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Fishery Bulletin 108(3) 
1999; Katsukawa, 2004). Today, however, many man- 
agers and scientists are turning to risk assessments to 
try to better manage stocks for which there are directed 
measures of stock status (e.g., Lane and Stephenson, 
1998; Peterman, 2004; Fletcher et al., 2005; Astles et 
al„ 2006). 
Risk assessments for data-poor stocks usually follow 
some type of semiquantitative method. In previous ex- 
amples of semiquantitative risk assessments, scientists 
have evaluated fishery impacts on bycatch and targeted 
species (Francis, 1992; Lane and Stephenson, 1998; 
Stobutzki et al., 2001a,), extinction risk (Musick, 1999; 
Roberts and Hawkins, 1999; Cheung et al., 2005; Mace 
et al., 2008), and impacts on ecosystem viability (Jen- 
nings et al., 1999; Fletcher et al., 2005; Astles et al., 
2006). These approaches allow for the inclusion of less 
quantitative information and a wide range of factors and 
can complement both stock and ecosystem assessments. 
In the United States, scientists of the National Ma- 
rine Fisheries Service (NMFS), National Oceanic and 
Atmospheric Administration, recently developed a risk 
assessment to assist managers and scientists in evalu- 
ating the vulnerability of stocks to overfishing ( Patrick 
et al., 2009). Vulnerability is a measurement of a stock’s 
productivity and its susceptibility to a fishery. Pro- 
ductivity refers to the capacity of the stock to recover 
rapidly when depleted, whereas susceptibility is the 
potential for the stock to be impacted by the fishery. In 
general, vulnerability is an important factor to consider 
when organizing stock complexes, developing buffers 
between target and limit fishing mortality reference 
points, and determining which stocks should be man- 
aged under a fishery management plan. This article de- 
scribes the method developed by scientists at NMFS for 
determining vulnerability, explores the various caveats 
and nuances in its underlying calculations, and presents 
an overview of its application to six U.S. fisheries. 
Materials and methods 
Determining vulnerability of stocks 
Several risk assessment methods were reviewed to deter- 
mine which approach would be flexible and broadly 
applicable across fisheries and regions. A modified ver- 
sion of a productivity and susceptibility analysis (PSA) 
was selected as the best approach for examining the 
vulnerability of stocks, owing to its history of use in 
other fisheries (Milton, 2001; Stobutzki et al., 2001a, 
2001b; Braccini et al., 2006; Griffiths et al., 2006; Zhou 
and Griffiths, 2008) and owing to recommendations by 
several organizations and working groups as a reason- 
able approach for determining risk (Hobday et al. 1 , 2 ; 
Rosenberg et al. 3 ; Smith et al., 2007). 
1 Hobday, A. J., A. Smith, and I. Stobutzki. 2004. Ecological 
risk assessment for Australian Commonwealth fisheries, 172 
p. Report R01/0934 for the Australian Fisheries Manage- 
ment Authority, Canberra, Australia. 
The PSA was originally developed to classify differ- 
ences in bycatch sustainability in the Australian prawn 
fishery (Milton, 2001; Stobutzki et al., 2001b) by evalu- 
ating the productivity (p) of bycatch stocks and their 
susceptibility (s) to the fishery. The values for p and s 
were determined by providing a score ranging from 1 
to 3 for a standardized set of attributes related to each 
index (i.e., 7 productivity and 6 susceptibility attri- 
butes). When data were lacking, scores could be based 
on similar taxa or given the most vulnerable score as 
a precautionary approach. The scores were then aver- 
aged for each index and displayed graphically on an x-y 
scatter plot (Fig. 1). The two-dimensional nature of the 
PSA leads directly to the calculation of an overall vul- 
nerability score ( v ) of a species, defined as the Euclidean 
distance of productivity and susceptibility scores: 
v = ^[(P-Z 0 ) 2 +(S-y 0 ) 2 ], (1) 
where x 0 and y 0 are the ( x , y ) origin coordinates, respec- 
tively. 
Stocks that received a low productivity score and a 
high susceptibility score are considered to be the most 
vulnerable to overfishing, whereas stocks with a high 
productivity score and low susceptibility score are con- 
sidered to be the least vulnerable. 
Since 2001, the PSA has been modified by others to 
evaluate habitat, community, and management compo- 
nents of a fishery (Hobday et al. 2 ; Rosenburg et al. 3 ). 
In general, these modifications have included expanding 
the number of attributes for scoring, exploring additive 
and multiplicative models for combining scores, and ex- 
amining a variety of alternative treatments for missing 
data. In the next section we review our application of 
a PSA to provide a uniform framework for evaluating 
the wide variety of fish stocks managed within the 
United States. 
Identifying productivity and susceptibility attributes 
With the expansion of the PSA to evaluate other man- 
agement factors (e.g., habitat impacts, ecosystem consid- 
erations, management efficacy), the number of attributes 
that could be considered in a PSA has increased con- 
siderably — in some instances to approximately sev- 
enty-five (Hobday et al. 2 ; Rosenberg et al. 3 ). Although 
~75 attributes have been recommended, Hobday et al. 2 
noted that the use of more than six attributes per index 
2 Hobday, A. J., A. Smith, H. Webb, R. Daley, S. Wayte, C. 
Bulman, J. Dowdney, A. Williams, M. Sporcic, J. Dambacher, 
M. Fuller, T. Walker. 2007. Ecological risk assessment for 
the effects of fishing: methodology, 174 p. Report R04/1072 
for the Australian Fisheries Management Authority, Can- 
berra, Australia. 
3 Rosenberg, A., D. Agnew, E. Babcock, A. Cooper, C. 
Mogensen, R. O’Boyle, J. Powers, G. Stefansson, and J. 
Swasey. 2007. Setting annual catch limits for U.S. fisher- 
ies: An expert working group report, 36 p. MRAG Americas, 
Washington, D.C. 
