Powell et al.: Multiple stable reference points in oyster populations: Crassostrea virginica in Delaware Bay 
125 
Q. 
CO 
O 
CD 
.Q 
E 
5.0x10 10 - 
4.5X10 10 - 
4.0X10 10 - 
3.5X10 10 - 
3.0x10 10 - 
2.5x10 10 - 
2.0x10 10 - 
1.5x10'°' 
, 10 . 
1 0x10 
5.0x1 0 9 - 
-0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 
Fraction of population dying 
Figure 15 
The relationship between unrecorded mortality and recruitment in 1953-2006 
for the natural oyster beds of Delaware Bay. Irrational (positive) values on the 
abscissa indicate survey imprecision. 
recruitment) (Fig. 16). Where- 
as other years also fall in this 
quadrant, when the stock is con- 
solidated at high abundance, the 
likelihood that recruitment will 
be above the median of all years 
is extraordinarily high. When 
the stock is dispersed, the like- 
lihood is not as great, but still, 
in most years, the population’s 
performance falls into quadrant 
4. Thus, stock dispersion has 
little influence on the outcome 
of recruitment events during the 
high-abundance regime. 
In contrast, occurrences when 
relatively more of the stock was 
found on the medium-mortal- 
ity beds during the low-abun- 
dance regime fall dispropor- 
tionately into quadrant 1 (low 
abundance + low recruitment) 
(Fig. 16). Eight of fourteen oc- 
currences in these years fall 
into this quadrant, a value sig- 
nificantly greater than expect- 
ed by an even distribution of 
points among the four quadrants 
(P<0.005), and 10 of 14 display 
low recruitment (quadrants 1 
and 3), a value significantly greater than expected by 
an even split (P-0.05). Thus, when the stock is con- 
solidated within its range, and in its low-abundance 
regime, a high-recruitment event is unlikely. During 
the late 1980s and early 1990s, the stock was at rela- 
tively low abundance, but more distributed among bed 
regions (Fig. 5). These years are more evenly distrib- 
uted among the four quadrants (Fig. 16). In particu- 
lar, three occur in quadrant 3, accounting for a high 
percentage of all such events, and five fall above the 
long-term median for recruitment. Thus, although a 
dispersed stock can result in low recruitment during 
the low-abundance regime, the chance of a high-re- 
cruitment event is much improved. 
One inference from these data is that high recruit- 
ment events are the result of spawning by oysters down- 
bay of the medium-mortality region, in waters of higher 
salinity. This inference is supported by the tendency 
for the high-mortality beds to recruit more consistently 
(Powell et al., 2008). The fact that quadrants 1 and 4 
are primarily represented by years when a consolidated 
stock distribution was present indicates that spawning 
potential differs between the two regimes. Perhaps it 
is no coincidence that the 1970 stock expansion was 
preceded by a tendency for the stock to expand at low 
abundance, thereby increasing the probability of a high 
recruitment event at low abundance. And perhaps it is 
no surprise that the decrease in recruitment during 
the first years of the 2000s (Powell et al., 2008) was 
preceded by a consolidation of the stock beginning in 
1996, which reduced the probability of a high-recruit- 
ment event. All of these observations would imply that 
a high recruitment is primarily driven by increased 
spawning potential on higher-salinity beds. Thus, the 
broodstock-recruitment relationship (Fig. 7) fails to 
emphasize a substantive impact from stock dispersion. 
The range in recruitment at a given abundance, blithe- 
ly inferred to represent stochastic variation about a 
mean, in actuality includes a large influence from stock 
distribution that cannot be readily represented by a 
simple mathematical relationship between observed 
recruitment and stock size. This dispersion imprint is 
a dominant contributor to the dynamics of a population 
at low abundance, but not at high abundance, when 
compensatory processes begin to become important, 
and helps explain why the 1970 regime shift was an 
unlikely event. 
The influence of geographic dispersion is also ob- 
served in the abundance-mortality diagram (Fig. 9). 
Not surprisingly, the high-abundance regime is asso- 
ciated with low mortality, regardless of the degree of 
consolidation of the stock (Fig. 17). This association 
conforms with the relationships observed for the brood- 
stock-recruitment relationship (Fig. 16). By contrast, 
the years characterized by consolidated and dispersed 
stock during the low-abundance regime are divergent, 
and again this divergence is similar to our conclusion 
drawn from the broodstock-recruitment relationship. 
The mortality rate should be lower when more oysters 
are found on the medium-mortality beds, and this 
