40 
Fishery Bulletin 95(1), 1997 
(A+0.458)), where L is total length in cm and A is 
age in years. Size at age in the absence of fishing 
mortality was assumed to be normally distributed 
with a coefficient of variation of length at age (v) of 
0.10 based on the observed variability in size at age 
for red snapper (Goodyear 1 ). The mean length of in- 
dividuals of age a in growth platoon p, l , was de- 
termined from mean size at age (L ) by using the 
normal distribution and the coefficient of variation 
of length at age as 
^ ap L a “FT'a^pV, 
where: 2 is the standard normal deviate for the p th 
percentife of the distribution. The simulation con- 
sidered 101 growth platoons in each age class. The 
resulting distributions of lengths at the beginning of 
the year for ages 1-10 are shown in Figure 1. Within- 
year growth was evaluated as 
W ap = W a _i, p exp(G ap ), 
where W ap is the weight (kg) of an individual in 
growth platoon p at age a, and G Qp - instantaneous 
growth rate of growth platoon p at age a. The G ap 
were estimated from lengths at age predicted from 
the von Bertalanffy growth equation. 
The weight of a fish at capture VF, was evaluated 
as 
W c = W ap Z ap (exp(G a -Z ap )~ l)/ 
(( Gap ~ Z ap > C 1 - ex P< ~ Z ap )), 
where Z is the total instantaneous mortality for 
growth platoon p at age a during the time period. 
Weight was converted to length with the length- 
weight equation (W = 1.158 x L 3 056 , r 2 =0.985, 
n =25,375) Growth, mortality, and catch were evalu- 
ated monthly. 
The period simulated was from 1954 to 1994, but 
catch and sample data were retained and analyzed 
for 1984-94, which corresponds to the time span of 
actual data from the fishery. Recruitment in the 
model was specified by year class from 1954 to 1994 
(Fig. 2). The values for 1972-94 follow the recruit- 
ment pattern observed in trawl surveys (Goodyear 1 ). 
Earlier values were arbitrarily varied around the 
level observed at the beginning of the time series 
because landings from shrimp trawlers (predomi- 
nantly juvenile fish) during these years were higher 
than those after 1972. 
The value of fishing mortality in the model is the 
product of a maximum potential value for the year 
and a selectivity value based on the fish’s age (Figs. 
3 and 4). A dome-shaped selectivity schedule was 
(ill 
Jk A3e2 
jiT Ttu 
A ge 3 
A ge 4 
Age 5 
: A96 6 
Tbw_ 
: A96 7 J 
; a„ 8 ^ 
ilW 
; Age 9 
I A ge 1 0 
' -r^T 
dfll-JfttW. 
0 10 20 30 40 50 60 70 80 90 100 
Total length (cm) 
Figure 1 
Simulated length-frequency distributions of red 
snapper, Lutjanus campechanus, at the begin- 
ning of the year for ages 1-10. 
selected on the basis of age distribution of the catch 
(predominantly from handlines) in the 1994 assess- 
ment (Goodyear 1 ). The value of the annual maximum 
for 1984-94 also follows the trend in the best estimates 
from the 1994 assessment, whereas earlier values were 
arbitrarily varied around the level observed at the be- 
ginning of the time series. The reduction in fishing 
mortality after 1990 was a response to management 
actions. The selectivity schedule (Fig. 4) was selected 
to produce a sample length frequency similar to that 
observed in the fishery (Fig. 5). Samples were trun- 
cated below 33 cm after 1990 to include the effects of 
changes in minimum size regulations at that time. 
The simulated observations of length (and age) 
were obtained from the simulated catch. The catch 
from a growth platoon in the population structure 
was picked at random. It was evaluated for inclu- 
sion as an observation on the basis of the ratio of its 
magnitude (N p ) to the maximum catch from any other 
growth platoon (N ). This was accomplished by 
drawing a uniform random number (R) between 0 
and 1.0. If the ratio N p /N max > R, the length and age 
attributes of the cell were included as an observation; 
otherwise, they were discarded. This convention caused 
the sampled growth platoon to be proportional to their 
magnitude in the simulated catch. The process was 
repeated for each month of the simulation until 1,000 
samples had been drawn. This provided 12,000 length 
