Patrick et al.: Use of productivity and susceptibility indices to assess vulnerability of fish stocks to overfishing 
307 
(e.g., productivity, susceptibility, habitat) does little to 
improve the accuracy of an assessment. Development of 
our PSA began with an initial examination and reduc- 
tion of these 75 attributes to 35 after removing those 
perceived as redundant or not directly related to our 
definition of vulnerability. The remaining attributes 
were evaluated in two phases. In phase 1, our team 
provided individual scores (i.e., “yes,” “no,” or “maybe”) 
to determine whether each attribute was 1) appropriate 
for calculating productivity or susceptibility of a stock; 
2) useful at different scales (i.e., for stocks of various 
sizes and spatial distributions); and 3) capable of being 
calculated for most fisheries (i.e., for data availability). 
Attributes receiving a majority of “yes” scores for all 
three questions were retained. In phase 2, attributes 
receiving mixed scores, as well as new attributes not 
previously identified, were evaluated in a group dis- 
cussion. Through this process, 18 (9 productivity, 9 
susceptibility) of the 35 attributes were selected and 
four new attributes were added, including 1) recruit- 
ment pattern; 2) management strategy; 3) fishing rate 
in relation to natural mortality; and 4) desirability or 
value of the fishery. Overall, 22 attributes were selected 
for the analysis (10 productivity, 12 susceptibility). The 
large set of attributes to be scored, compared to previous 
versions of the PSA, is largely a result of the susceptibil- 
ity index, including both catchability and management 
attributes (see Susceptibility attributes section below). 
We also recognized that the PSA would mainly be used 
to evaluate extremely data-poor stocks; thus, a larger set 
of attributes would be useful to ensure that an adequate 
number of attributes were scored. 
Productivity attributes 
Many of the productivity attributes are based on 
Musick’s (1999) qualitative extinction risk assessment 
and the PSA of Stobutzki et al. (2001b). However, the 
scoring thresholds have been modified in many cases to 
better suit the distribution of life history characteris- 
tics observed in U.S. fish stocks (Table 1). Information 
on maximum length, maximum age, age-at-maturity, 
natural mortality, and von Bertalanffy growth coeffi- 
cient were available for more than 140 stocks considered 
to be representative of U.S. fisheries (see Patrick et al., 
2009). For these attributes, a range of scoring categories 
was evaluated by using analysis of variance (ANOVA) 
and post hoc tests to identify attribute scoring thresh- 
olds that produced significantly different bins of data. 
To ensure consistency in these attributes, the optimal 
scoring thresholds from the ANOVA were also compared 
to published relationships among maximum age and 
natural mortality (Alverson and Carney, 1975; Hoenig, 
1983), von Bertalanffy growth coefficient (Froese and 
Binohlan, 2000), and age at maturity (Froese and Bino- 
hlan, 2000). Overall, we found this approach produced 
sensible categories compared to the approach of inde- 
pendently dividing each attribute into equal bins or 
using a quantile method. We defined the following 10 
productivity attributes. 
3.0 
2.5 
s 2.0 
1.5 
★ jJ% 
1*T a *** 
-m v 
A .. ,v ' ^ Ir - 
%&&& , 4k. A 
4 Jr 
■ 
AS 
1 
e# 
ST 
□ 
* 
3.0 2.5 
(High) 
2.0 
Productivity score 
1.0 
(Low) 
Alaska shark complex 
? BSAI skate complex 
CA nearshore groundfish 
CA current pelagics 
NE groundfish 
HI swordfish longline 
HI tuna longline 
SA GOM longline 
3.0 
2.5 
1 2.0 
1.5 
1.0 
B 
o 
,,r~ : a 
: V • 
A A 
A 
l - ub 
A 
m, 
-i. v y , '~U' 
at a. A- Jk 
- Hg; 
. 
V 
3.0 
2.5 
(High) 
2.0 
Productivity score 
1.5 1.0 
( Low ) 
Data quality good 
,x Data quality 
moderate 
Figure 1 A Data quality poor 
(A) Overall distribution of productivity and susceptibility 
x-y plot for the 166 stocks evaluated in this study, dif- 
ferentiated by fishery. BSAI = Bering Sea and Aleutian 
Islands. SA GOM= South Atlantic and Gulf of Mexico. 
(B) Associated data quality of each datum point of the 
166 stocks evaluated in this study (see Appendix 1 for 
a list of the species in these fisheries). 
Intrinsic growth rate (r) This is the intrinsic rate of 
population growth or maximum population growth that 
would occur in the absence of fishing at the lowest 
population size (Gedamke et al., 2007). Density-depen- 
