133 
Multiple stable reference points 
in oyster populations: implications 
for reference point-based management 
Eric IN. Powell (contact author ) 1 
John JVS. KSinck 2 
Kathryn A. Ashton-Alcox 1 
John N. Kraeuter 1 
Email address for contact author: eric@hsrl.rutgers.edu 
1 Haskin Shellfish Research Laboratory 
Rutgers University 
6959 Miller Ave. 
Port Norris, New Jersey 08349 
2 Center for Coastal Physical Oceanography 
Crittenton Hall 
Old Dominion University 
Norfolk, Virginia 23529 
Abstract — In the second of two com- 
panion articles, a 54-year time series 
for the oyster population in the New 
Jersey waters of Delaware Bay is 
analyzed to examine how the pres- 
ence of multiple stable states affects 
reference-point-based management. 
Multiple stable states are described 
by four types of reference points. 
Type I is the carrying capacity for 
the stable state: each has associ- 
ated with it a type-II reference point 
wherein surplus production reaches 
a local maximum. Type-II reference 
points are separated by an intermedi- 
ate surplus production low (type III). 
Two stable states establish a type-IV 
reference point, a point-of-no-return 
that impedes recovery to the higher 
stable state. The type-II to type-III 
differential in surplus production is 
a measure of the difficulty of rebuild- 
ing the population and the sensitivity 
of the population to collapse at high 
abundance. Surplus production pro- 
jections show that the abundances 
defining the four types of reference 
points are relatively stable over a wide 
range of uncertainties in recruitment 
and mortality rates. The surplus pro- 
duction values associated with type- 
II and type-III reference points are 
much more uncertain. Thus, biomass 
goals are more easily established than 
fishing mortality rates for oyster 
populations. 
Manuscript submitted 29 November 2007. 
Manuscript accepted 9 September 2008. 
Fish. Bull. 107:133-147 (2009). 
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. 
All federal fisheries, and some state 
fisheries, are managed under biologi- 
cal reference-point guidelines under 
which a specific yearly allocation or 
quota is advised to constrain fishing 
mortality (e.g., Wallace et al. 1 ). The 
biological reference-point approach 
for federal fisheries mandated by the 
Magnuson-Stevens Fishery Conser- 
vation and Management Act (Anony- 
mous, 1996) requires management 
of fish populations at a biomass that 
provides maximum sustainable yield. 
In this system, sophisticated survey, 
analytical, and modeling procedures 
are used to identify selected biological 
reference points, such as the target 
biomass, B msy , and the carrying capac- 
ity, K. Fishing mortality is then set 
in relation to reference point goals. 
Normally, B is defined in relation 
to carrying capacity, the biomass 
present without fishing, where natu- 
ral mortality balances recruitment 
(e.g., May et al., 1978; Johnson, 1994; 
Mangel and Tier, 1994; Rice, 2001). 
This stable point is characterized by 
a population for which most animals 
are adults, where natural mortality 
rates are low, and where recruitment 
is limited by compensatory processes 
such as resource limitation constrain- 
ing fecundity. B m is most commonly 
defined as based on the well-known 
Schaefer model that stipulates the 
guiding premise that surplus pro- 
duction is highest at y (Hilborn and 
Walters [1992]; see Restrepo et al. 
[1998] for more details on the federal 
management system). 
The raison d’etre for reference- 
point-based management is the de- 
velopment of equilibria between re- 
cruitment (and growth) and mortality 
at target host densities (the archetype 
being B msy ). Unfortunately, for man- 
aging oyster populations, obstacles ex- 
ist in meeting this objective because 
oyster populations do not appear to be 
inherently equilibrious, particularly 
those subjected to MSX, a disease 
caused by the protozoan Haplospo- 
ridium nelsoni, or Dermo, a disease 
caused by the protozoan Perkinsus 
marinus. Time series of oyster abun- 
dance typically show wide interan- 
nual variations, mediated in no small 
measure by year-to-year differences 
in natural mortality rate, although 
overfishing has also been an impor- 
tant contributing agent (e.g., Mann 
et al., 1991; Rothschild et ah, 1994; 
Burreson and Ragone Calvo, 1996; 
Ragone Calvo et al., 2001; Jordan et 
1 Wallace, R. K., W. Hosking, and S. T. 
Szedlmayer. 1994. Fisheries manage- 
ment for fishermen: A manual for help- 
ing fishermen understand the federal 
management process. NOAA MASG 
P-94-012, 56 p. 
