230 
Fishery Bulletin 106(3) 
Greater precision in management implementation 
reduced the variance of F t for a given catch, which in 
turn allowed higher fishing mortality rates without an 
increased probability of overfishing (Fig. 5A). The 
higher rates then translated into larger annual 
catch levels (Fig. 5B). 
In general, higher P* was associated with larger 
catch (Fig. 6A). Biomass increased over time for all 
P* examined, but more quickly when risk of overfishing 
was smaller (Fig. 6B). Consequently, catch increased 
more quickly for smaller risk, and thus the overall 
range of catch shrank over time across levels of P*. 
Discussion 
work extends common methods by explicitly considering 
uncertainty in the limit reference point, uncertainty 
in management implementation, and the level of risk 
acceptable to managers. 
A limit reference point used with PASCL can be a 
single value, such as F MSY or a proxy for jF msy , but 
it need not be a single value. For example, the F lim 
used to manage U.S. west coast groundfish is a func- 
tion of standing biomass (Punt, 2003). Uncertainty in 
the limit, whether a single value or function, could be 
modeled with any appropriate distribution. Similarly, 
uncertainty in management implementation can be 
incorporated with flexibility. 
Choice of harvest-control rules 
The proposed probabilistic approach to setting annual 
catch levels, PASCL, is quite flexible. It incorporates 
many of the projection methods common in stock 
assessment, which can be based on size-structured, 
age-structured, or unstructured population models. 
It can incorporate any sources of uncertainty consid- 
ered important; for example, environmental influences, 
demographic stochasticity, and multispecies effects. Our 
A 
B 
4.4 
4.2 - 
4.0 - 
o 3.8 - 
03 
O 3.6 - 
3.4 - 
3.2 - 
3.0 - 
2008 2009 2010 2011 2012 2013 2014 
Figure 5 
Median annual (A) fishing mortality rate and (B) catch level 
(100 t) from projections with managed risk of overfishing 
set at P*=0.1 and uncertainty in management implementa- 
tion, defined by the coefficient of variation CV, set at CV=0.1 
(dashed), CV=0.2 (solid), or CV=0.3 (dotted). 
PASCL will not be the best choice for setting annual 
catch levels in every stock. In particular, data-poor 
stocks will likely require a different approach, such 
as assemblage management or the use of expert judg- 
ment. For rebuilding overfished stocks, other projection 
approaches may be more suitable (Jacobson and Cadrin, 
2002; Punt, 2003). During rebuilding, harvest policies 
are typically based on the probability of stock recovery 
within a specified time horizon, rather than on 
the less restrictive constraint of preventing over- 
fishing. As overfished stocks recover, however, a 
method such as PASCL could be applied to prevent 
the stock from another decline and the need for 
future rebuilding plans. 
In one school of thought, choice of a harvest- 
control rule should be based on the likelihood of 
meeting long-term management objectives. In this 
regard, the efficacy of PASCL could be compared 
to that of other control rules by simulating the 
assessment and management processes in con- 
junction with stock dynamics (Cooke, 1999; Punt, 
2003). Such management strategy evaluations can 
be useful for shedding light on which control rules 
work best under various conditions. However, they 
are complex, and thus difficult to program, verify, 
explain, and modify as circumstances change. 
Moreover, most fishery management is in fact 
based on short-term to medium-term consider- 
ations, and management strategies are likely to 
change to meet social, biological, or environmental 
conditions. When a major objective of management 
is to avoid overfishing, PASCL should be quite 
effective, and it may simultaneously meet more 
complex objectives. An advantage of simple control 
rules such as PASCL is that they can be applied 
after each assessment without major redesign. 
In our example, we computed annual catch levels 
as targets. With slight modification, the method 
can be used to compute annual catch limits and 
targets simultaneously. For example, a catch limit 
(or acceptable biological catch) might be set to 
prevent overfishing based on scientific uncertainty 
(e.g., process and estimation error), and a catch 
target might then be set lower than the limit to 
