Carlson et al.: Life history and population dynamics of Carcharhinus isodon 



285 



simulations were run with Microsoft Excel spreadsheet soft- 

 ware (Math Tools, Ltd., 1999) equipped with risk analysis 

 and matrix algebra software and Microsoft Visual Basic for 

 Applications (Crystal Ball, 2000). 



Results 



Age, growth, and maturity 



The precision of band counts was high among the readers 

 (authors). The first set of readings resulted in two or three 

 out of three band count estimates agreeing in 97.7% of the 

 cases, and an APE of B.S'X. Percent disagreement in band 

 counts among the three readers was 42.9'7f within ±1 band, 

 5.6% within ±2 bands, and 0.4% within ±3 bands. After con- 

 sultation, we reached agreement in 239 out of 247 (97%) 

 vertebrae. Samples where counts had differed among the 

 readers were discarded. 



Although monthly changes in marginal increment 

 analysis were found, peaks were not statistically differ- 

 ent (single factor ANOVA; df=6, P=0.371). An increase in 

 increment growth occurred from April until June, followed 

 by a slow decrease and leveling until October (Fig. 2). The 

 decrease in incremental growth from June through October 

 was not large enough to indicate a double band formation 

 (Natanson et al., 1995); thus bands were assumed to form 

 once a year. A similar trend of increment growth was also 

 reported for the blacknose shark i Carcharhinus acronotus) 

 by Carlson etal. (1999). 



The values oi K (0.24/yr versus 0.35/yr for females, and 

 0.41/yr versus 0.49/yrfor males) and L (1560 mm versus 

 1442/mm for females, and 1338/mm versus 1309/mm for 

 males) obtained with the original von Bertalanffy (1938) 

 growth equation (Eq. 1) and the modified equation of 

 Fabens ( 1965) (Eq. 2) were somewhat different, but the fits 

 to the observed data were similar (Table 1; Fig. 3). Because 

 of the similarity between the models and the general and 



ubiquitous use of equation 1 (von Bertalanffy, 1938), we 

 present and compare further age and growth results using 

 only the von Bertalanffy (1938) model. 



Observed and back-calculated von Bertalanffy param- 

 eters and growth rates differed between males and females 

 (Table 1 and Table 2). For both sexes, growth was rapid un- 

 til age 4—5, slowing down for males thereafter, whereas the 

 reduction in growth rate for females was not so accentuated 

 (Fig. 3). Females had a lower growth coefficient (K=Q.2AI 

 yr) than males (/f=0.41/yr), and a higher theoretical maxi- 

 mum size (L.=1560 mm for females versus 1338 mm for 

 males). Significant differences (log-likelihood ratio= 14.46; 

 P<0.001) between von Bertalanffy growth curves of males 

 and females were found. Theoretical longevity estimates 

 were 14.4 and 8.5 yr for scenario 1, and 9.9 and 7.2 yr for 

 scenario 2, and the oldest aged sharks were 8.0 and 8.1 yr 

 for females and males, respectively. 



We found no significant differences (Kruskal-Wallis 

 X'^=().\Q\, P=0.751) in age distribution between sexes (Fig. 

 4). The most frequently occurring age classes were ages 4-t-, 

 3-I-, and 2-i- for males, and ages 2-i- and 3+ for females, each 

 comprising between 19-22% and 18-24% of the samples 

 for each sex, respectively. Young-of-the-year sharks (age 

 0-I-) made up 7.3% of all males and 11.1% of all females, 

 whereas adults (ages 5-8) constituted 17.1% and 22.2%, 

 respectively. 



Back-calculated size at birth was estimated at 538 mm 

 TL for both male and female sharks and matched well the 

 known size at birth in the northeastern Gulf of Mexico 

 (480-530 mm TL; Carlson, unpubl. data) (Table 2). Back- 

 calculated mean lengths were smaller than observed 

 lengths and when these were compared among older-aged 

 sharks. Lees phenomenon (Ricker, 1992) was apparent. 



Median total length at maturity differed between males 

 and females (Fig. 5). For males, the size at which 50% of 

 the population reached maturity was 1187 mm TL, which 

 corresponds to an age at maturity of -3.9 yr. The small- 

 est mature male found was 1000 mm TL and the largest 



