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Fishery Bulletin 99(2) 
Table 1 
Parameter estimates or range of values used in yield-per-recruit and biomass 
simulations for black drum, Pogonias cromis, on the east coast of the U.S. Data 
taken from Jones and Wells (1998) for the Chesapeake Bay and Murphy and 
Taylor (1989). 
Parameter 
Chesapeake Bay 
NE Florida 
Method 
tc 
5-25 yr 
age composition of catches 
t r 
5 yr 
lyr 
life history information 
to 
-2.3 yr 
-1.3 yr 
growth curve 
K 
0.105 yr 
0.124 yr 
growth curve 
117.3 cm 
117.2 cm 
growth curve 
27.5 kg 
25.5 kg 
converted from L x 
z 
0.08-0.12 
catch curves and longevity 
M 
0.00-0.12 
longevity 
P 
3.11 
length-weight regression 
Murphy and Taylor, (A'=0. 124; 1989 ) for 
black drum sampled from the north- 
east coast of Florida. Hence, we also 
used estimates of K from the north- 
east coast of Florida in our modeling 
to ensure that results would reflect the 
available scientific data from the U.S. 
East Coast. For both areas, asymp- 
totic mean weight, W m , was converted 
from an allometric weight-length rela- 
tionship (6=3.11; Jones and Wells, 
1998). This slight deviation from iso- 
metric growth (6=3.0) may result in a 
small overestimation of yield (less than 
7%) which Ricker (1975) dismissed as 
inconsequential to further calculations. 
Because we focused on the relative 
yields that result from varying t 0 and 
F at different levels of M, differences 
in yield should be even less than this 
absolute level (Barbieri et ah, 1997). 
Age of recruitment to the fishing area, t r , was unknown 
for this fishery and was set to age 1 for the Florida fishery 
and age 5 for the Chesapeake Bay fishery, a year less than 
the youngest adult black drum caught in the Bay during our 
three-year study. Fisheries-based data included Z, F , M, and 
f . Estimates of the instantaneous total mortality, Z, for fully 
recruited black drum were obtained from catch-curve anal- 
ysis and maximum age procedures, and ranged from 0.08 
to 0.12 (Murphy and Taylor, 1989; Jones and Wells, 1998). 
Although we had direct estimates of total mortality, Z, we 
lacked independent estimates of instantaneous fishing mor- 
tality, F, and instantaneous natural mortality, M. However, 
the estimate of Z allowed us to estimate current levels of 
fishing mortality, F CUR(i) , for different values of M, as 
Fcvru, = Z~M„ (3) 
where M t = 0.02-0.12. 
We estimated the most probable value of M by extrapolat- 
ing to maximum age estimates realistic for an unfished 
fishery. This range of M was lower than that predicted 
with a multiple regression developed by Pauly ( 1980; 
M= 0.16-0.30). Using our lower estimate of M, we made our 
modeling more sensitive to potential growth overfishing; 
therefore management strategies would be conservative. 
Ricker yield model 
Ricker’s yield model is used to simulate the potential 
for growth overfishing over the life of a cohort by mea- 
suring available biomass at age under various levels of 
F (King, 1995). Mortality and growth are opposing effects 
that result in a maximum biomass during the lifetime at 
the age of maximum biomass, t critical ■ The model equa- 
tion is from Saila et al. (1988): 
where Y e = estimated lifetime equilibrium yield referenced 
to an arbitrary recruitment biomass of 1000 g; 
B i = biomass at age; 
F t = instantaneous fishing mortality at age; 
Z ( = total mortality at age; 
G ( = growth in weight-at-age; and 
t- = age where t i is calculated from the age of first 
capture, t c , to the last fishable age, t L . 
When calculated at F= 0, the model produces estimates 
of equilibrium yield for the unfished stock. Computations 
were performed by using the computer program Ricker 
modified from the Basic Fisheries Science Programs pack- 
age (Saila et al., 1988). 
Parameter values used in simulations are summarized 
in Table 1. Estimates of growth parameters B j} and G l 
for Chesapeake Bay and Florida black drum were ob- 
tained from Jones and Wells (1998) and Murphy and Tay- 
lor (1989). Because of the long life of black drum, we 
grouped parameters into 5-year intervals to increase com- 
putation efficiency. Simulations used six values of M (0.02, 
0.04, 0.06, 0.08, 0.10, and 0.12) and six levels of F (0.0, 
0.02, 0.04, 0.06, 0.08, and 0.10). This model is not used to 
calculate optimum yield as is the Beverton-Holt yield-per- 
recruit model. By integrating the area under the curves, 
reduction in stock biomass at a given level of F can be 
compared with biomass of the unfished stock, thus demon- 
strating the loss of trophy-size fish that are prized in rec- 
reational fisheries. 
Simulations were done to model two scenarios of fish- 
ing mortality and their effect on biomass: 1) uniform low 
F over the life span, and 2) very high F in the first 5-year 
interval and uniform low F over the remaining lifetime. 
In the first scenario the chosen level of F was partitioned 
equally over 12 age intervals. (Because we lacked age-spe- 
cific estimates of F, the most straightforward approach 
was to equally partition F across age intervals.) In the sec- 
ond scenario fish in the first 5-year interval were given 
an F='2.0 and thereafter experienced the chosen level of F 
2 
