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Fishery Bulletin 107(2) 
evidence (Osman et al., 1989; Powell et al., 2002b, 2004; 
Hofmann et al., 2004). 
In Delaware Bay, recruitment rates below 2 x 10 9 spat 
are disproportionately associated with abundances of 
less than 3xl0 9 oysters (Fig. 7). The distribution of 
years in the four quadrants of the broodstock-recruit- 
ment diagram was 17, 9, 9, and 18 for quadrants 1, 2, 3, 
and 4 (as defined in Fig. 10), respectively (Table 2). This 
distribution was unlikely by chance, given the expecta- 
tion that one-quarter of the years should fall into each 
quadrant: P-0.10, P<0.10; P<0.10; P<0.10, for quadrants 
1-4, respectively (binomial test: p = 0.25, q = 0.75). Twice 
as many high-recruitment events were associated with 
high abundance than with low abundance, and about 
twice as many low-recruitment events were associated 
with low abundance than with high abundance. The 54- 
yr average recruitment rate, expressed as the number 
of spat per >20-mm oyster per year, was 0.959. The 
median was lower, at 0.600. The long-term likelihood 
of a one-year population-replacement event (i.e. one 
spat per >20-mm oyster) was 17 in 54, and 
a recruitment rate half that high occurred 
in 27 of 54 years (Fig. 3). 
Only four massive recruitment events 
(>1.7 x 10 9 spat) occurred over the 54 years 
(Fig. 7). The rarity of these occurrences is 
not unusual (e.g., Loosanoff, 1966; Hofstet- 
ter, 1983; Oviatt, 2004; Southworth and 
Mann, 2004). The events were not predict- 
ed by the broodstock-recruitment curve. 
In most years, however, the broodstock-re- 
cruitment relationship was relatively pre- 
dictive, and the vast majority of recruits 
sustaining the population over the 54 years 
accrued from the 50 more-standard recruit- 
ment events. Nevertheless, even in average 
recruitment years, variability about the 
curve was large, about 4xl0 9 spat. 
Mean first-passage times calculated from 
one-year transition probabilities (Table 2) 
varied from 3 to 8 years (Table 3). Return 
intervals were about 3 years for a popula- 
tion beginning in quadrant 1 (low recruit- 
ment and low abundance) returning to 
quadrant 1, and for a population beginning 
in quadrant 4 (high recruitment and high 
abundance) returning to quadrant 4. The 
longest return intervals were associated 
with quadrant 3 (low recruitment and high 
abundance) as a destination. A population 
beginning in quadrant 2 or quadrant 3 was 
somewhat more likely to fall to quadrant 1 
than to move to quadrant 4. Thus, overall, 
populations at low abundance were likely 
to remain there (quadrant 1) because of 
low recruitment, whereas populations at 
high abundance were likely to remain there 
because of high recruitment. Quadrants 1 
and 4 have the characteristics expected of 
stable states. 
The broodstock-recruitment relation- 
ship (Fig. 7) indicated that the number of 
recruits per adult declined at high abun- 
dance. Note in particular (Fig. 3) that 
the number of recruits per adult was not 
unusually high during the 1970-85 high- 
abundance period, with the exception of 
1972. In fact the number of one-year re- 
placement events (i.e. one spat per adult) 
was lower for a longer time during this 
Figure 9 
The relationship between oyster abundance and box-count mortality 
for the eastern oyster ( Crassostrea virginica ) on the natural oyster 
beds of Delaware Bay during 1953-2006. The solid line is the curve 
described by Equation 6 fitted to the data. Dotted lines mark the 
54-yr medians of abundance and box-count mortality (Table 4). (A) 
represents entire data set; (B) focuses on the region of the diagram 
encompassing abundances below 5 x 10 9 , an abundance range in which 
an increase in mortality frequently occurs due to epizootic events. 
Years characteristic of regime shifts are identified in A only. 
