. Im- 
portantly, with this approach the role of the Scientific 
and Statistical Committee in quantifying scientific un- 
certainty (by determining o, a purely technical issue) 
and the role of the PFMC in deciding a preferred level 
of risk aversion to overfishing (by choosing P*, which 
is a policy decision), are both duly respected. Coupling 
these two independent actions will help determine the 
ABC harvest level in a manner that is responsive to the 
mandates of the reauthorized MSA. 
