FISHERY BULLETIN: VOL. 81, NO. 3 



100 



80 







n 60 



n 40 



E 



20 



O- 1 



r 

 o 



~ i — 



10 



— I — 

 20 



~ I — 

 30 



40 



50 



"~ I — 

 60 



~ I — 

 70 



— I 

 80 



Fork Length - cm 



FIGURE 8. — Maturation in Pristipomoides filamentosus female. 

 Stage III represents gravid/spawning individuals. Only samples 

 collected during the spawning season are presented. Points repre- 

 sent means bracketed by standard deviations. Sample sizes are 

 given above each length class. 



growth rate, is completely counterintuitive to our un- 

 derstanding of the trade offs involved in optimizing 

 growth and reproductive processes. Rather, it is 

 more likely that episodic growth leaves an in- 

 complete time record in the otolith (i.e., increments 

 are not deposited) while concurrently, changes in 

 otolith length are tightly coupled to changes in fork 

 length (see Figure 5 where r 2 = 0.899). The resulting 

 process would tend to underestimate At and thus to 



overestimate ^- This hypothesis of interrupted 



otolith growth could explain the anomalous trend in 

 otolith growth rates; consequently, we have regarded 

 all data from otolith lengths > 6,000 /xm to be equivo- 

 cal. We excluded these points from the remaining 

 analyses, reducing the data set by 13% (2,957 or- 

 dered pairs to 2,577). 



It is evident from Figure 7 that for otoliths <6,000 

 ju.m the logarithmic transformation was effective in 

 linearizing the trend line and in stabilizing the vari- 

 ance, allowing the formulation of an analytical model 



describing the functional relationship between —r 



and 2. We write 



log. 



(■&) 



dt 



a 



pe+e 



(2) 



where 2 is otolith length in /Am, t is time in days, a and 

 /? are model parameters, and e is a normal random 

 variable with mean zero and finite variance. When 

 this model is cast in the form of Equation (1) and in- 

 tegrated, the solution is 



530 



f= (e"/?)" 1 (e/fc -1) 



(3) 



where T is the estimate of age in days, and L is the to- 

 tal length of the otolith along the postrostral radial 

 axis. Thus, to estimate the age of a sample specimen, 

 one need only acquire estimates of a, /?, and L. 



Von Bertalanffy Growth Curve 



A regression of log-transformed otolith growth rate 

 against otolith length (Equation (2)) was performed 

 for each of the 81 otolith samples. The age of each 

 specimen was then estimated by Equation (3). 



The fork length of the sample specimens is plotted 

 against the point estimate of age in Figure 9. Because 

 13 of the 81 determinations were duplicates based on 

 left and right otoliths from the same fish, and 4 of the 

 remaining preparations had excessive coefficients of 

 variation (>20%), only 64 points are presented. 

 These data were fitted to the von Bertalanffy growth 

 model (Ricker 1979) using a nonlinear regression 

 routine (NLIN Procedure) (Statistical Analysis Sys- 

 tem 1979). In this three-parameter formulation, L„ 

 signifies the asymptotic upper bound on growth in 

 length, K is an instantaneous growth-rate constant, 

 and t is a scaling factor equal to the X-intercept. 

 When the model was freely fitted to the data, an un- 

 realistically low estimate of L x resulted (Table 2, 

 solid line in Figure 9). As part of a related study in 



j 40 - 



2,000 



"i — i — i — i — r 



4 6 



— i 1 — i — i — i — i 1 — i — i — r 



10 12 14 16 18 years 



*9« 



FIGURE 9. — Estimated growth curve for Pristipomoides filamen- 

 tosus. Solid line represents a freely fitted von Bertalanffy curve 

 whereas the L„ parameter was constrained to 78.0 cm in the fit 

 of the dotted line. 



