492 



Fishery Bulletin 103(3) 



Data analysis 



For each shark species and sex, we were interested in 

 determining the length at which 50% of the individuals 

 in a population reached full sexual maturity. That length 

 is the median length at maturity, hereafter referred to 

 as "median maturity." 



Many shark species show abrupt transitions in the 

 sizes of reproductive organs near length at maturity. 

 To locate such transitions in clasper length, we fitted 

 "split" linear regressions to CLI data plotted against 

 FL. Split regressions consist of two simple linear re- 

 gressions fitted to different nonoverlapping data ranges 

 that meet at a point called the breakpoint (Kovac et al., 

 1999). A split regression has the form 



CLI = f(FL 

 CLI = g(FL 



-p) + h for FL < p 



p) + h for FL a p, 



where f and g are slope parameters for the two limbs 

 of the regression, and h andp are they-axis and .r-axis 

 coordinates of the breakpoint, respectively. The param- 

 eters f, g, h, and p were estimated by least squares by 

 using the curve fitting routine in the Sigmaplot sta- 

 tistical and graphing package (Sigmaplot, vers. 9.01, 

 Systat Software Inc., Richmond, CA). The length at the 

 breakpoint was corrected for downward rounding of FL 

 by adding 0.5 cm. 



Maturity ogives were fitted to the direct maturity 

 data separately by sex by using probit analysis (Pear- 

 son and Hartley, 1962). The analyses were performed 

 on individual FL measurements, but we also calcu- 

 lated the proportions of mature individuals in 10-cm 

 length classes to illustrate the trends. Probit analysis 

 assumes that the length at which a randomly selected 

 fish reaches maturity is normally distributed. Two pa- 



rameters, the mean and standard deviation of the nor- 

 mal distribution, were fitted. Each maturity ogive is 

 the cumulative distribution function for the associated 

 normal distribution. The probit function was fitted by 

 maximum likelihood, and 95% confidence limits were 

 estimated by the bootstrap method. The mean of the 

 normal distribution is an estimate of the median ma- 

 turity, and it was corrected for downward rounding of 

 FL by adding 0.5 cm. 



All shark length measurements provided in the pres- 

 ent study are FL, unless otherwise stated. For com- 

 parison with our results, we converted measurements 

 from the literature to FL where necessary using the 

 regression equations in Table 1. Literature reports of 

 total length were assumed to be TL nat unless otherwise 

 stated. Scientists working on sharks in the northeast- 

 ern United States, and eastern Canada have typically 

 measured lengths over the curve of the body rather 

 than as straight line distances (Natanson 1 ; Campana 2 ; 

 Pratt 3 ), notwithstanding some published statements to 

 the contrary (Pratt, 1979; Kohler et al., 1995). 



Results 



Porbeagle shark 



In male porbeagles, CLI showed two strong inflection 

 points: the first at about 110 cm, and the second, esti- 



2 Campana, S. E. 2004. Personal commun. Bedford Insti- 

 tute of Oceanography, P.O. Box 1006, Dartmouth, Nova Scotia, 

 Canada B2Y 4A2. 



3 Pratt, H. L. 2004. Personal commun. Mote Marine 

 Laboratory, 24244 Overseas Highway, Summerland Key, 

 FL 33042. 



