Booth et al.: Age validation, growth, mortality, and demographic modeling of Triakis megalopterus 
105 
Table 1 
Fixed parameter values estimated during this study or obtained from Smale and Goosen’s study (1999) that were used in the 
demographic analysis of Triakis megalopterus. TL=total length. 
Parameter 
Description 
Value 
Source 
Theoretical maximum size 
1711.07 mm TL 
This study 
k 
Growth coefficient 
0.11 /yr 
This study 
*0 
Theoretical age at zero length 
-2.43 yr 
This study 
M 
Natural mortality rate 
0.14 /yr 
This study 
F 
Fishing mortality rate 
O.yr- 1 
This study 
0 
‘50 
Length at 50% maturity 
1450 mm TL 
Smale and Goosen (1999) 
‘50 
Length at 50% selectivity 
1326 mm TL 
This study 
Inverse rate of maturity 
29 mm TL 
This study 
Inverse rate of selectivity 
26 mm TL 
This study 
^max 
Maximum age 
26 years 
This study 
E, 
Number of female embryos per adult female 
at length l in a calendar year given a gestational 
period of 20 months and a sex ratio of 1:1 
20 
0.5 x — x (0.2/ - 21.74) 
12 v ’ 
Smale and Goosen (1999) 
E, =0.5x — x(0.2Z-21.74) 
1 12 v 1 
(Smale and Goosen, 1999). 
Uncertainty in the model outputs was estimated with 
Monte-Carlo simulation (Cortes, 2002). For each simu- 
lation, i, random lengths were drawn around the pre- 
dicted von Bertalanffy growth model with an estimat- 
ed growth model standard deviation of 110 such that 
L' a =L a +e p , and e p ~ iV(0,110 2 ). These length estimates 
were used to draw random variable for the length-at- 
maturity as + e and £ V ~N( 0,16 2 ). The standard 
deviation corresponded to that required to obtain the 
1 st and 99 th percentiles at 1391 mm TL and 1500 mm 
TL, the lengths at first and 100% maturity reported 
by Smale and Goosen (1999). Natural mortality was 
assumed to be log-normally distributed with a coeffi- 
cient of variation of 20%, such that M ( =M ( ex p(%), and 
£ m ~N( 0,0. 2 2 ). No adjustments were made for log-normal 
bias. A total of 1000 simulations were conducted, and 
standard error and 95% confidence intervals were cal- 
culated for A, p, T , P Q , E a , E v E 2 , and E :i by using the 
percentile method (Buckland, 1984). 
Three-dimensional isopleth plots were constructed to 
assess the response of the conditional intrinsic rate of 
population increase parameter, r, to different inputted 
combinations of fishing mortality and the age at which 
50% of sharks were selected. 
Results 
All aquarium specimens were either moribund or had 
died in the aquarium and had decreased in length by 
the end of the study. These sharks were not included 
in the estimation of the growth parameters but were 
included in the validation aspect of the analysis. The 
vertebrae from 25 male (1123.2 ±404 mm TL) and 71 
female (1258.0 ±397 mm TL) sharks were processed for 
age estimation. Vertebrae were interpreted without dif- 
ficulty up to the margin of the corpus calcareum where 
magnification needed to be increased to accurately inter- 
pret the remaining band pairs (Fig. 1). No distinctive 
features were identified in reading the vertebrae of T. 
megalopterus. 
Of the 96 vertebrae examined, 86 were considered 
suitable for aging. Age estimates ranged from 0+ to 
25 years. Of the 15 OTC-injected specimens examined, 
only seven fluoresced (three captive and four wild speci- 
mens) under ultraviolet light and confirmed that one 
vertebral band pair was deposited annually (Table 2; 
Fig. 1). The maximum validated age was from a shark 
that was 25 years old. An age-length key is presented 
in Table 3. 
There was no significant difference in the accuracy 
of age assessments between readings (paired /-test; 
P>0.05). There was a 45% agreement on all age assess- 
ments, 80% agreement between age readings within 
1 year, and 94% agreement between readings within 
2 years. There was a strong positive correlation be- 
tween the first and second readings (r 2 =0.97) that was 
not statistically different from unity (/-test on slopes; 
P>0.05) (Fig. 2). There was no evidence for systematic 
age bias between readings (/ 2 -test; P>0.05). Band pair 
counts were considered to be reasonably precise with 
an estimated IAPE of 5.02%. 
Of the three models assessed, the von Bertalanffy 
was considered to be the most parsimonious (Schnute: 
