FISHERY BULLETIN; VOL. 87. NO. 1 



and the variance in growth rate o", within each of 

 the i = 1,15 intervals of otolith length (Table 2) show 

 that as otolith length increased both d{OL)ldt and 

 o^ declined. The estimated age (in years) at the 

 point of transition between each of the 15 otolith 

 length intervals (i.e., upon completion of growth 

 through interval k) was 



Aget = 



1 

 365 



k 



I 



i-i d(,OL)ldt, 



A(OL) 



where A(OL) is 500 fim in the application presented 

 here. 



Otolith length upon completion of growrth through 

 interval k was converted to the equivalent FL (see 

 Figure 1), and the data fitted to the von Bertalanffy 

 growth equation. Because this model poorly repre- 

 sents growth during the early life history, only data 

 representing otolith length intervals in excess of 

 3,000 i^m (i.e., ages >0.8 year) were used in the 

 regression analysis (see Discussion). Table 2 also 

 provides a statistical weight for each of the age esti- 

 mates. Weighting was desirable because 1) the sam- 

 ple size of each mean varied, 2) the o^, were 

 heterogeneous (proportional to the square of the 

 mean), and 3) compounding of error occurred be- 

 cause of the additive property of the estimator. 

 Weights were calculated as the reciprocal of the sum 

 of standard errors of the means through interval k. 

 The weighted least squares fit to the von Bertalanffy 

 equation (Fig. 4) was 



FL = 442 (1 - exp(- 0.234 (Age + 0.892))), 



with 99.99% of the total variation in FL explained 

 by the model, and with asymptotic standard errors 



for L„, K, and «„ equal to 14.85 mm, 0.0180 yr-\ 

 and 0.078 year, respectively. 



The results of the Monte Carlo simulation indicate 

 that the estimation procedure was unbiased. Follow- 

 ing 50 computer replications of the same sampling 

 procedures outlined above, there was no detectable 

 bias in the estimation of either K or L^, even 

 though the coefficients of variation for the standard 

 errors of these statistics were both small (0.64 and 

 0.84%, respectively). Moreover, variance estimates 

 derived from the approximately normal simulation 

 sampling distributions of K and L„ provided a basis 

 for placing confidence intervals on the point esti- 

 mates as follows: P(0.213<A:< 0.255) = 0.95 and 

 P(421 < L„ < 463) = 0.95. 



Annual Marks on the Otoliths 



On occasion, hyaline and opaque zones were evi- 

 dent in the sagittae of gindai (Fig. 5). These were 

 most easily viewed with light reflected off otoliths 

 immersed lateral side up in water. Typically, how- 

 ever, the zonations were poorly developed or absent 

 entirely. Nonetheless, of the 440 otoliths examined, 

 some banding was evident in 171 (39%), and it was 

 possible to classify the margins of these as either 

 hyaline or opaque. The seasonal expression of hya- 

 line or opaque zones on the margins of these oto- 

 liths shows what appears to be an annual periodicity; 

 otoliths sampled during the November-December 

 bimonthly period were characterized almost exclu- 

 sively by the presence of hyaline margins (94%). Just 

 2 months later (January-February), only 13% of the 

 otolith samples were similarly classified (Fig. 6). 

 Thereafter, the percentage of otoliths with hyaline 

 margins was never elevated, at least through the 



Table 2.— Summary statistics of otolith growtli by 500 jim intervals in otolith length. 



