Pajuelo et al.: Age and growth of Pomadasys incisus 



853 



Z., = 



.y +(.v;' 



and the seasonalized von Bertalanffy growth model 

 (Pitcher and Macdonald, 1973) 



L, = L 



\-e 



-Al/-/„ )-{ — sin(2;r(/-/, )) 



where Lc = the length-at-capture; and 



V = a constant derived from the relationship of 

 total length to otolith radius (Francis, 1990). 



The von Bertalanffy growth curve was fitted to the backcal- 

 culated length-at-age by means of Marquardt's algorithm 

 for nonlinear least squares parameter estimation (Gay- 

 anilo et al., 1996). 



where A, = the smallest age in the sample; 

 A., = the largest age in the sample; 

 Tg = the age at zero length; 

 L, = the length-at-age; 

 L„ = the predicted asymptotic length; 

 yj = the estimated mean length of Aj-year-old 



fish; 

 ^2 = the estimated mean length of A2-year-old 



fish; 

 C = the amplitude of the fluctuation in seasonal 



growth; 

 t^ = the point of the minumum growth {t^=WP+ 



0.5); and 

 k = the Brody growth constant (Schnute, 1981; 

 Sparre and Venema, 1995). 



The models were fitted to data with the Marquardt's algo- 

 rithm for nonlinear least squares parameter estimation 

 (Gayanilo et al., 1996). A nonparametric, one-sample 

 test was applied to test for residual randomness and a 

 Bartlett's test was used to test for their homoscedasticity. 

 Von Bertalanffy growth model parameters were also esti- 

 mated for observed W, as a function of age by substituting 

 weights in place of lengths in the growth equation and 

 incorporating b derived by the weight-length regression 

 (Sparre and Venema, 1995): 



W, = WJ]-e 



-l(i-r„l,* 



where W, = the weight at age; and 



W^= the predicted asymptotic weight. 



Backcalculated size of each fish at the time of forma- 

 tion of each annulus was determined by a backcalculation 

 formula consistent with the body proportional hypothesis 

 (Campana, 1990; Francis, 1990). The measurements were 

 the following: the radius of the ('*' band (Ri, 0.01 mm, dis- 

 tance from the center of the otolith to the outer margin of 

 the annulus) and the radius of the otolith at capture (Re, 

 0.01 mm, distance from the center of the otolith to the pe- 

 riphery). These measurements were always made along the 

 longest axis of the otolith ( Fig. 1 ). The relationship between 

 the radius of the otolith at capture iRc) and the total length 

 was estimated as a power function (nonlinear relationship). 

 It is estimated by fitting the data by a regression of log(L,) 

 on log(i?c) consistent with the body proportional hypothesis 

 (BPH). The length of an individual when the i"' band was 

 laid down {Li, mm) was calculated as 



Li = (Ri/Rc)'Lc, 



Results 



Of the 878 fish examined, 377 (42.9%) were males and 412 

 (46.9%) females. The remaining 89 (10.1%) individuals 

 were immature and could not be identified macroscopically. 

 Fish varied in size from 103 to 304 mm L,, and weighed 

 between 8.7 and 137.1 g W,. Males varied from 143 to 298 

 mm L,, and total mass was from 9.3 to 114.7 g W^. Female 

 total length varied between 134 and 304 mm and total 

 mass was from 13.2 to 137.1 g. Immature fish varied from 

 103 to 186 mm L, and from 8.7 to 29.6 g W,. No significant 

 differences were found between males and females in 

 mean size (Student's i-test, <=1.03<<qq5 yg7=1.65) or weight 

 (Student's <-test, t=1.57<tgQ^ jg.j=1.65). 



Sagittae of bastard grunt are ovate and laterally com- 

 pressed. Annuli were clearly differentiated under reflected 

 light on a black background: the opaque zones are milky in 

 appearance and the hyaline zones relatively transparent 

 (Fig. I). The number of annuli counted for each individual 

 were similar for the two readers. Of the 878 otoliths ex- 

 amined, 22 (2.5%) were rejected as unreadable, three were 

 completely translucent, eight were broken, and 11 had 

 poorly defined growth zones. Of the remaining 856 otoliths, 

 consensus was reached for 812 (94.8%). The index of aver- 

 age percent error ( I APE ) of band counts for each reader did 

 not differ greatly, and was slighly lower for the first author 

 (2.47) than for the second (2.69). The precision of the age es- 

 timates was also expressed as the CV as recommended by 

 Campana (2001). The level of precision was approximately 

 5% for both readers. 



Marginal increments were measured for 812 individuals. 

 In the otoliths with one and two annuli (fast-growing young 

 individuals), the lowest monthly mean marginal incre- 

 ments were recorded in January and increased throughout 

 the year (Fig. 2). The marginal increments in the otoliths 

 with three and more than three annuli (moderate and slow- 

 growing individuals) also followed a similar trend. Thus, 

 irrespective of the age of the fish, the marginal increments 

 declined markedly and then rose progressively only once 

 during a 12-month period. Therefore, only one annulus is 

 formed in December-February. 



Alternating opaque and hyaline zones were clearly visible 

 on the otoliths. Up to seven marks, assumed to be annuli, 

 were visible in the otoliths sampled. Two- and three-year-old 

 fish were the dominant age classes and over 80% offish were 

 three years old or less (Table 1). Over 45% of the growth was 

 achieved by the end of the first year. By the end of the second 

 year, fish had attained 60% of the mean observed length. 



The three growth models provided a good fit to the data 

 (Table 2, Fig.3). Length-at-age was adequately described 



