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Fishery Bulletin 107(2) 
al., 2002; Powell et al., 2008). In the first of two com- 
panion contributions, we described the case for oyster 
populations in Delaware Bay. A 54-year time series 
documents two regime shifts, circa-1970 and circa-1985, 
with intervening and succeeding intervals having the 
attributes of alternate stable states ( sensu Gray, 1977; 
Peterson, 1984; Knowlton, 2004). Within these periods 
are substantial population excursions produced by vary- 
ing rates of recruitment and natural mortality, but the 
alternate stable states are demarcated by even larger 
excursions in abundance. Moreover, these periods of 
relative stability delineated by regime shifts are per- 
sistent and transcend a range of climatic conditions 
(Soniat et al., in press). 
Population dynamics of the Delaware Bay oyster pop- 
ulation is not solely a function of disease, but stable- 
point abundances are at least partially a byproduct of 
disease, and disease has played a role in regime shifts 
(Powell et al., 2008). The classic view of carrying ca- 
pacity fails when disease accounts for a substantial 
fraction of natural mortality and this compromises an 
estimate of B m Some have attempted to redefine car- 
rying capacity in diseased populations in relation to 
the abundance (population density in classic disease 
models, e.g., Kermack and McKendrick [1991], Hethcote 
and van den Driessche [1995]) at which each diseased 
animal will produce, in its lifetime, a single infection 
event (e.g., Heesterbeek and Roberts, 1995; Swinton 
and Anderson, 1995). This abundance is always below, 
usually well below, the original K. When abundance 
rises above this level, the influence of disease increases, 
as does the chance of epizootic mortality. This increase 
restrains population abundance below the predisease 
K (e.g., Kermack and McKendrick, 1991; Hasiboder et 
al., 1992; Godfray and Briggs, 1995; Frank, 1996). This 
approach is not well tailored to diseases such as MSX 
and Dermo for which environment is a potent modu- 
lator of effect and in which rapid transmission rates 
are not requiring of host-to-host contact. Furthermore, 
the existence of multiple apparently stable states and 
regime shifts imply that the standard Schaefer model, 
from which such basic biological references points as 
B are derived, also does not provide the appropriate 
framework for managing oyster populations because 
this model has only a single stable state. 
These ratiocinations lead to three salient questions 
pertinent to developing management goals for oyster 
stocks: 1) Can reference points be defined that consis- 
tently permit fishing without jeopardizing the sustain- 
ability of the stock? 2) Must management goals be set 
within the context of each of several multiple stable 
states? 3) How does regime change affect the usefulness 
of reference points and can management goals be set to 
increase the probability of regime shift to a preferred 
stable state? In this contribution, we use the case of 
the Delaware Bay oyster stock in New Jersey waters to 
examine these questions. In a companion contribution, 
we describe the long-term survey time series and the 
relationships of broodstock abundance with recruitment 
and mortality (Powell et al., 2009). In this contribu- 
Table 1 
The bed groups (by location: upbay and downbay) and 
subgroups (by mortality rate) for the eastern oyster 
( Crassostrea virginica) collected on twenty beds in 
Delaware Bay, as shown in Figure 1. Mortality rate 
divides each of the primary groups, themselves being 
divided by location, a surrogate for upbay-downbay vari- 
ations in dredge efficiency and fishery-area management 
regulations. 
Bed group/subgroup 
Bed name 
Upbay group 
Low mortality 
Medium mortality 
Downbay group 
Medium mortality 
High mortality 
Round Island, Upper Arnolds, 
Arnolds 
Upper Middle, Middle, Sea 
Breeze, Cohansey, Ship John 
Shell Rock 
Bennies Sand, Bennies, New 
Beds, Hog Shoal, Hawk’s 
Nest, Strawberry, Vexton, 
Ledge, Egg Island, Nantuxent 
Point, Beadons 
tion, we develop a surplus production model to relate 
these relationships with stock performance over a range 
of abundances. Following discussion of the results of 
simulations with this model, we consider the basis for 
an MSY - based management system for oyster popula- 
tions and the implications of multiple stable states in 
the decision-making process. 
Model formulations and statistics 
Powell et al. (2008, 2009) have provided an overview 
of the oyster populations in Delaware Bay during the 
1953-2006 time period. Analyses of the Delaware Bay 
oyster resource of New Jersey routinely reveal a divi- 
sion between the upbay group of eight beds (Round 
Island, Upper Arnolds, Arnolds, Upper Middle, Middle, 
Sea Breeze, Cohansey, and Ship John [Fig. 1]) and the 
downbay group of twelve beds (Shell Rock, Bennies 
Sand, Bennies, New Beds, Nantuxent Point, Hog Shoal, 
Hawk’s Nest, Strawberry, Vexton, Beadons, Egg Island, 
and Ledge). Salinity, natural mortality rate, and growth 
rate are higher downbay. Dredge efficiencies are signifi- 
cantly higher downbay (Powell et al., 2002, 2007). Both 
regions can be subdivided on the basis of natural mortal- 
ity rate and productivity. In the upbay group, natural 
mortality rates and growth rates are significantly lower 
for the upper three beds, Round Island, Upper Arnolds 
and Arnolds, than for the remaining beds. Henceforth 
these two groups will be termed the low-mortality and 
medium-mortality beds (Table 1). In the downbay group, 
growth rates and mortality rates are lower for Shell 
Rock, leading to its designation as a medium-mortality 
bed; the reminder are high-mortality beds (Table 1). 
