225 
A probability-based approach 
to setting annual catch levels 
Email address for Kyle W. Shertzer: Kyle.Shertzer@noaa.gov 
Abstract — The requirement of set- 
ting annual catch limits to prevent 
overfishing has been added to the 
Magnuson-Stevens Fishery Conser- 
vation and Management Reauthoriza- 
tion Act of 2006 (MSRA). Because this 
requirement is new, a body of applied 
scientific practice for deriving annual 
catch limits and accompanying tar- 
gets does not yet exist. This article 
demonstrates an approach to setting 
levels of catch that is intended to keep 
the probability of future overfishing 
at a preset low level. The proposed 
framework is based on stochastic pro- 
jection with uncertainty in population 
dynamics. The framework extends 
common projection methodology by 
including uncertainty in the limit 
reference point and in management 
implementation, and by making 
explicit the risk of overfishing that 
managers consider acceptable. The 
approach is illustrated with applica- 
tion to gag ( Mycteroperca microlepis), 
a grouper that inhabits the waters 
off the southeastern United States. 
Although devised to satisfy new leg- 
islation of the MSRA, the framework 
has potential application to any fish- 
ery where the management goal is 
to limit the risk of overfishing by 
controlling catch. 
Manuscript submittted 28 September 2007. 
Manuscript accepted 15 February 2008. 
Fish. Bull. 106:225-232 (2008). 
The views and opinions expressed or 
implied in this article are those of the 
author and do not necessarily reflect 
the position of the National Marine 
Fisheries Service, NOAA. 
Kyle W. Shertzer (contact author) 
Michael H. Prager 
Erik H. Williams 
National Oceanic and Atmospheric Administration 
Southeast Fisheries Science Center 
Center for Coastal Fisheries and Habitat Research 
101 Pivers Island Road 
Beaufort, North Carolina 28516 
The Magnuson-Stevens Fishery Con- 
servation and Management Reautho- 
rization Act of 2006 (MSRA) requires 
that each Fishery Management Plan 
in the United States “establish a 
mechanism for specifying annual 
catch limits ... at a level such that 
overfishing does not occur in the fish- 
ery ...” (MSRA, 2006). This require- 
ment, which reflects an increased 
emphasis on conservation, is new in 
the sense that prevention of overfish- 
ing is mandated to be through annual 
catch limits (ACLs), rather than only 
through such less restrictive mea- 
sures as trip limits, size limits, or 
days allowed at sea. Because the stat- 
ute requires ACLs to be implemented 
by 2011 in all fisheries (by 2010 for 
fisheries where overfishing is occur- 
ring), discussion has begun on ways 
to compute them. Accompanying the 
discussion of ACLs is the discussion 
of corresponding annual catch targets 
(ACTs), levels of catch set as quotas 
in the fishery. 
In this study, we propose a method 
for setting annual catch levels that 
are treated as targets, but equally 
well could serve as limits. The meth- 
od is based on stochastic projection 
with uncertainty in population dy- 
namics. It extends usual projection 
methodology by including uncertainty 
in the limit reference point and in 
management implementation, and by 
making explicit the overfishing risk 
that managers consider acceptable. 
This probabilistic approach was de- 
vised specifically to satisfy the U.S. 
statute, but we expect it should be 
useful whenever the management ap- 
proach is to limit the risk of overfish- 
ing by controlling catch. 
From a technical point of view, 
the requirement to set ACLs is in- 
teresting in that overfishing is de- 
fined in terms of a fishery input (i.e., 
fishing-induced mortality rate), yet 
the control mechanism is defined in 
terms of a fishery output (i.e., catch). 
(Review of inputs and outputs in 
fishery management can be found 
in Morison [2004] and Walters and 
Martell [2004].) Values connecting 
inputs and outputs mathematically 
are stock abundance and age struc- 
ture, which change from year to year. 
Ideally, then, a method to set catch 
levels would take into account both 
uncertainty in the estimates of cur- 
rent stock abundance and structure 
and the expectation that abundance 
and structure will change with time. 
Current harvest-control rules for 
fisheries usually depend on a limit 
reference point, and uncertainty in 
estimating the limit reference point 
should also be considered. The limit 
reference point (typically the fishing 
rate at maximum sustainable yield 
(F MS y) or a P rox y f or if* i s general- 
ly considered to represent the level 
at which overfishing occurs (Mace, 
2001 ). 
Given the uncertainties in popu- 
lation dynamics, stock assessment, 
and fishery management, it is argu- 
ably impossible to fish without some 
risk of overfishing. Rather than at- 
tempting to achieve zero probability 
of overfishing, our approach avoids 
