Powell et al.: Multiple stable reference points in oyster populations 
145 
states in the population time series (Fig. 9). For each 
of these type-I reference points, a maximum in surplus 
production also exists. The presence of two stable states 
assures a type-III reference point that is a measure of 
the ease of transition between the two stable states and 
provides information on the likelihood that management 
can artificially impose a transition. In Delaware Bay, 
the type-III surplus production value may be negative. 
In this case, a type-IV reference point exists, a point- 
of-no-return. If the type-III reference point is positive, 
a quasi-stable state exists at low abundance that can 
be stabilized by overfishing. The existence of a positive 
type-III reference point imposes a particular conundrum 
to management in that rebuilding requires a reduction 
in fishery yield as abundance increases over a substan- 
tive abundance range. 
The simulations show the uncertainty imposed by 
the limitations on accurate knowledge of the biological 
relationships. One noteworthy observation is that the 
location of the reference points undefined by a specific 
surplus production value (e.g., S t =0), namely types II 
and III, are relatively stable in position with respect to 
population abundance over a wide range of uncertain- 
ties in recruitment and mortality rates (Table 2). The 
surplus production values associated with these refer- 
ence points are much more uncertain (Table 2). Thus, 
location is much better known than scale. As recom- 
mended by Beverton et al. (1984), different models are 
likely to be needed for short-term catch forecasts and 
estimation of abundance goals. 
We describe reference points in the context of multiple 
stable states. The simplicity of the B msy -K couple so 
emphasized in fisheries management fails when mul- 
tiple stable states exist. That they may often exist is 
now well considered, although not yet inculcated into 
the oracle of fisheries management. Multiple stable 
points assure 1) that a type-III reference point exists, 
2) that this point will impede the attainment of impru- 
dently formulated rebuilding goals, 3) that a type-IV 
point-of-no-return may exist that establishes a barrier 
to rebuilding, as well as imposing the conditions at 
high abundance necessary for stock collapse, and 4) 
that a carrying capacity may exist at abundances well 
below historically high abundances and well below the 
simplistic promulgation of B msy as half the carrying 
capacity established by the higher stable state. Use of 
the latter may impose impossible requirements for re- 
building a stock because the promulgated goal exceeds 
the carrying capacity for the controlling regime. 
Acknowledgments 
We recognize the many people who contributed over the 
years to the collection of the 54 years of survey data 
analyzed in this report, with particular recognition 
of the contributions by H. Haskin, D. Kunkle, and B. 
Richards. We appreciate the many suggestions on con- 
tent provided by S. Ford and D. Bushek. The study was 
funded by an appropriation from the State of New Jersey 
to the Haskin Shellfish Research Laboratory, Rutgers 
University, and authorized by the Oyster Industry Sci- 
ence Steering Committee, a standing committee of the 
Delaware Bay Section of the Shell Fisheries Council of 
New Jersey. 
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