Powell et al.: Multiple stable reference points in oyster populations: Crassostrea virginica in Delaware Bay 
123 
Figure 12 
The relationship between box-count mortality and recruitment for the 
eastern oyster ( Crassostrea virginica ) in 1953-2006 for the natural 
oyster beds of Delaware Bay. Dotted lines indicate the 54-yr medians 
of box-count mortality and recruitment. 
than is any other population state. Once 
there, the population is much more like- 
ly to remain there than move to any of 
the other three quadrants. High recruit- 
ment with low mortality is a relatively 
stable state. 
Unrecorded mortality Box-count mor- 
tality is generally a measure of mortality 
of larger animals. Presumably, much of 
the mortality unrecorded by box counts 
is associated with predation in the first 
year of life and, therefore, likely would 
not show a discernible relationship with 
recruitment. Estimates of survival to 
one year of age indicate that mortality 
rates are at least a factor of three to five 
above the population average for older 
animals (Powell et al., 2009), confirming 
that much of the unrecorded mortality is 
juvenile mortality. The assumption that 
juvenile mortality rate varies randomly 
with respect to other indices of popula- 
tion dynamics is supported by compari- 
sons with abundance, recruitment, and 
box-count mortality (Figs. 13-15). 
Influence of regime shifts 
on biological relationships 
Both the broodstock abundance-recruit- 
ment (Fig. 7) and abundance-mortality 
(Fig. 9) curves have outlying points. These are more 
common in the former than in the latter. Arguably, data 
for years when regime shifts occur should not be used 
in defining such relationships because the purpose of 
such relationships is to understand and model the typi- 
cal population dynamics of the stock. Stock dynamics 
during regime shifts are atypical. 
The abundance-mortality relationship (Fig. 9A) shows 
only a single outlying point This outlier (X), the only 
case of epizootic mortality at stock abundances great- 
er than 5xl0 9 , marks the regime shift year of 1985, 
when stock abundance reverted to the low-abundance 
state after more than a decade of high abundance. The 
1968-70 period, during which time conditions supported 
a dramatic population expansion, did not leave an indel- 
ible imprint. All three years were characterized by low 
mortality, but many other such years displayed similar 
abundance levels. 
In contrast, the abundance-recruitment scatterplot 
(Fig. 7) contains four clear high-recruitment outliers. 
In this case, the 1985 regime shift is not unusual. 
Other low-recruitment years show high abundance. 
The 1968-70 period contains one of the four outliers 
(Fig. 7) and the years 1972-74 contain the other three. 
The inference drawn from Figure 2 is that these four 
outliers are of two types. One outlier is the previously- 
mentioned outlier that occurred during the 1968-70 
period and represents the unusual event that dramati- 
Table 7 
Mean first passage times and the distribution of occurrence 
of the eastern oyster ( Crassostrea virginica ) population in 
each quadrant after an infinite number of steps were calcu- 
lated from the Delaware Bay oyster recruitment-mortality 
distribution (Fig. 12). The observed distribution of occur- 
rences is given in Table 6.))Arrows indicate trajectories 
between quadrants. Quadrants are defined in Figure 10. 
Quadrant 
1 
2 
3 
4 
Mean first passage 
time (yr) 
4.45 
3.72 
9.97 
4.52 
2 -a- 
4.83 
3.79 
9.91 
4.17 
3 — > 
5.94 
6.52 
3.78 
6.80 
4 — > 
4.92 
4.65 
9.08 
4.05 
Distribution of 
occurrence after 
infinite steps 
0.225 
0.264 
0.264 
0.247 
cally impacted the stock. The other three are associated 
with an unusual transit of abundance above carrying 
capacity (Powell et al., 2008, 2009) and represent events 
that had no long-term consequences for the stock, ex- 
cept to maintain abundance near the carrying capacity 
