Sun et a\ . Age and growth of Xiphias gladius 



825 



Figure 4 



The section of three typical second anal fin rays of sword- 

 fish. Ray radius (S) measured from focus to edge; annuli for 

 estimated age 1+ (Al. age 5+ (B) and age 11+ (C). 



to successive rings were used to back-calculate lengths at 

 presumed previous ages (Ehrhardt, et al., 1996). For the 

 relationship between ray radius and LJFL and the back- 

 calculation of lengths-at-age, the following two methods 

 were used. 



Method I 



The relationship between ray radius (S) and LJFL (L) 

 was determined by using the standard linear regression 

 procedure, L = a + bS (Berkeley and Houde, 1983). This 

 relationship and the distance from focus to successive 

 growth bands, which we assumed to be based on annual 

 growth events, were used to back-calculate the lengths at 

 presumed ages by the following formula (Fraser, 1916): 



-a = ^(L-a), 

 o 



where L = LJFL at time of capture; 



L^ = LJF'L when band /; was formed; 



a = the intercept on the length axis from the 



regression line of length (L) on ray radius (S), 



e.g. L = Q + hS; and 

 S„ = the distance from ray focus to band n. 



Method II 



The relationship between ray radius and LJFL was 

 determined by using a power function procedure, L = aS* 

 (Ehrhardt, 1992; Ehrhardt et. al,, 1996). Parameters of 

 this function were estimated by nonlinear least square fits 

 to the observed data. This relationship and the distance 

 from focus to successive growth bands were used to back- 

 calculate the lengths at presumed ages by the following 

 formula (Tserpes and Tsimenides, 1995; Ehrhardt et al., 

 1996): 



where b 



L.-\^\L, 



the exponent of the regression of length (L) on 

 ray radius (S) which is assumed to be a power 

 function of the form L = a S ^. 



The data of the back-calculated length-at-age from method 

 I and method II were then applied to the following stan- 

 dard von Bertalanffy growth equation (standard VB) and 

 to the generalized growth function (generalized VB) (Rich- 

 ards, 1959): 



Standard VB: 



L, =L„(l-e-*"-'"'); 



Generalized VB: 



L, =L,„(l-e 



-A'il-mK(-f„l\i-" 



where L, = the mean LJFL at age t; 

 L„ = the asymptotic length; 

 tg = the hypothetical age at length zero; 

 k and K = the growth coefficients; and 



m = the fitted fourth growth-function parameter. 



Parameters of the above two equations for male and fe- 

 male were estimated, respectively, by fitting a curve to the 

 observed back-calculated LJFL-at-age by using a nonlinear 

 least square procedure (Gauss-Newton method. NLIN of 

 SAS Institute, 1990). The measure of goodness-of-fit chosen 

 was r~. A multivariate statistical procedure (Hotelling's T'^) 

 was used to test for differences in growth between males 

 and females (Bernard, 1981) for the two growth models and 

 two methods. The r- values were ranked between the two 

 different growth functions with the smaller as 1. A non- 

 parametric test (Friedman 1937, 1940 1 was then employed 



