Shertzer et al Probability-based approach to setting annual catch levels 
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account for the implementation of uncertainty. 
In a projection over multiple years, however, lim- 
its and targets should remain coupled, because 
simulated catch feeds back to abundance levels 
and thus affects catch levels (limits and targets) 
in the next year. 
Correlation of fishing mortality rates 
PASCL, as implemented through Equation 2, 
implicitly treats the two variables F lim and F t as 
independent. In some applications, the two may 
be correlated. To examine this correlation, we 
conducted a simulation analysis, in which an age- 
structured population model was used to generate 
data that were then used in a catch-age assess- 
ment model. In the population model, parameter 
values representing natural mortality, somatic 
growth, maturity, fishery selectivity, steepness, 
recruitment variability, landings, and indices of 
abundance were generated at random by using 
levels from other simulation studies (Maunder and 
Deriso, 2003; Williams and Shertzer, 2003). For 
simplicity, the simulation included one fishery and 
one index of abundance. The population was initi- 
ated near its unfished state and was subjected to 
a 27-year linear increase in fishing mortality rang- 
ing from 0 to 2 times the rate at F MSY (F hm ). Based 
on 10,000 simulations, the assessment output pro- 
vided no evidence of correlation between estimates 
of F lim and terminal-year F t (r=-0.004, P=0.694), 
supporting the assumption of independence. In any 
given application, however, if correlation between 
F lim and F t is considered important, PASCL could 
be applied by using Equation 3. 
A 
B 
Figure 6 
Contours of (A) median annual catch levels (landings plus 
discard mortalities) and (B) median spawning biomass, both 
in units of 100 metric tons, and plotted as functions of time 
(years) and the acceptable risk of overfishing (P*). Uncertainty 
in management implementation was set at CV=0.2. 
Implementation uncertainty and bias 
Uncertainty in implementation is a common, but often 
ignored, reality of natural resource management (John- 
son et al., 1997). This source of uncertainty was quan- 
tified here by a normal distribution with an assumed 
coefficient of variation. In some cases, the distribution 
could be estimated from data on performance of the 
fishery — a scenario we expect to become more common 
as annual catch targets are applied more widely. Our 
example showed that more precise management allowed 
higher fishing rates, and thus larger catches, without 
increased probability of overfishing. Similarly, larger 
catches would result from more precision in stock 
dynamics or assessments. This outcome underscores 
the economic benefits of timely monitoring, enforcement, 
and compliance. 
A notable feature of PASCL is that managers may 
choose the level of risk that they consider acceptable. 
This choice could reflect socio-economic considerations, 
in addition to biological factors such as productivity 
and vulnerability of the stock. In some cases, higher 
risk of overfishing may be desired, for example if short 
term loss of yield outweighs long-term benefits (Shertzer 
and Prager, 2007). In other cases, managers may be 
more precautionary. Either way, establishing the level 
of risk as an explicit choice increases transparency in 
the management process. 
A simplifying assumption of our application was that 
annual catch, although imprecise, was centered about 
the target catch level. In many fisheries, however, the 
distribution of annual catch may be asymmetric in 
either direction of the target. Such asymmetric distri- 
butions can easily be accommodated in PASCL. When 
annual catch falls above or below the target, managers 
may consider adjusting target catch in subsequent years 
accordingly. 
Conclusion 
Over the next several years, as science responds to 
legislation, a body of practice will be developed to imple- 
ment annual catch limits and targets. In managing 
U.S. federal fisheries, new approaches must address the 
MSRA requirements to end and prevent overfishing. The 
