Powell et al.: Multiple stable reference points in oyster populations 
141 
0 . 6-1 ,- 0.6 
Abundance (billions) 
Figure 6 
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, from Equation 10, m 0 from Equation 5 using the 54-year median 
<P 0 , and m bc from Equation 12. This simulation assumes compensation in the 
broodstock-recruitment curve, median unrecorded (mostly juvenile) mortal- 
ity, but a box-count mortality rate that de-emphasizes epizootic mortality at 
low abundance. Epizootics are assumed to occur in half of the years when 
abundance is in the correct range, in comparison to the simulations shown in 
Figures 4 and 5. Surplus production as plotted is the average of an epizootic 
and a nonepizootic year. Catch estimates are conditional on the assumption 
of long-term persistence of a chosen abundance level and distribution of the 
entire stock in habitats permitting growth to market size. 
Four types of reference points 
are elucidated. Each of them 
marks critical spots in the ambit 
of oyster population dynamics that 
must be included in a successful 
management plan. If the oyster 
population in Delaware Bay has 
two distinct regimes, minimally, 
two sets of reference points ex- 
ist. It is a critical corollary of the 
multiple-stable-state theorem that 
such should be the case. Modern 
fisheries management scientists, 
although cognizant of the impor- 
tance of regime shifts, have not 
yet inculcated the concept of mul- 
tiple stable states into manage- 
ment philosophy and, consequent- 
ly, continue to focus solely on the 
highest abundance state. 
Maximum sustainable yield gen- 
erally is considered to occur at half 
carrying capacity. For the high- 
abundance regime, IV# sy occurs at 
almost precisely (Figs. 3-7), 
as expected from standard fisher- 
ies theory (Haddon, 2001; Zabel et 
al., 2003). For the low-abundance 
regime, N L msy occurs at a value dis- 
tinctly above K -\ thus the lower 
surplus production dome is dis- 
tinctly skewed. Some portion of 
this skewness may be inadequate 
extrapolation of the population 
dynamics to abundances below 
0.8 xlO 9 that have not yet been 
observed. Either IV# or N L 
might be chosen as abundance 
goals. N H msy yields the highest surplus production 
and, consequently, the highest fishery yield, and, all 
else being equal, would be the desirable goal for re- 
building oyster abundance above present-day levels. 
Over the 54-year time series for Delaware Bay, the 
abundance level has been near carrying capacity for 
about one-third of the years and well below IV# for 
most of the remaining years (Fig. 9). Thus, historical 
observations provide credence for the viability of this 
abundance goal. 
However, an alternative exists, N L . This second 
type-II reference point exists at lower abundance and 
maximizes fishery yield in the low-abundance regime 
(Fig. 9). The population has been near this level for 
about two-thirds of the years since 1953 and, for most 
of this time, this population dynamic has been little 
influenced by fishing mortality. Thus, a substantive 
choice exists in managing the Delaware Bay oyster 
stock. Is it a viable choice to seek through management 
to transition the population to the high-abundance state 
and thereby rebuild the population to the higher IV# sy 
target? 
The impact of type-ill and type-IV reference points 
The two other reference points become important at 
this juncture. The type-III reference point describes 
the valley between the two surplus production 
maxima. If negative, two stable states exist, asso- 
ciated with the lower and higher maxima in sur- 
plus production (e.g., Fig. 7). If positive, one stable 
state exists. The other lower maximum in surplus 
production is a quasi-stable state (e.g., Figs. 4-6). 
Surrounding the surplus production minimum is a 
region in which unwise harvest goals could create a 
region of negative surplus production and establish 
through overharvesting the second and lower stable 
state. Thus, this reference point is a measure of the 
relative degree of impedance present in the popula- 
tion dynamics to transiting to the higher stable state. 
This impedence exists naturally and is a rebuilding 
obstacle for management. This impedance can be 
deepened by inappropriate harvest goals. 
If the minimum in surplus production is below zero, 
the type-IV reference point above it marks the thresh- 
