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Fishery Bulletin 107(2) 
old for population collapse or the point-of-no-return 
abundance (e.g., Collie et al., 2004) below which the 
population is unlikely to regain the higher abundance 
state (Fig. 8). It is the critical point generating the 
regime shift from high abundance to low abundance. 
That is, once abundance drops to this point, abun- 
dance will resolutely fall to the lower carrying capac- 
ity and the population subsequently will resist the 
reverse course even in the absence of fishing (Fig. 8). 
Once crossed, no anthropogenic manipulation short of 
Herculean measures to enhance abundance will allow 
the population to recover. In the years succeeding the 
1985 MSX epizootic, population abundance increased 
to levels representative of the type-III and type-IV 
reference points a number of times, falling back below 
these barriers in one to two years (Fig. 9). Two occur- 
rences are noteworthy, one during 1987-89 before the 
onset of Dermo and one during 1996-98 after Dermo 
replaced MSX as the dominant disease agent causing 
mortality. In both cases, the population failed to suc- 
cessfully cross the type-IV barrier. In neither case 
was fishing responsible for this failure. 
Uncertainty in the natural mortality rate presents 
a critical impediment to successful stock assessment 
(e.g., Beverton et al., 1984; Clark, 1999; Bradbury 
and Tagart, 2000). The population trajectories shown 
in Figures 3-7 differ principally in the degree and 
type of uncertainty in mortality and that controls the 
amplitude of the surplus production excursion between 
the lower type-II and upper type-II points, as well as 
the existence of a type-IV reference point. The rar- 
ity of regime shifts in the observed time series, the 
observed stability of the stable states, and the long 
mean first passage times for some population shifts 
(Powell et al., 2009) all suggest that the valley be- 
tween regimes is difficult to cross. Thus, very likely 
the surplus production minimum in the Delaware Bay 
oyster stock is below zero or nearly so (Fig. 9). The 
population “resists” the flip between stable states 
and the degree of this “resistance” is a function of 
the depth and breadth of the valley between surplus 
production maxima. 
The existence of the type-IV reference point influ- 
ences management in two ways. If the population is 
above it, adequate precaution must 
be included to limit the probabil- 
ity of a population decline of this 
magnitude as close to zero as pos- 
sible. The precautionary approach 
is a standard component in man- 
agement (e.g., FAO, 1995; Restrepo 
et al., 1998), but the assessment 
of risk is rarely undertaken (e.g., 
Francis and Shotton, 1997). Note 
in Figure 7 that the type-IV point 
is closer to N^ lsy than N H msy is to 
K H . Thus, management at MSY 
carries with it an increased risk 
of stock collapse. On the other 
hand, if the population is below the 
type-IV reference point, rebuilding 
goals must be restrained to the ob- 
jectives associated with the lower- 
abundance stable state, N L msy be- 
ing the obvious target. The key to 
this assessment is the value of the 
type-III reference point and par- 
ticularly whether that value falls 
below zero. 
Options for rebuilding 
Most oyster revitalization programs 
have rebuilding goals and most are 
premised on recruitment enhance- 
ment (e.g., Haven and Whitcomb, 
1983; Abbe, 1988; Leffler, 2002). 
This is typically accomplished 
through judicious shell planting, 
that also improves habitat integ- 
rity (Powell et al., 2006; Powell 
and Klinck, 2007). Both restora- 
--0.2 
o 
O) 
- -0.3 
o 
o 
- -0.4 
--0.5 
--0.6 
Abundance (billions) 
Figure 7 
The relationship of surplus production (Eq. 14), the rates of recruitment, 
unrecorded mortality, and box-count mortality, and a conditional estimate 
of catch expressed as the fraction of the stock, for parameters defined by, for 
recruitment, Ij, from Equation 10 above N= 4.5x 10 9 and 1) from Equation 11 
at lower abundance, m 0 from Equation 5 using the 54-year median <J> 0 , and 
m hc from Equation 12. This simulation assumes a linear relationship between 
broodstock abundance and recruitment at low abundance, median unrecorded 
(mostly juvenile) mortality, and a box-count mortality rate that emphasizes 
epizootic mortality at low abundance. In comparison to simulations depicted 
in Figures 4-6, this simulation has a combination of relatively high natural 
mortality and relatively low recruitment. Catch estimates are conditional on 
the assumption of long-term persistence of a chosen abundance level and dis- 
tribution of the entire stock in habitats permitting growth to market size. 
