Jones and Weils: Yield modeling for Pogonias cromis 
331 
partitioned equally over the remaining 11 age intervals. 
Hence, in the second scenario the lifetime Z was greater 
than 2.0. The second scenario was chosen to model ex- 
tremely severe F on young fish that could be experienced 
from both directed fisheries and bycatch where young fish 
predominate. 
Cohort biomass and harvesting time 
The maximum possible yield for a year class occurs at the 
age ^t CRITICAL ) when the biomass of the cohort is at its 
maximum in the absence of fishing. For comparison with 
the Beverton-Holt and Ricker yield-per-recruit modeling 
results, we estimated t critical f° r black drum following 
Quinn and Deri so (1999) with the following equation: 
^ CRITICAL = ^0 + 1 ^ + ~ j > ) 
where m = MIK, 
P = the length-weight allometry coefficient, and 
t 0 , K , and M are defined as in Equation 1. 
Parameter estimates or the range of values used in calcu- 
lations are listed in Table 1. Age at maximum biomass can 
be compared to mean age in the catch to indicate whether 
further juvenesence is possible. 
To calculate the proportion of potential growth span (P a ) 
remaining when black drum enter the exploited phase of 
life (Beverton and Holt, 1957), we used the quantity (Be- 
verton, 1963): 
p g = a-i c /Lj, ( 6 ) 
where L^, the asymptotic length, was obtained from Jones 
and Wells (1998); and Z c , the average length at first cap- 
ture, was obtained by converting t c to length with the von 
Bertalanffy growth curve reported for black drum in Ches- 
apeake Bay (Jones and Wells, 1998) and Florida (Murphy 
and Taylor, 1989). Both parameters are based on total 
length in cm. 
Results 
Modeling with parameters from Chesapeake Bay 
Yield-per-recruit curves on F showed that the yield of 
black drum in Chesapeake Bay could be maximized by 
decreasing t c to 10-15 yr over most of the range of M 
(0.06-0.12) and F used in our simulations (Fig. 1; Table 
2). The gains in yield-per-recruit could be substantial. For 
example, at the estimated current levels of fishing mortal- 
ity for black drum in Chesapeake Bay (F CUR - 0.04-0.06), 
yields could be increased 58% at M= 0.06 and 89% at 
M=0.08 by decreasing current t c from 25 yr to 15 yr. 
Yield-per-recruit curves showed marked peaks only at 
the lowest levels of M (0.02; 0.04) when t c <10-15 or at 
higher levels of M when f c <10 (Fig. 1). Otherwise, curves 
were asymptotic or rising, and F MAX was reached only at 
the highest fishing mortalities (F MAX > 2.0; Table 2). When 
M was 0.02, curves peaked for t c up to 20 yr, resulting 
in F max <0.4. However, because an M of 0.02 predicts a 
maximum age of over 200 yr in an unexploited stock and 
because there is no indication of such longevity in black 
drum, we rejected this scenario as improbable. When M 
was 0.04, curves peaked for f c <15, for ages constituting 
less than five percent of the catch and well below the mean 
age (25 y) in the catch in the Chesapeake Bay fishery. At 
higher values of M when t ( ,>10, curves were asymptotic or 
rising and F MAX occurred only at the highest levels of F. 
Although yields increased continuously with F for M> 0.04, 
increases in yield beyond F- 0. 1-0.3 were very small. 
For M> 0.06 and t> 5, estimates of F CUR were below the 
levels giving maximum potential yield-per-recruit ^ MAX* 
and F 0 l (Fig. 1; Table 2). For M- 0.06, F CUR equals 0.06 at 
most and F 0 l equals 0.07, indicating that, although below 
the maximum potential yield-per-recruit, estimated cur- 
rent levels of harvest are only slightly below this more 
conservative benchmark of F. When M>0.06, F 0 1 is great- 
er than 0.08 and always above F CUR , indicating that cur- 
rent levels of harvest are below this conservative bench- 
mark. In contrast, if M<0.04 and t ( <10, F 0 1 is higher than 
F cur (Table 2) indicating that there is some justification 
for decreasing F. However, as mentioned previously, we be- 
lieve these levels of M<0.04 to be unrealistically low for 
this species. 
Curves of biomass on age showed that biomass de- 
creased with increases in M or F (Table 3). Lifetime co- 
hort biomass of an unfished stock decreased by 85% from 
M= 0.02 to M=0.12. Within a given M, increased F resulted 
in decreased lifetime cohort biomass. For example, when 
the most credible combinations of M and F CUR were mod- 
eled (M= 0.06, F cur = 0.06; M=0.08, F CUR = 0.04), biomass 
declined 59% and 42%, respectively, from that of the un- 
fished stock (Fig. 2). 
Similar patterns were shown when we modeled heavy 
fishing in the first 5 years (F=2.0), and uniform low mor- 
tality was evident thereafter. Curves of biomass on age 
showed a much larger decrease in biomass with increasing 
M and F (Fig. 3; Table 4). Maximum biomass at minimum 
fishing mortality (F=0.02; M=0.02-0.12) was 81-67% less 
than seen without heavy early mortality. For example, un- 
der the most likely combinations of M and F CUR for the 
Chesapeake Bay fishery, biomass was reduced approxi- 
mately 82-87% (M=0.06 F CUR = 0.06; M=0.08 F CUR =0M). 
Values of t C RiTCAL estimated by using different values of 
M were relatively high for black drum in Chesapeake Bay. 
Increasing M resulted in a decrease in t CRmCAL from 25 
yr at M-0.02 to 10 yr at M= 0.12. This finding indicates 
that, for the range of M considered in our study, maxi- 
mum theoretical cohort biomass, in the absence of fishing, 
is achieved before black drum reach age 25. This occurs 
at the lowest value of M, approximately the mean age of 
capture in Chesapeake Bay. For the most likely combina- 
tions of M and F (M= 0.06 F CUR = 0.06; M= 0.08 F CUR = 0.04), 
t critical declined from 13(M=0.08)-15(M=0.06) yr in the 
unfished stock to 10 yr in the fished stock. In this example, 
t critical below the mean age of capture in the Bay, 26 
yr, and potential yield is lost to natural mortality. 
