Burton: Age, growth, and mortality of Lutjanus griseus 
255 
valued by anglers for its fighting ability at all sizes (Ma- 
nooch, 1984). Recreational landings averaged 60,685 kg 
for north Florida compared with 290,266 kg for south Flor- 
ida annually between 1986 and 1997. Commercial land- 
ings averaged 20,931 kg for north Florida and 122,013 kg 
for south Florida for the years 1986-97. 
In this study I describe the growth of gray snapper land- 
ed from the headboat and commercial fisheries of the east 
coast of Florida, including the Atlantic waters of Monroe 
County, FL. I attempt 1) to describe the age and growth of 
gray snapper from the east coast of Florida, 2) to validate 
growth increments on otoliths as annuli, 3) to estimate 
natural mortality (M), and 4) to estimate total mortality 
(Z) from catch curve analysis. I also compare size at age, 
growth rates, and mortality rates between the fish in the 
northern (Indian River County northward) and southern 
portions of Florida. I undertook this study to provide fish- 
ery managers with a current, validated age-growth study, 
not restricted in either fishery or geographic scope, to use 
in current stock assessments. 
Materials and methods 
Gray snapper were sampled from the landings of head- 
boats and commercial fishing vessels from St. Augustine, 
Florida, through the Florida Keys by National Marine 
Fisheries Service (NMFS) port samplers from 1994 to 
1997. Samples were not available from the Marine Rec- 
reational Fisheries Statistics Survey (MRFSS) owing to 
logistical and contractual problems. Fish samples were 
taken as available, independent of size, sex, or season. The 
left sagittal otolith was removed from each fish, rinsed 
with water, and stored dry. Otoliths were sectioned accord- 
ing to the methods of Potts and Manooch ( 1995). 
I sorted the sectioned otoliths by 50-mm-TL intervals 
and read them in ascending order, as an aid in deter- 
mining size at first annulus formation. Reflected light re- 
vealed alternating opaque and translucent rings. Opaque 
rings were presumed to be annuli and ages (in years) were 
assigned to specimens equal to the number of opaque 
rings. I measured the distance from the focus to the edge 
(otolith radius), the focus to successive opaque rings (an- 
nular measurements), and the distance between the dis- 
tal edge of the last opaque zone and the otolith edge (mar- 
ginal increment). 
I analyzed marginal increments to validate the annual 
periodicity of ring deposition. Monthly mean marginal in- 
crements were calculated by age and for all ages com- 
bined. Means were plotted against month of capture, the 
minima indicating the month of annulus formation. 
I regressed fish total weight (IF) on fish total length ( TL ), 
by area, using all gray snapper sampled by the headboat 
survey from 1982 to 1997 (n = 10,705). I examined both a 
direct nonlinear fit by using nonlinear least squares esti- 
mation (SAS Institute, Inc., 1987) and a linearized fit of 
the log-transformed data, examining the residuals to de- 
termine which regression was appropriate. Fish sampled 
from commercial fisheries were excluded from these analy- 
ses because they were eviscerated. 
The relation of total length to otolith radius was esti- 
mated by regression: 
L = a + b (R), 
where L = total length in mm; and 
R - otolith radius in ocular micrometer units. 
Linear regression equations were developed for all data 
pooled as well as for north Florida and south Florida. 
Back-calculated size of each fish at the time of formation 
of each annulus was determined by substituting the mea- 
surement to each annulus into a body-proportional equa- 
tion (Francis, 1990): 
L = {(a + bS i ) / (a + 6/?)]L, 
where L ( = fish total length (mm) at annulus i; 
R = otolith radius; 
a = intercept from the L-R regression; 
b = slope from the L-R regression; and 
S l = measurement to the 1 th annular ring. 
Back-calculated size at time of formation of the last an- 
nulus was used in order to provide length-at-age data 
unbiased by differences in time of year of sampling. Area- 
specific data were developed by substituting coefficients 
from the area-specific L-R regressions into Francis’s ( 1990) 
body-proportional equation. Use of a single back-calcula- 
tion per fish avoids the violation of assumption of inde- 
pendence among sample elements (Vaughan and Burton, 
1994), but this method does not necessarily provide all 
available information about the growth of all cohorts. 
Theoretical growth parameters were estimated by fit- 
ting the back-calculated lengths at age to the von Berta- 
lanffv ( 1938) growth equation: 
L, = L [ 1 - exp [-K(t - t n ))], 
where L t = total length at age t\ 
L = theoretical asymptotic length; 
K = Brody growth coefficient; and 
t 0 = theoretical age when fish length = 0. 
Parameter estimates were obtained by using nonlinear 
regression analysis (SAS Institute, Inc., 1987). Theoreti- 
cal lengths at age were derived for back-calculated lengths 
at age by using the last annulus (Vaughan and Burton, 
1994). 
I estimated the instantaneous rate of natural mortality 
(M), by area, using several methods. I used Hoenig’s ( 1983) 
longevity-mortality relationship, 
ln(Z) = 1.709 -1.084 x lnR„ mv ), 
where t niax = the maximum age encountered; and estimates 
of M are for relatively unexploited stocks. 
I used a second equation which adjusts for sample size 
in fioenig ( 1983), who reasoned that with a larger sample 
