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Fishery Bulletin 99(2) 
Figure 1 
(A) Mean monthly marginal increment by area for gray snapper, all ages combined; (B) monthly percentage of fish with a marginal 
increment = 0. 
size there is a greater probability of encountering the true 
maximum age of the fish: 
Z = \n(2n + 1 )/(t max -t c ), 
where n = the sample size; and 
t { = the first age fully represented in the catches. 
I used the Pauly (1980) method 
logioM = 0.0066 - 0.279 x log 10 L oo + 
0.6543 x log 1(> /t + 0.4634 x log 10 T, 
where L m = the asymptotic length; 
K = the Brody growth coefficient from the von Ber- 
talanffy ( 1938) growth equation; and 
T = the mean annual seawater temperature (°C). 
I derived the latter from sea surface temperature readings 
from buoys operated by NOAA’s National Oceanographic 
Data Center during 1998. Finally, I estimated M by using 
the regression of Ralston ( 1987); 
M = 0.0189 + 2.06 x K, 
where K - the Brody growth coefficient. 
Observed ages at length for all years combined were 
used to develop age-length keys (ALK) for each area (Rick- 
er, 1975). I assigned aged fish (my samples) to 25-mm-TL 
intervals and calculated age distribution (as a percentage) 
for each size interval. Area-specific age-length keys were 
used to convert length frequencies from each area and 
fishery, weighted by the corresponding annual landings, 
into age frequencies by assigning ages to unaged fish from 
the length frequencies. Length-frequency data and annu- 
al landings data were acquired from the South Atlantic 
headboat survey, the MRFSS, and the Trip Interview Pro- 
gram (TIP) 5 survey. Total instantaneous mortality rate, Z, 
was estimated by the absolute value of the slope of the 
descending right limb of the plot of log t , age frequency on 
age (catch curves) (Beverton and Holt, 1957). Only fully 
recruited ages (age groups to the right of the top of the 
dome of the curve) were used to estimate Z because the 
age group at the top of the catch dome may not be fully 
vulnerable to the fishing gear (Everhart et al., 1975). 
Results 
Age determination and validation of annuli 
A total of 98% (1243 of 1260) of gray snapper sampled had 
legible cross-sectioned otoliths. Opaque rings were distinct 
and easily counted. Otolith radius was correlated with fish 
length across all ages: 
North Florida: 
TL = ( 10.02 x OR) - 52.98 (r I 2 =0.90, n=519), 
South Florida: 
TL = (9.90 x OR) - 91.68 (r 2 =0.78, n= 724), 
Areas combined: 
TL = (11.05 x OR) - 130.32 (r 2 =0.89, n=1243). 
Marginal increment analyses showed one minimum per 
year in June, validating the annual periodicity of otolith in- 
crements (Fig. 1A). The monthly percentage of fish with a 
marginal increment equal to zero (Fig. IB) showed a single 
maximum and provided further evidence that annulus for- 
mation occurred yearly in June or July. To satisfy Beamish 
and McFarlane’s (1983) assertion that individual ages need 
to be validated, I analyzed marginal increments by age for 
5 Trip Interview Program. 1998. Administered by Southeast 
Fisheries Science Center, NMFS, NOAA, 75 Virginia Beach Dr., 
Miami, FL 33149 
