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Fishery Bulletin 107(2) 
while awaiting the rare sequence of events generating 
a natural transition to the alternate stable state. 
Harvest goals 
Included in Figures 4-7 is an estimated allowable catch 
as a fraction of the stock. The values of surplus produc- 
tion given in Figures 4-7 are expressed in numbers, 
perforce as they are the data source from which the 
underlying biological relationships are derived. The 
estimate is provided with some trepidation because the 
present model does not take into account the differential 
in growth across the salinity gradient and therefore 
tends to overestimate the number of animals of market 
size in the population as a whole. Moreover, the model 
assumes absolute constancy in the relationship of brood- 
stock to recruitment. Thus, the model may overestimate 
the fraction of the stock available for harvest in any 
given year. The formulation of Klinck et al. (2001) is a 
preferred option to obtain fishery allocations. Finally, the 
model consistently predicts a higher harvestable fraction 
at low abundance than at high abundance. An abettor 
in this trend may be the reliance of setting larvae more 
and more on the shell resource at low abundance than 
on the standing crop of living individuals. However, some 
portion of this outcome is likely due to an inability to 
accurately extrapolate the primary biological relation- 
ships below 0.8 xlO 9 animals. Such low abundances 
have not been observed and therefore the extrapolation 
is likely to be increasingly in error at lower and lower 
abundances. We do not give complete credence, therefore, 
to the proportional increase in harvestable fraction at 
low abundance indicated by the surplus production tra- 
jectories depicted in Figures 4-7. 
From Figure 3 we observe that the range of abun- 
dances assigned to the various reference points varies 
little among simulations describing a range of assump- 
tions about natural mortality and recruitment rate. 
By contrast, the range of surplus production is pro- 
digious. Thus, an abundance goal distinguishing an 
overfished from a sustainable stock, e.g., N , is well 
constrained, whereas an overfishing definition, e.g., 
fmsyt is very poorly delimited. Clearly any successful 
approach to management must minimize the chance 
that the added mortality by fishing overcomes the in- 
ertia militating against abundance decline. Further, 
the uncertainty of the level of surplus production at 
its minimum and maxima (Fig. 5) necessitates precau- 
tion as the increased mortality from fishing may be 
sufficient to stabilize a quasi-stable state at low abun- 
dance. Both require, for oysters, that fishing mortality 
be maintained at a small percentage of the natural 
mortality rate, thereby permitting the inertia of the 
system to guard against an abundance decline and 
reducing the chance that a rare population expansion 
might be prematurely terminated. Even at N msy , fishing 
mortality rate is likely not to exceed 5-10% of the stock 
(Figs. 4-7). The history of the Delaware Bay fishery 
provides strong corroboration that removals exceed- 
ing 15% are not sustainable (Powell et al., 2008) and 
offers strong evidence that removals below 5% of the 
stock limit the long-term impact of disease epizootics 
on abundance. Direct application of the Klinck et al. 
(2001) model in Delaware Bay has routinely returned 
values in the range of 1-3%. In addition, Powell and 
Klinck (2007) discuss the impact of fishing on the shell 
resource and the degradation of the shell beds upon 
which the population depends for its existence. That 
analysis independently argues for fishing mortality 
rates distinctly below the predisease mortality rate, at 
approximatly 10%. 
It is noteworthy that allowable fishing mortality rates 
<10% of the stock are more similar to the mortality 
rates of the longest-lived bivalves, such as geoducks 
and ocean quahogs (e.g., Bradbury and Tagart, 2000; 
NEFSC 2 ), than other species with life spans of the same 
order as the oyster, emphasizing the fact that oysters 
in the Mid-Atlantic region are much more akin in their 
population dynamics to long-lived k-selected species 
than to short lived r-selected ones. 3 Low recruitment 
significantly restricts the ambit of the oyster’s popula- 
tion dynamics and significantly constrains allowable 
fishing mortality rates over a wide range of abundance 
values. A perusal of the broodstock-recruitment curve 
(Fig. 7 in Powell et al., 2009) shows that recruitment 
rate typically falls within the range of 0.25 to 1 spat per 
adult animal per year. Both this recruitment level and 
the <10%-per-year natural mortality rate is consistent 
with theoretical predisease generation times that likely 
exceeded 10 years (Mann and Powell, 2007) and the fact 
that reproduction continues to be consistent with an 
animal characterized by longer generation times. 
Conclusions 
The oyster population in Delaware Bay exhibits a popu- 
lation dynamics that is not normally described in com- 
mercial species. One reason is the presence of distinct 
and dynamically stable multiple stable points delimited 
by temporally rapid regime shifts. The result of this 
complexity is a series of reference points identified by the 
trajectory of surplus production, which departs dramati- 
cally from the simple Schaefer curve (e.g., Zabel et al., 
2003). We define four reference point types in terms of 
surplus production, its derivative, and the rate of change 
of this derivative (Table 2). In Delaware Bay, the surplus 
production trajectory likely manifests two stable points 
and the carrying capacities associated with them and 
these agree relatively well with the observed stable 
2 NEFSC (Northeast Fisheries Science Center). 2001. 33 rd 
northeast regional stock assessment workshop (33 rd SAW): 
Stock assessment review committee (SARC) consensus 
summary of assessments. NMFS NEFSC Ref. Doc. 01-18, 
281 p. 
3 Gulf of Mexico conditions with rapid growth (Ingle and 
Dawson, 1952; Butler, 1953; Hayes and Menzel, 1981) and 
multiple spawns per year (Hopkins, 1954; Hayes and Menzel, 
1981; Choi et al., 1993, 1994) are examples of C. virginica 
under more r-selected conditions. 
