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Fishery Bulletin 109(2) 
certainty in fisheries assessments. Methods that aim 
to quantify the variance of assessment model outputs, 
given an assumed model structure, include asymptot- 
ic statistics, bootstrapping, and the use of Bayesian 
methods (Hilborn and Walters, 1992; Quinn and De- 
riso, 1999; Punt and Hilborn, 1997). These techniques 
are commonly applied in stock assessments, although 
they all are conditioned on some combination of 1) an 
assumed model structure; 2) prespecified parameters 
(e.g., natural mortality); 3) the particular data sets the 
analyst uses, which may be a subset of those available; 
and 4) the statistical weights that are assigned to the 
data elements. Moreover, it is often true that in as- 
sessments of data-poor species, more parameters are 
fixed than in those of data-rich species — a situation 
that leads to the paradoxical situation where estimates 
of uncertainty are frequently greater for assessments 
where more is known (e.g., Pribac et ah, 2005). It is 
also not uncommon that estimated confidence intervals 
are later shown to have been unrealistically narrow 
(Stewart and Hamel, 2010). 
Uncertainty associated with having selected a par- 
ticular model from a set of competing models can be 
assessed by using sensitivity tests, and, in a few cases, 
model averaging has been used to account for uncer- 
tainty due to model structure (e.g., Brandon and Wade, 
2006; Brodziak and Piner, 2010). Model averaging is 
only effective, however, when all selected models are 
fitted to the same data sets. In principle, Monte Carlo 
methods can be used to quantify model uncertainty 
if probabilities can be assigned to the various models 
and data sets under consideration (e.g., Restrepo et al., 
1992). However, these methods are not without their 
limitations (Poole et al., 1997), and assigning probabili- 
ties to, for example, alternative values of a prespecified 
parameter can be difficult (e.g., Kolody et al., 2008). 
The reauthorized MSA and National Standard Guide- 
lines define the overfishing limit (OFL) as the current 
catch that results from fishing at a rate (F Msy ) that is 
expected to produce the long-term maximum sustain- 
able yield (MSY); catches in excess of the OFL, or fish- 
ing mortalities in excess of F MSY , constitute overfishing. 
Furthermore, the acceptable biological catch (ABC) is 
the maximum allowable ACL and is defined as a catch 
which is lower than the OFL to account for scientific 
uncertainty. On the U.S. west coast, the Pacific Fishery 
Management Council (PFMC) has adopted a policy of 
defining the ABC as the product of the OFL and a frac- 
tional factor or “buffer” that is based on the probability 
that the ABC exceeds the true (but unknown) OFL, a 
value termed P* (Shertzer et al., 2008; PFMC, 2010). A 
P*= 0.5 is equivalent to fishing at F MSY , with no precau- 
tionary reduction to account for scientific uncertainty. 
Thus, the approach adopted by the PFMC requires the 
development of an ABC control rule that maps a policy 
decision (P'*< 0.5) to a buffer that is used to reduce the 
OFL to an ABC. 
We outline and apply the approach developed by 
members of the Scientific and Statistical Committee 
of the PFMC to calculate these factors for groundfish 
and coastal pelagic species on the basis of results from 
historical analyses. With a historical analysis, we sum- 
marize the results of all the assessments that have been 
conducted for a particular stock. Importantly, repeat 
assessments conducted for the PMFC often incorporate 
a variety of changes that include many of the model 
specification problems identified above. Although our 
approach is purely empirical and somewhat ad hoc, it is 
a pragmatic way to address the new legislative require- 
ment to account for scientific uncertainty and to set 
precautionary catch limits. It was formally adopted by 
the PFMC for use in setting total allowable groundfish 
catches for the 2011-12 biennium (PFMC, 2010). 
Materials and methods 
Sources of uncertainty 
Calculation of an OFL typically involves three steps: 1) 
estimation of current exploitable biomass ( B t )\ 2) projec- 
tion of the population biomass into the future for some 
number of years; and 3) application of an estimate of 
F M sy the forecasts of future biomass. Although there 
are clear uncertainties associated with each step, the 
Scientific and Statistical Committee elected to focus 
first and foremost on variation in the estimation of the 
biomass in the terminal year of groundfish and coastal 
pelagic species stock assessments. That biomass is a 
significant source of uncertainty is aptly illustrated 
in Figure 1, which shows the results of the 15 Pacific 
whiting ( Merluccius productus ) stock assessments that 
have been conducted for the PFMC over the last 18 
years (Stewart and Hamel, 2010). It is instructive to 
examine this species because it is one of the most data- 
rich 1 * * * * stocks managed by the PFMC, is of substantial 
economic importance, and has been assessed largely 
on an annual basis for many years. However, estimates 
of biomass have been highly variable from a historical 
perspective, in spite of considerable scientific resources 
having been devoted to evaluating the status of this 
stock. Note, for example, that estimated spawning bio- 
masses in 1985 ranged from 1.2 to 5. 9xl0 6 metric tons 
(t) over the 15 stock assessments, representing a 5-fold 
range in abundance. 
There are many reasons for this type of “among” as- 
sessment variability in stock size estimates, including 
differences in 1) overall model structure; 2) altered 
fixed values and prior distributions for important 
parameters; 3) changes in the availability of data; 4) 
the composition of the review panel; 5) the makeup of 
the analytical team that conducted the assessment; 
and 6) the modeling software that was used. Impor- 
1 Data-rich stock assessments contain many informa- 
tive data elements, which typically would include catch 
(landings+discards), life history information (growth, natu- 
ral mortality, and reproductive parameters), annual age or 
length compositions sampled from the fishery, and trend 
indices. 
