Powell et al.: Multiple stable reference points in oyster populations: Crassostrea virgmica in Delaware Bay 
115 
dance remained relatively stable from 1987 through 
2001 (Fig. 2). Recruitment was not unusual (Fig. 3). 
However, natural mortality rose dramatically, from 
the 10% level immediately after 1986, to often exceed 
20-30% throughout the 1990s (Fig. 4). The fraction of 
deaths contributed by the high-mortality beds did not 
change markedly over the 1990s, although the fractions 
of deaths did rise incrementally in 1990 compared to the 
few preceding years (Fig. 6). The dispersal pattern of 
the 1980s remained through 1995 (Fig. 5), despite the 
increased mortality rate on the high-mortality beds. 
The response of the stock to Dermo became more ap- 
parent in 1996, when the stock began a rapid contraction 
to its refuge on the medium-mortality beds. This con- 
traction in dispersion occurred at the same time as in- 
creased recruitment on these beds (Fig. 5) and counter- 
weighed the accumulating losses of individuals farther 
downbay (Fig. 6), so that total abundance did not change. 
The post-2000 era 
Although the time series is still limited in scope, a 
change in population dynamics is evident around 2000. 
Beginning in 2000, the recruitment rate declined pre- 
cipitously and remained low at least through 2006 (Fig. 
3). Total abundance declined with continuing high mor- 
tality on the high-mortality beds (Fig. 6), but stock 
consolidation continued, with an increasing proportion 
of animals on the medium-mortality beds. As a conse- 
quence, mortality in the population as a whole declined 
(Fig. 4). The fraction of total mortality contributed by 
the high-mortality beds declined to its lowest level since 
the 1950s and remained low (Fig. 6) because consolida- 
tion of the stock upbay limited the number of individuals 
available to die on the high-mortality beds. 
Overview of fishing activities 
The analysis that follows makes reference to two distinc- 
tive types of fishing on the Delaware Bay oyster beds 
of New Jersey. From 1953 through 1995, a “bay-season” 
fishery occurred, in which a portion of the beds was 
opened, usually for 2-6 weeks in the spring. Oysters 
were removed en masse and transplanted downbay to 
leased grounds. Based on recent dredge efficiency esti- 
mates (Powell et al., 2007), the method for transplanting 
was relatively nonselective for oyster size; oysters were 
moved more or less in proportion to their contribution 
to the size-frequency distribution of the population. In 
most years, the fishery was limited by the 40% rule. 
As a consequence, target beds varied during the pro- 
gram from year to year as the relative abundance of 
the resource varied. 
Since 1996, a direct-market fishery has been pros- 
ecuted for the most part on beds from Shell Rock down- 
bay (Fig. 1). In this fishery, market-size oysters are 
taken directly off the beds and marketed immediately 
or stored for a time on leased grounds before they are 
marketed. The vast majority of animals removed by this 
fishery have exceeded 63 mm (Powell et al., 2005). 
Model formulations and statistics 
Basic population dynamics Quantification of the Dela- 
ware Bay time series has been described in Powell et al. 
(2008). Natural mortality fractions were obtained from 
box counts under the assumption that 
N — N, + N, ( 1 ) 
oysters boxes t Live oysters ^ > ’ 
where N = the number of individuals; and 
t - any given year. 
Hence 
N, 
<*> bc = 
boxesf 
Ni + Ni 
boxesf Live oysters f 
( 2 ) 
where <P bc = mortality expressed as the fraction of indi- 
viduals alive at the end of year t that died 
during the next year, based on box counts 
(be). 
In Delaware Bay, boxes appear to remain intact, on 
the average, for a little less than one year (Powell et 
al., 2001; Ford et al., 2006). On the other hand, dredge 
efficiencies indicate that some boxes may be old (Powell 
et al., 2007). The degree to which the two biases coun- 
terweigh is unclear; however, box counts are clearly 
adequate to identify significant changes in yearly mor- 
tality rates (Ford et al., 2006). We consider box counts 
to be the best available basis for estimating the natural 
mortality rate of adult oysters. 
However, boxes very likely do not adequately measure 
the mortality of juvenile animals. Juvenile shells are 
taphonomically more active (Cummins et al., 1986a, 
1986b; Powell et al., 1986; Glover and Kidwell, 1993) 
and thus can be expected to remain intact for a rela- 
tively short time. In addition, deaths of smaller animals 
do not leave intact boxes as often because many deaths 
are caused by shell-crushing predators (Powell et al., 
1994; Alexander and Dietl, 2001; Milke and Kennedy, 
2001). Inasmuch as the mortality rate of juvenile ani- 
mals is likely to be underestimated by box counts, the 
fraction dying, but not recorded by box counts, <J> 0 , was 
obtained by difference: 
0>o = 
t N t - N t _, ) - ( R t _, - - a> f N t ^ ; 
N t-i + R t-i 
(3) 
where <P f = the fraction taken by the fishery; 
R = the number of recruits into the popula- 
tion; and the first parenthetical term on 
the right-hand side represents the differ- 
ence in abundance between two consecutive 
surveys. 
Mortality unrecorded by box counts, <J> 0 , varied randomly 
over the time series, with a 54-yr mean of 0.274 and a 
54-yr median of 0.311 (Powell et al., 2008). 
