Wilson and Nieland: Age and growth of Lut/cinus ccimpechanus 
655 
The periodicity of opaque annulus formation was deter- 
mined by marginal increment analysis and by plotting 
the proportion of otoliths with opaque margins by month 
of capture (Beckman et ah, 1988). To assess the possi- 
bility of false annulus formation among either younger 
or older red snapper, those individuals of age <5 yr and 
those >5 yr were also analyzed as above. Fork lengths 
at 100% maturity, 420 mm for males and 440 mm for 
females (Render, 1995), are achieved at about age 5. If 
one opaque and one translucent zone are shown to be 
formed each year, validation of annuli as being accreted 
once yearly is accomplished. 
Ages of red snapper were estimated from opaque annu- 
lus counts and date of capture with the equation 
Age (days) = -182 + ( annulus count x 365) + 
((m - 1) x 30) + d , 
where m = the ordinal number ( 1-12) of the month of cap- 
ture; and 
d = the ordinal number (1-31) of the day of the 
month of capture. 
The 182 days that were subtracted from each age estimate 
are an accommodation for the uniform 1 July hatching 
date which was assigned for all specimens (Render, 1995; 
Collins et al., 1996). Age in yr was derived by dividing 
the age in days by 365. Thus a red snapper captured on 
1 January which exhibits five opaque annuli (including 
an opaque margin [see below]) in its otoliths would have 
an estimated age of 1644 days or 4.5 yr. Our age esti- 
mation method also assumed that opaque annulus for- 
mation at the otolith margin uniformly commenced in 
January. The small number of individuals captured in Sep- 
tember, October, November, and December that evidenced 
early formation of opaque annuli had their ages adjusted 
by subtracting 365 days from their age estimates. Con- 
versely, a larger number of individuals captured in Janu- 
ary, February, and March had otoliths with translucent 
margins — evidence of an assumed delay in opaque annu- 
lus formation. The age estimates of these were augmented 
by the addition of 365 days. 
Total length-TW regressions were fitted with linear re- 
gression to the model TL = a TW h from log 10 -transformed 
data. Male and female regressions were compared with 
analysis of covariance (SAS, 1985). Only those red snap- 
per for which sex could be determined were used to fit 
growth models. Von Bertalanffy growth models of TL at 
age were fitted with nonlinear regression by least squares 
(SAS, 1985) in the form 
TL t =L„( 
where TL t = TL at age t\ 
L x = the TL asymptote; 
k = a growth coefficient; 
t = age in yr; and 
t 0 = a hypothetical age when TL is zero. 
Growth models were generated for three groups of red 
snapper within which the age and TL of all individuals 
were extant: 1) all specimens, 2) all specimens of known 
sex, and 3) specimens of known sex for which growth 
models were fitted independently for each sex. Likelihood 
ratio tests (Cerrato, 1990) were used to test for differences 
between males and females, both in growth models and in 
growth parameter estimates. Significance level for statis- 
tical analyses was 0.05 unless indicated otherwise. 
Results 
During eight years of variable collection effort, 3791 red 
snapper from recreational ( n =274 ) and commercial ( n =35 1 7 ) 
catches were sampled for morphometric data and sagittal 
otoliths. Among the 1438 male and 1542 female specimens 
for which sex could be determined, females ranged from 
242 to 1039 mm TL and from 0.16 to 22.79 kg TW; males 
were 245-946 mm TL and 0.19-13.70 kg TW. Composite 
ranges for all specimens of either known or unknown sex 
were 104-1039 mm TL and 0.02-22.79 kg TW; however, 
67.6% of 3787 available TL were between 325 and 525 mm 
and 80.0% of 3718 available TW were less then 2.5 kg (Fig. 
1). Neither the slopes (df=2,932; F=3.41; P<0.065) nor the 
intercepts (df=2,932; F- 3.16; P<0.075) of the TL-TW regres- 
sions were found to differ significantly between males and 
females; thus data for the two sexes were combined and a 
single predictive equation was generated 
TW=l.n x 10- 8 (PL) 304 
Sagittae of red snapper are ovate, laterally compressed, 
and have an indented sulcus acousticus on the proximal 
surface (Fig. 2A). Although one can count purported an- 
nuli in relatively small whole otoliths of red snapper less 
than age 5 (Futch and Bruger, 1976), it is difficult to dis- 
cern annuli in the larger otoliths of older individuals. Thin 
transverse sections of these older otoliths showed semidi- 
stinct translucent and opaque annuli that alternated from 
the core to the growing edge (Fig. 2, B and C).The presump- 
tive first annulus posed the most consistent problem for 
the readers. This annulus appeared as a diffuse “smudge” 
of opaque material variously located from totally isolated 
and somewhat distant from the core (Fig. 2B) to contig- 
uous to and continuous with the otolith core (Fig. 2C). 
Annulus counts ranging from 0 to 53 and edge condi- 
tions were determined by at least one reader for all 3791 
individuals sampled. Reader 2 considered all the otolith 
sections to be of sufficient quality to produce annulus 
counts; reader 1 provided annulus counts from all but two 
sections. After the initial counts, consensus between read- 
ers was achieved for 2804 individuals A second reading 
of the 987 sections for which annulus counts differed pro- 
duced consensus for 3762 individuals. The degree of agree- 
ment in red snapper opaque annulus counts between the 
two readers in each of the two readings was assessed. Av- 
erage percent error (APE), coefficient of variation (CV), in- 
dex of precision (D), and percentages of absolute differenc- 
es in counts are given in Table 1. 
