Andrews et al.: Radiometric age validation of Megalops atlanticus 
391 
where t = 
A 210 Pb, ( . = 
A 226 Ra 
TIMS = 
R 0 = 
X = 
T = 
the radiometric age at the time of capture; 
the 21l, Pb activity corrected to time of cap- 
ture; 
the 226 Ra activity measured with TIMS; 
the activity ratio of 210 Pb: 226 Ra initially 
incorporated; 
the decay constant for 210 Pb (ln(2)/22.26 yr); 
and 
the core age (2 yr). 
The radiometric age calculation for the juvenile age-group 
was determined by iteration of an equation derived from 
Smith et al. ( 1991), 
A 210 Pb„ 
A 226 Ra T „ 
= 1- (1 -R n ) 
1-e 
-M aet \ 
Xt 
( 2 ) 
where all equation components were as defined above. 
A radiometric age range, based on the analytical uncer- 
tainty, was calculated for each sample by applying the cal- 
culated error for 210 Pb and 226 Ra activity determinations 
to the measured 210 Pb: 226 Ra. Calculated error included the 
standard sources of error (i.e. pipetting, spike, and cali- 
bration uncertainties), alpha-counting statistics for 210 Pb 
(Wang et al., 1975), and an analysis routine used to run 
226 Ra samples on the thermal ionization mass spectrom- 
eter (Andrews et al., 1999b). 
Age estimate accuracy 
To compare annulus-derived age with radiometric age, a 
plot of the annulus-derived age estimate and measured 
210 Pb: 226 Ra activity ratio was compared graphically to 
the expected 210 Pb: 226 Ra activity ratio from ingrowth. 
This comparison included a graphical compensation for 
the 210 Pb: 226 Ra gradient in the core sample. This model 
assumed a linear mass-growth rate for the first two years 
of growth. Annulus-derived age range and the analytical 
uncertainty of the activity ratio were plotted with each 
data point. A direct comparison of annulus-derived age 
and radiometric age was made in a plot where a regression 
of the data was compared to a line of agreement or slope of 
one. A paired two-sample /-test was used to determine if a 
significant difference existed between the age estimates. 
Von Bertalanffy growth functions were fitted to the ra- 
diometric ages with FISHPARM software (Saila et al., 
1988) and plotted with the annulus-derived ages and 
growth functions from Crabtree et al. (1995) for a visual 
comparison. High and low radiometric age and the size 
range of each sample were plotted for each data point. 
No statistical comparison was made between the growth 
functions because of the low number of samples and wide 
confidence interval for each parameter. 
Results 
Six age groups and nine individual otolith cores were se- 
lected for radiometric analyses (Table 1). Of the age group 
samples, three male samples and three female samples 
were selected to span the estimated age range of each 
sex. Male age groups were 2-4 yr, 18-21 yr, and 31-36 yr. 
Female age groups were 3—4 yr, 15-24 yr, and 48-50 yr. For 
each age group the capture dates were within a 6-month 
period, except the 2-4 yr male age group where the period 
spanned 7 months. Individual otolith core samples ranged 
in annulus-derived age from 13 yr to 32 yr for males and 
35 yr to 55 yr for females. The greatest annulus-derived 
ages were for females; the oldest female was estimated to 
be 55 yr and the oldest male was 36 yr. Fork length was 
lowest for the juvenile age groups and did not overlap with 
older age groups. There was some overlap between the 
middle and old age groups. Males were typically smaller 
than females; the largest male was 1620 mm FL and the 
largest female was 2045 mm FL. The number of otoliths 
used in each age group ranged from 4 to 1 1 with the fine- 
cleaned sample weight ranging from 0.3314 to 1.0718 g. 
The individual core samples ranged in weight from 0.0884 
g to 0.1366 g. These samples are the lowest weights and 
the first individual otolith cores ever used for radiometric 
age determination. 
Activities of 210 Pb and 226 Ra were determined and com- 
bined to form an activity ratio for each sample (Table 2). 
The 210 Pb activity spanned a wide range and increased 
from juveniles to adults by as much as 88 times. The low- 
est activities were for the juvenile samples (0.003 and 
0.005 disintergrations per gram |dpm/g] ) and the highest 
activity was 0.265 dpm/g (±6.0%) for the largest male 
( 1620 mm FL). The activity of 226 Ra varied by an order 
of magnitude and ranged from 0.044 dpm/g (±1.53%) to 
0.401 dpm/g (±1.02%). Calculated 210 Pb: 226 Ra ranged, as 
predicted, between 0 and 1; the lowest activity ratios were 
for the juvenile samples and the highest were for large 
adults. All low and high ratios were within the limits of 0 
to 1 (values >1 are mathematically undefined; Eqs. 1 and 
2) except for the largest female (2045 nun FL), which had 
an upper limit that exceeded 1. Radiometric age of the ju- 
venile samples was very close to the expected age (Table 
3) . Exogenous 210 Pb was, therefore, either not present or 
present in negligible quantities. This was inferred to be 
true for the core, or juvenile region, of adult Atlantic tar- 
pon otoliths. 
Comparison of annulus-derived ages and radiometric ag- 
es indicated there were differences in the aging results for 
each technique (Table 3 ). In most cases, the precision among 
the otolith readings could not explain the differences. 
In four cases, the different age estimates overlapped, but 
the extent of overlap was at the extreme of the age range. 
The lowest radiometric ages were one year for the samples 
from juvenile fish and the highest was 78.0 yr for the larg- 
est adult female. 
A graphical comparison of the expected 210 Pb: 226 Ra dis- 
equilibria from ingrowth with the measured 210 Pb: 226 Ra in- 
dicated there was variation in the measured results above 
and below what was expected (Fig. 1). The low radiomet- 
ric age for the juvenile age-groups indicated that uptake 
of exogenous 210 Pb (R 0 ; Campana et al., 1990) by juveniles 
was insignificant. Therefore, the best model for ingrowth 
of 210 Pb from 226 Ra in tarpon otoliths was for R 0 = 0.0. 
