Patrick et al.: Use of productivity and susceptibility indices to assess vulnerability of fish stocks to overfishing 
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dent compensation is at a maximum in these depleted 
conditions and therefore r is a direct measure of stock 
productivity. The scoring thresholds were taken from 
Musick (1999), who stated that r should take precedence 
over other productivity attributes because it combines 
many of the other attributes defined below. 
Maximum age (t max ) Maximum age is related to natu- 
ral mortality rate (M), where M is inversely related to 
maximum age (Hoenig, 1983). The scoring thresholds 
were based on the ANOVA applied to the observed fish 
stocks considered to be representative of U.S. fisheries 
(see Patrick et al., 2009). The t max for a majority of these 
fish ranges between 10 and 30 years. 
Maximum size (L ma J Maximum size is also correlated 
with productivity, and large fish tend to have lower levels 
of productivity (Roberts and Hawkins, 1999), although 
this relationship varies phylogenetically and is strongest 
within higher taxonomic levels (e.g., genus, family). The 
scoring thresholds were based on the ANOVA applied to 
the observed fish stocks considered to be representative 
of U.S. fisheries (see Patrick et al., 2009). The L max for 
a majority of these fish ranges between 60 and 150 cm 
total length (TL). 
Growth coefficient (k) The von Bertalanffy growth 
coefficient measures how rapidly a fish reaches its maxi- 
mum size. Long-lived, low-productivity stocks tend to 
have low values of k (Froese and Binohlan, 2000). The 
scoring thresholds of 0.15 and 0.25 were based on the 
ANOVA applied to the observed fish stocks considered 
to be representative of U.S. fisheries (see Patrick et al., 
2009). This observed range of k is roughly consistent 
with the values obtained from Froese and Binohlan’s 
(2000) empirical relationship k = 3/ t max of 0.1 and 0.3, 
based upon t max values of 10 and 30. 
Natural mortality (M) Natural mortality rate directly 
reflects population productivity because stocks with 
high rates of natural mortality will require high levels 
of production to maintain population levels. For several 
methods of estimating M, one must rely on the negative 
relationship between M and t max , including Hoenig’s 
(1983) regression based upon empirical data, the quan- 
tile method that depends upon exponential mortality 
rates (Hoenig, 1983), and Alverson and Carney’s (1975) 
relationship between mortality, growth, and t max . The 
scoring thresholds from the ANOVA applied to the fish 
stocks considered to be representative of U.S. fisheries 
were 0.2 and 0.4, roughly consistent with those produced 
from Hoenig’s (1983) empirical regression of 0.14 and 
0.4, based on t max values of 10 and 30. 
Fecundity Fecundity (i.e. , the number of eggs produced 
by a female for a given spawning event or period) varies 
with size and age of the spawner; therefore we followed 
Musick’s (1999) recommendation that fecundity should 
be measured at the age of first maturity. As Musick 
(1999) noted, low values of fecundity imply low popula- 
tion productivity, but high values of fecundity do not 
necessarily imply high population productivity; thus, 
this attribute may be more useful at the lower fecun- 
dity values. The scoring thresholds were taken from 
Musick (1999) and were fecundities values of 1,000 
and 100,000. 
Breeding strategy The breeding strategy of a stock 
provides an indication of the level of mortality that may 
be expected for the offspring in the first stages of life. 
To estimate offspring mortality, we used Winemiller’s 
(1989) index of parental investment. The index ranges 
from 0 to 14 and is scored according to 1) the place- 
ment of larvae or zygotes (i.e., in a nest or in the water 
column; score ranges from 0 to 2); 2) the length of time 
of parental protection of zygotes or larvae (score ranges 
from 0 to 4); and 3) the length of gestation period or 
nutritional contribution (score ranges from 0 to 8). To 
translate Winemiller’s index into our ranking system, 
we examined King and McFarlane’s (2003) parental 
investment scores for 42 North Pacific stocks. These 
42 stocks covered a wide range of life histories and 
habitats, including 10 surface pelagic, three mid-water 
pelagic, three deep-water pelagic, 18 near-shore ben- 
thic, and nine offshore benthic stocks. Thirty-one per- 
cent of the stocks had a Winemiller score of zero, and 40 
percent had a Winemiller score of 4 or higher; therefore 
0 and 4 were used as the scoring thresholds. 
Recruitment pattern Stocks with sporadic and infre- 
quent recruitment success often are long lived and thus 
might be expected to have lower levels of productivity 
(Musick, 1999). This attribute is intended as a coarse 
index to distinguish stocks with sporadic recruitment 
patterns and high frequency of year-class failures from 
those with relatively steady recruitment. Thus, the pro- 
portion of years in which recruitment was above aver- 
age (e.g., the percentage of successful year classes over 
a 10-year period) was used for this attribute. Because 
this attribute was viewed as a coarse index, we chose 
10% and 75%- as the scoring thresholds, so that scores 
of 1 and 3 allowed us to identify relatively extreme dif- 
ferences in recruitment patterns. 
Age-at-maturity (f mof ) Age at maturity tends to be 
strongly related to both maximum age (t max ) and natu- 
ral mortality (M), where long-lived, lower-productivity 
stocks will have higher ages at maturity than short-lived 
stocks (Beverton, 1992). The scoring thresholds from 
the ANOVA applied to the fish stocks considered to be 
representative of U.S. fisheries were ages 2 and 4. These 
values are lower than those obtained from Froese and 
Binohlan’s (2000) empirical relationship between t mat 
and t max , which were ages 3 and 9 based upon values of 
t m ax of 10 and 30. However, Froese and Binohlan (2000) 
used data from many fish stocks around the world, 
which may not be representative of U.S. stocks. For the 
PSA, thresholds that were obtained from the ANOVA 
were applied to stocks considered representative of U.S. 
fisheries. 
