140 
Fishery Bulletin 107(2) 
ferential in abundance in the 1950s primarily a result of 
the higher fishing mortality rates during that time. 
Carrying capacity is defined by a set of criteria that 
are normally thought to be unique (Table 2). Inter- 
estingly, in Delaware Bay oyster populations, a sec- 
ond type-I reference point may exist, depending on the 
presence of a reference point of type IV, as considered 
subsequently. This type-I reference point, if present, is 
at 1.93 xlO 9 , nearly a factor of 5 lower in abundance 
than the classic carrying capacity. However, this value 
is also similar to the abundance observed during the 
low-abundance phase of the population (Fig. 9), an out- 
come anticipated of a population with multiple stable 
points (Gray, 1977; Peterson, 1984) in which community 
compositions are theorized to resolve themselves into 
preferred states that can be exchanged only through 
triggering mechanisms capable of overcoming the iner- 
tia of the individual states. Soniat et al. (1998) argued 
that inertia is an important attribute of oyster popula- 
tion dynamics and that this inertia minimizes the in- 
fluence of short-term environmental shifts. The 54-year 
time series of Delaware Bay supports the importance of 
inertia and suggests some reasons for how population 
dynamics are internally stabilized. 
Both recruitment and mortality have abundance-de- 
pendent rates. The high-abundance regime is inherently 
stable. Mean first passage times ( sensu Rothschild and 
Mullen, 1985; Redner, 2001; Rothschild et al., 2005) 
for transitions to the alternate stable state typically 
exceed 6 yr (Powell et al., 2009). Given a population at 
high abundance: that population will tend to maintain 
itself because high abundance, on the average, gener- 
ates higher recruitment, and also, on the average, is 
associated with lower rates of natural mortality. Thus, 
high abundances have a strong internal self-sustain- 
ing mechanism. However, the 1970-85 period occurred 
prior to the onset of Dermo disease in Delaware Bay. 
Whether a high abundance state is sustainable under 
any environmental conditions with Dermo as the prin- 
cipal agent of mortality is unknown. 
The low-abundance regime is stable only if the sur- 
plus production minimum separating the two maxima 
is negative. The differential between the two carrying 
capacities, K H and K L , is a factor of 4.82. Powell et al. 
(2009) discuss the tendency for the Delaware Bay oyster 
population to contract to a habitat of refuge on the me- 
dium-mortality beds (Table 1) as abundance falls. This 
occurs due to the gradient in natural mortality that 
increasingly penalizes the popula- 
tion downestuary. The differential 
in bed area between the entire bay 
and the medium-mortality beds 
is a factor of 2.46 excluding the 
two lowermost and least produc- 
tive beds, Egg Island and Ledge, or 
2.70 including them. Thus, habitat 
area, though likely a contributor 
to the differential in the two car- 
rying capacities, does not explain 
adequately the differential between 
K L and K H , and this agrees with 
the observation (Figure 5 in Powell 
et al., 2009) that contracted and 
dispersed population distributions 
both prevailed for extended periods 
during the low-abundance regime. 
Surplus production targets Bever- 
ton et al. (1984) distinguish between 
short-term catch forecasts used to 
generate a yearly TAL and long- 
term strategic assessments used to 
set abundance goals. The constant- 
abundance reference point imple- 
mented with the model of Klinck et 
al. (2001) is particularly useful in 
maintaining a population close to 
an abundance target and has been 
used for short-term catch forecasts 
but does not lend itself to long-term 
strategic assessments. The purpose 
of this study was to develop refer- 
ence points that might be used to 
set abundance goals. 
0.6-i ,-0.6 
0 2 4 6 8 10 12 
Abundance (billions) 
Figure 5 
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, T t from Equation 10, m 0 from Equation 5 using the 54-year 
median 4> 0 , and m bc from Equation 12. This simulation assumes compensation 
in the broodstock-recruitment curve, median unrecorded (mostly juvenile) 
mortality, and a box-count mortality rate that emphasizes epizootic mortality 
at low abundance. This simulation differs from the simulation in Figure 4 in 
a higher level of unrecorded mortality. Catch estimates are conditional on the 
assumption of long-term persistence of a chosen abundance level and distribu- 
tion of the entire stock in habitats permitting growth to market size. 
