116 
Fishery Bulletin 107(2) 
Forces modifying abundance: broodstock-recruilment 
relationship A linear fit to the broodstock and recruit- 
ment data returned a regression coefficient of only 
0.076 (Fig. 7). The relationship was strongly compen- 
satory. A variety of broodstock-recruitment models 
might be applied (e.g., May et ah, 1978; Hilborn and 
Walters, 1992; Kraeuter et al., 2005), given the scatter 
of data at high abundance and the paucity of extremely 
high values. We used a relationship that produced 
declining recruitment at high abundance (overcom- 
pensation sensu Hancock, 1973; McCann et al., 2003), 
because shellfish can achieve densities sufficient to 
limit growth and reproduction (e.g., Frechette and 
Bourget, 1985; Frechette and Lefaivre, 1990; Powell 
et al., 1995). Application of the simple filtration model 
of Wilson-Ormond et al. (1997) indicated that present- 
day abundances, even on the medium-mortality beds, 
are below such densities, but abundances in the 1970s 
were very likely high enough and medium-mortality 
abundances circa 2002 (Fig. 2) may have been high 
enough to restrict growth. Thus, from Hilborn and 
Walters (1992): 
where R = the number of spat in millions; and 
N, 
oyster abundance in millions. 
Fitting this curve to the data for the high- and medium- 
quality strata (Fig. 1) yields a - 0.3746, and /3 = 5121.9 
(Figs. 7 and 8). We compared the result of Equation 4 
to the result of a best-fit linear regression with zero 
intercept (Fig. 8). The linear relationship is 
R t =0.493 N t . 
(5) 
R t = N t _ lt 
a l+ ; 
U-l 
(4) 
Broodstock and box-count mortality Box-count esti- 
mates of natural mortality are also related to trends 
in abundance (Fig. 9). At abundances greater than 
4 x 10 9 , mortality was low. The fraction dying each year 
averaged 9.6% for these nonepizootic years, defined for 
convenience as years in which the fraction dying was 
less than 20%. The nonepizootic death rate was rela- 
tively independent of abundance, although the lowest 
mortalities, less than 6%, occurred at abundances 
below 6 x 10 9 . 
Of the 14 epizootic years in the 54-yr record, defined 
in our study as deaths exceeding 20% of the stock, 13 
occurred at abundances less than 3xl0 9 (Fig. 9). The 
exception was 1985. Of the 32 years with abundances 
less than 3 x 10 9 , 14 were epizootic years. Of these 32, 
only one had a fractional mortality be- 
tween 0.15 and 0.20. Accordingly, two 
divergent outcomes existed over a range 
of low abundances. In some years, the 
fraction dying approximated the long- 
term mean for high-abundance years, 
about 9.6%. In other years, epizootic 
mortalities occurred. Epizootic events 
also occur rarely at very low abundanc- 
es. Note on Figure 9 that no mortality 
fraction exceeded 0.17 at abundances 
below 1.5 xlO 9 . Thus, a complex rela- 
tionship exists between abundance and 
mortality. 
We apply an admittedly ad hoc em- 
pirically derived equation to describe the 
relationship between box-count mortality 
and abundance depicted in Figure 9: 
Figure 7 
The broodstock-recruitment relationships for eastern oyster (Crassostrea 
virginica), 1953-2006. The solid line is the best-fitted Ricker curve 
(Eq. 4). The dashed line is a second-order polynomial fit (see Kraeuter 
et al., 2005). Note that the polynomial fit overestimates recruitment at 
high abundance. Dotted lines (vertical and horizontal) mark the 54-yr 
medians of abundance and recruitment. 
=co + K\og e (N t _ 1 + p ) 
-(pN^ + xN^e 
N f _ i- 
t-i-v 
2v 
(6) 
where to = 0.055; 
k = 0.03; 
P = 1.0; 
cp = 0.0025 
X - 0.1; 
xp = 2.2; 
v = 0.8; and 
N is expressed as billions of 
animals. 
