254 



Fishery Bulletin 102(2) 



specimen by using the following equation (Hayashi, 1976. 

 Prince et al., 1988; Sun et al., 2002): 



MIR = {R-r n )l{r n -r n _ 1 ), 



where R = spine radius; and 



r n and r nl = radius of rings n and re— 1. 



The mean MIR and its standard error were computed 

 for each month by sex for all ages combined, and also for 

 the ages 1-5 and 6-11 for males and 1-5 and 6-12 for 

 females. 



Growth estimation 



Growth for males and females was estimated by back-cal- 

 culation of lengths at presumed ages. Two methods were 

 used. Method 1 was based on the assumption that the rela- 

 tionship between spine radius (R) and LJFL (L) is linear, 

 i.e., L=a 1 +6 1 i? (Berkeley and Houde, 1983; Sun etal, 2002), 

 whereas method 2 was based on the assumption that this 

 relationship is a power function, i.e., L=a R h - (Ehrhardt, 

 1992; Sun et al., 2002). The parameters of the relationships 

 were estimated by maximum likelihood, assuming log-nor- 

 mally distributed errors. Akaike's information criterion 

 (AIC, Akaike, 1969) was used to select which of the linear 

 and power functions best represented the data: 



AIC = -21nL + 2p, 



where InL = logarithm of likelihood function evaluated 

 at the maximum likelihood estimates for the 

 model parameters, and 

 p = number of model parameters. 



The equations used to back-calculate the lengths at 

 presumed ages were 



where L, = the mean LJFL at age t; 

 L x = the asymptotic length; 



o 



the hypothetical age at length zero; 



M/? <L_a,) 



h, 



5-] L 



R) 



linear relationship 

 power relationship 



where L n = LJFL when ring n was formed; 

 L = LJFL at time of capture; and 

 r n = radius of ring n. 



The standard von Bertalanffy growth function (stan- 

 dard VB) (von Bertalanffy. 1938) and the Richards func- 

 tion (Richards, 1959) were then fitted to the mean back- 

 calculated male and female lengths-at-age from methods 

 1 and 2, assuming additive error. 



Standard VB: 



L,=L (l-c'"" ■»), 

 Richards function: 



L ( =L.(l-e- K " '"•)''"' , 



k and A' = the growth coefficients; and 



m = the fourth growth-equation parameter. 



An analysis of residual sum of squares lARSS) was used to 

 test whether the growth curves for the two sexes were dif- 

 ferent (Chen et al., 1992; Tserpes and Tsimenides. 1995; 

 Sun et al., 2001 ), and the log-likelihood ratio test was used 

 to determine whether the Richards function provided a 

 statistically superior fit to the data than the length-at-age 

 standard VB growth function. 



Results 



Of the 1166 dorsal spines sampled, 1135 (97%) (699 males 

 and 436 females) were read successfully. The average per- 

 cent error (APE) was 6.31% (5.91% for males and 6.93% for 

 females) and the coefficient of variation (CV) was 8.93% 

 (8.36% for males and 9.81% for females). Of the 31 spines 

 that could not be read, 22 were considered unreadable 

 because the existence of multiple rings made the identifi- 

 cation of annuli difficult or resulted in aging discrepancies 

 between readings, and the remaining nine spines were 

 unreadable because of abnormal growth. 



The length-frequency and weight -frequency distribu- 

 tions for the 1166 individuals are shown in Figure 3. 

 These individuals ranged from 78 to 221 cm LJFL 

 (mean=177.62, SD = 16.13, «=720l or 1 to 49 kg RW 

 (mean=22.13, SD = 5.68) for the males and from 80 to 232 

 cm LJFL (mean=179.96, SD=17.90, n = 446) or 2 to 58 kg 

 RW (mean=23.65, SD=7.34) for the females. The females 

 were significantly larger than the males (r-test, P<0.05). 

 Table 1 summarizes the relationships between EFL and 

 LJFL and TL, and that between LJFL and weight. The 

 latter relationship differed significantly between males 

 and females (analysis of covariance; P<0.05). 



At least the first or second ring in 417 (60%) of male 

 spines and 300 1 69%) of female spines was visible. The 

 ring radii statistics by sex is summarized in Figure 4. All 

 other specimens were assigned inner rings and final age 

 estimates based upon these data. The mean ring radii by- 

 age group, for males and females, after correction for miss- 

 ing early rings, are listed in Table 2. The maximum age 

 of the sampled sailfish, after correction for missing early 

 rings, was 11 years for males and 12 years for females. 

 The maximum ages before correction were 8 years for 

 both sexes. 



The monthly means of the marginal increment ratio 

 (MIR) for males of all ages during May-August were high 

 (-0.72) but declined markedly thereafter and reached a 

 minimum of 0.46 in November (Fig. 5). Similarly, the MIR 

 for females dropped from 0.71 in September to a minimum 

 of 0.47 in November (Fig. 6). The monthly means of MIR 

 did not differ significantly from each other over the period 

 December-March (ANOVA, P^O.86, P 9 =0.96). However, 

 the monthly means of MIR from April through August for 

 males and from April through September for females were 



