Liu et ai.: Age and growth of Alopias superciliosus 
483 
the dorsal fin and were used for age analysis in this 
study because these are the only vertebrae readily 
available at market. 
X-ray radiography (Cailliet et al., 1983; Cailliet, 
1990; Joung, 1993) and staining of vertebrae 
(Stevens, 1975; Casey et al., 1985; Tanaka, 1991; 
Joung, 1993) are two methods commonly used to 
enhance the clarity of bands on vertebrae. The sil- 
ver nitrate technique of Stevens (1975) was tried but 
no increase in clarity of bands was observed; hence, 
we did not use the technique. The x-ray method, 
which is simpler and yields better clarity of bands 
with a Java video image analysis system, was used. 
A Rigaku industrial x-ray apparatus (model: 
radioflex 90 GSB) with Fuji industrial x-ray film (fine 
grain and high contrast) was used to take x-radio- 
graphs of vertebral centra. Banding patterns in ev- 
ery x-radiograph were counted three times by one of 
the authors during a three-month period; only those 
centra whose band counts were the same for at least 
two of the three readings were accepted for further 
analysis. Growth bands included fast-growth and 
slow-growth zones. The radii of each band and ver- 
tebrae were measured on a line from the nucleus 
(notochord) to the outer edge of each band and to the 
outer margin of each vertebrae with x-radiography 
and the Java video image analysis system (Fig. 2). 
The time of band formation was estimated from 
monthly change of marginal increment (MI) with the 
following equation: 
M/ = (R-r n )/(r n -r n _ 1 ), 
where R - the vertebral radius; and 
r n and r , = radii of the ultimate and penultimate 
bands, respectively. 
121°E 122°E 123°E 124°E 
Figure 1 
Sampling area for Alopias superciliosus in northeast- 
ern Taiwan waters. 
The asymptotic weight was obtained by substitut- 
ing into the weight-length relationship; the VBGE 
on weight can be expressed as 
W t =W 00 [l-e~ K{t ~ to) ) b , 
where W f = the weight at age t; 
W co = the asymptotic weight; and 
b - the exponent of the weight-length 
relationship. 
In addition, Tanaka and Mizue’s (1979) method was 
used to identify the ultimate band on the basis of 
the following stages: opaque zone, narrow translu- 
cent zone (the width of translucent zone is smaller 
than half width of opaque zone), and wide translu- 
cent zone (the width of translucent zone is larger than 
half width of opaque zone). 
The growth of bigeye thresher sharks was described 
with the von Bertalanffy growth equation (VBGE) as 
L t =L M (l-e“* u -‘ o) ), 
where L ( = 
L m = 
K = 
the length at age t\ 
the asymptotic length; 
the growth coefficient; and 
the theoretical age at zero length. 
The parameters of VBGE were estimated from a 
Walford plot (Walford, 1946). 
Length-frequency distributions of 821 individuals 
(330 males, 491 females), grouped by season and sex, 
were analyzed with the computer package MULTIFAN 
(Fournier et al., 1990) to estimate the parameters of 
von Bertalanffy growth equations. Initial values of 
the L ^ and K were adapted from those obtained in 
the previous section. 
The relation between precaudal length and verte- 
bral radius was tested with an F-test, and the differ- 
ence in regression lines between sexes was tested 
with analysis of covariance. 
Results 
The relation between precaudal length and vertebral 
radius showed a slightly curved trend for both sexes 
(Fig. 3) and was statistically significant (P<0.05). 
