GRUBER and COMPAGNO: TAXONOMIC STATUS AND BIOLOG^' OF BIGEYE THRESHER 



conform to the von Bertalanffy (1938) model ( Wass 

 1973; Stevens 1975). Holden (1974, 1977) has 

 shown that it is possible, as a first approximation, 

 to obtain parameters for a von Bertalanffy growth 

 curve independently of field data. Using a modifi- 

 cation of von Bertalanffy 's (1938) basic equation, 

 Holden (1974) rearranged the formula as follows: 



It + T - It = (L 



ma.\ 



/^)(1 



.~KT^ 



(2) 



where // = length at fertilization 

 It + T = length at birth 



T = gestation period 

 Lmax = maximum observed size 

 K = growth constant. 



We have evaluated these parameters from data 

 given in the literature, and solution of this equa- 

 tion, including generation of the growth 

 curve, was accomplished with computer programs 

 written by Allen (1966). 



If Still well and Casey (1976) are correct in their 

 assertion in that males mature at 300 cm TL 

 compared with 350 cm TL for females, then time 

 to maturity can be estimated from Figure 12. 

 Assuming parturition in the bigeye thresher at 

 100 cm (lower curve. Figure 12), then males 

 mature in a little over 3.5 yr while females become 

 sexually active (i.e., reach 350 cm TL) between 

 their fifth and sixth year. Bigeye threshers mea- 

 suring 4 m TL would be about 10 yr old and the 

 biggest members of this species (480 cm) would be 

 at least 20 yr old. 



AGE inONTHS) 



FIGURE 12. — Von Bertalanffy-type growth curve for Alopias 

 superciliosus. The curve is based on parameters of: maximum 

 total length of 420 cm; length at birth 100, 130 cm TL and 

 gestation period of 12 months. The lower and upper curves 

 represent a growth rate in sharks bom at 100 and 130 cm TL. 

 respectively. If this model is correct, males mature in approxi- 

 mately 3'/2 yr compared to 4y2 yr for females. The largest of these 

 sharks would be between 10 and 20 yr of age. 



It should be reemphasized that this curve is but 

 a first approximation since the assumptions of 

 the von Bertalanffy model may not actually be 

 satisfied by growth of the bigeye thresher. Thus 

 this curve cannot substitute for field data and 

 must be validated by independent methods. 



No previous attempts have been made to deter- 

 mine the age of a bigeye thresher. We stained a 

 few vertebral centra of the bigeye thresher 

 LJVC-0355— 287 cm TL female— from the mono- 

 spondylous precaudal region (centra 30-31, 33, 

 as counted from the head) using the alizarin 

 technique of LaMarca ( 1966) and the silver nitrate 

 technique of Stevens (1975), to demonstrate 

 growth rings on the inner surfaces of the calcified 

 double cones. This technique revealed a central 

 clear area surrounded by at least eight dark rings 

 concentric with and interspaced by lighter rings 

 (Figure 13). The clear area is about 14.1 mm 

 across, and the double cone 25.2 mm in horizontal 

 diameter in centrum 33. It is not known if the 

 dark rings are annual (added once a year), but 

 presumably the central clear area represents the 

 maximum size of the fetal vertebral centrum. 



A comparison of Figure 12 with the data given in 

 Figure 13 shows that if the rings are annual, 

 the von Bertalanffy model considerably under- 

 estimates rate of growth in the bigeye thresher. 

 However, we are not aware of any published 

 work showing that growth rings in the centrum of 

 warm- water sharks are annual. Several temper- 

 ate water elasmobranchs lay down annual growth 

 rings but the (temperate water) basking shark, 

 Cetorhinus maximus, forms a pair of rings each 

 year (Tanaka and Mizue 1979). So in the absence 

 of some confirming data giving the interval be- 

 tween ring formation, we cannot estimate the age 

 of the bigeye thresher by counting circuli in the 

 vertebral centrum. 



Beside the length-weight relations developed by 

 Guitart Manday (1975) and Stillwell and Casey 

 (1976), the only other growth data are deductions 

 made by Stillwell and Casey concerning allom- 

 etry. Based on measurements from 12 adult bigeye 

 threshers (8 males, 4 females) they concluded that 

 head, eye, and mouth dimensions become propor- 

 tionally shorter as growth proceeds. In contrast, 

 the height of the first dorsal, interspaces between 

 fins, and clasper length all increase. Some differ- 

 ences between males and females in proportional 

 growth were noted in their study. 



Data from several sources (Nakamura 1935; 

 Springer 1943; Bigelow and Schroeder 1948; 



631 



