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Fishery Bulletin 103(2) 



expected maximum size, resulting in an inflated asymp- 

 tote and low growth coefficient. Branstetter and Stiles 

 (1987) also encountered this problem with bull sharks 

 (Carcharhinus leucas) but rather than fit an alterna- 

 tive growth model, those authors hand-fitted a curve 

 through the upper data points. Results such as these 

 may seriously bias estimates of k and any resulting 

 population models because several indirect estimates 

 of natural mortality (M) and longevity rely heavily on 

 accurate estimates of k from a growth model (Fabens, 

 1965; Pauly, 1980; Chen and Watanabe, 1989; Jensen, 

 1996). For example, the method of Jensen (1996) for 

 estimating M yields values ranging from 0.05/yr (with 

 results from the von Bertalanffy model) to 0.23/yr (with 

 results from the Gompertz model). Similarly, theoretical 

 longevity estimates determined by the method of Fabens 

 (1965) are 115.5 years and 21.6 years from the von Ber- 

 talanffy model and the Gompertz model, respectively. 



In general, our estimates of age and growth for fe- 

 male spinner sharks from the von Bertalanffy model 

 were similar to those reported by Allen and Wintner 

 (2002) for spinner sharks collected off South Africa. 

 Growth coefficients in their study were about 0.13/yr, 

 L x was 250 cm FL, and observed longevity for females 

 was up to 19+ years. Branstetter (1987), in his study 

 on sharks collected in the Gulf of Mexico, reported an 

 observed longevity up to 11+ years (combined sexes) and 

 growth coefficients of about 0.21/yr. Because differences 

 in life history traits (e.g., growth rates, size and age 

 at maturity) between populations of blacktip and bull 

 sharks from South Africa and United States waters 

 have been proposed (Wintner and Cliff, 1995; Wintner 

 et al., 2002, respectively), results from our study for 

 spinner shark may be expected to be more similar to 

 those of Branstetter (1987) rather than those of Allen 

 and Wintner (2002). Although techniques (e.g., counting 

 winter bands on sagittal vertebral sections) in Brans- 

 tetter (1987) were similar to ours, the differences are 

 likely a result of low sample size in the earlier study. 



The index of average percent error (IAPE) in aging 

 was at the higher end of the range of estimates pro- 



vided in other studies that also used sagittal sections 

 for aging. Values have been reported as low as 3.0% for 

 the oceanic whitetip shark (Carcharhinus longimanus) 

 (Lessa et al., 1999), and up to 13.0% for the black- 

 tip shark (Carcharhinus limbatus) (Wintner and Cliff, 

 1995). Although IAPE indices are most commonly used 

 to evaluate precision among age determinations, IAPE 

 does not test for systematic differences and does not dis- 

 tinguish all sources of variation (Hoenig et al., 1995). 

 In addition, comparing IAPE values among studies may 

 not be valid unless the study species is the same and 

 from the same geographic area (Cailliet and Goldman 

 2004). 



Although bands were readily discernible in most sam- 

 ples, the inexperience of one of the authors (reader 2) 

 in reading and counting vertebral bands likely led to 

 the higher IAPE and systematic bias. Generally, most 

 systematic bias is a shift to increasing or decreasing 

 counts with age (Morison et al. 1998), yet the bias in 

 this study was the result of reader 2 consistently over 

 aging sharks from the final agreed age regardless of the 

 band count of the sample. Percent agreement was simi- 

 lar for samples above 115 cm FL as it was for samples 

 below this size. Although a reference collection was 

 aged by reader 2 prior to beginning this study, finely 

 honed skills through experience are key elements in the 

 technique of aging. 



The trend in marginal increment analysis indicated 

 that band formation occurs once a year during winter 

 months — a result common to most studies where rela- 

 tive marginal increment analysis is used for carcharhi- 

 nid sharks (e.g., Natanson et al., 1995; Carlson et al., 

 1999; Carlson et al., 2003). However, high variance in 

 marginal increment analysis (MIR) within each month 

 resulted in months not being statistically different, 

 which is a widespread occurrence when using this meth- 

 od. Marginal increment analysis has been criticized as 

 one of the most abused methods for validation of band 

 formation (Campana, 2001). Problems with differentiat- 

 ing bands on the vertebral edge and application to older 

 age classes may provide misleading results (Campana, 



