596 



Fishery Bulletin 93(3), 1995 



where S = spine radius; and 



r = radius of the most recent annulus. 



n 



The mean MIR and the standard deviation were 

 computed for each month and age separately. Mar- 

 ginal increment analysis was not performed for age 

 1 because the first annulus was usually missing, nor 

 for ages greater than 5 because of a lack of sufficient 

 number of samples. 



Estimates of theoretical growth in length were 

 obtained by fitting mean monthly length-at-age data 

 to two forms of the von Bertalanffy growth equation: 

 1 ) the standard form and 2 ) the generalized form as 

 proposed by Chapman (1961). 



L t =L^l-e- k ^) 

 L { ^ S) -(L^ S) -l { l - s, )e- kn - Su 



V<l-<5) 



(1) 



(2) 



where L t = LJFL at age t, L = asymptotic length, k = 

 growth coefficient, t Q - theoretical age at zero length, 

 l Q = length at zero age, and 8 = fitted fourth function 

 parameter. 



Mean data were used in order to assign equal 

 weight to all observations. Only mean values from 

 samples of greater than five fish were used. Growth 

 parameters of both models were estimated iteratively 

 by using the Simplex minimization algorithm 

 (Wilkinson, 1988). The measure of goodness of fit was 

 the coefficient of determination (r 2 ). Date of birth was 

 set at 1 June because swordfish spawn in the Medi- 

 terranean sea in early summer (Palco et al., 1981). 



Growth parameters were estimated for males, fe- 

 males, and sexes combined, and sex differences were 

 tested by analysis of the residual sum of squares 

 (ARSS) as suggested by Chen et al. (1992). This 

 method is a modification of the ARSS originally de- 

 veloped for the comparison of linear models (Zar, 

 1984). 



Back calculations of length at age were estimated 

 in two ways. 



1 From a modified version of the direct propor- 

 tion formula (Fraser, 1916; Lee, 1920): 



L n -e = (S n /S)(L-c), 



where L n = LJFL when the annulus n was formed; 

 L = LJFL at time of capture; 

 c = intercept on length axis from linear re- 

 gression of length on spine radius; 

 S n = distance from spine focus to annulus n; and 



S = spine radius. 



2 From the formula of Monastyrsky ( Bagenal and 

 Tesch, 1978): 



L n = (SJSn 



where L n = LJFL when the annulus n was formed; 



L = LJFL at time of capture; 



b - the exponent of the regression of length 

 (L) on spine radius (S) which is assumed 

 to be a power function of the form L-aS b ; 



S n = distance from spine focus to annulus n; 

 and 



S = spine radius. 



The constant b was calculated from the logarithmic 

 form of the power function. 



In both cases the relation between spine radius 

 and LJFL was determined for males and females and 

 for sexes combined. Moreover, the regression lines 

 for males and females were tested for equality of 

 slopes and if significant differences were found, in- 

 tercepts were tested by means of analysis of covari- 

 ance (Dixon and Massey, 1985). No back calculations 

 were attempted for age one because the first annu- 

 lus was missing in the vast majority of the speci- 

 mens. All statistical inferences were based on the 0.05 

 significance level. 



Results 



Of the 1,325 swordfish sampled, 1,100 were aged 

 successfully (521 males and 579 females). The lengths 

 of individuals ranged from 62 to 210 cm (Fig. 2). In 

 64 of the 225 unreadable spines, no annuli could be 

 identified because the opaque-translucent zonation 

 was unclear. The remaining 161 spines were consid- 

 ered unreadable owing to the existence of multiple 

 bands which made the identification of annuli diffi- 

 cult or which resulted in ageing discrepancies be- 

 tween the readers, or both. 



Up to 9 rings, assumed to be annuli, were visible 

 in the anal-fin spines sampled. Sample sizes for all 

 age classes were greater than 20, except for class 9 

 (15). Two-year-old fish were the dominant age class 

 and over 80% of the fish were less than 5 years old. 

 Differences in mean size between the successive age 

 classes were calculated to reveal any peculiarities in 

 growth patterns. In theory, absolute growth was ex- 

 pected to be rapid at first and to decrease progres- 

 sively in later life. The pattern observed for sword- 

 fish generally agreed with these expectations (Table 

 1). Monthly means of MIR indicated that an annu- 



