LA ROC HE KT AL.: AGE AND CROWTH OF I'AROl'HRYS VETULUS 



25 50 



ESTIMATED AGE (days) 



75 



Figure 5.— Gompertz curve and equation fitted to length at age of 331 larval and transforming, field-caught Parophrys vetulus 



with at least one otolith growth increment. 



period characterized by reduced growth in 

 length (Rosenberg and Laroche 1982). 



The plot of otolith diameter on standard length 

 of pelagic larval and transforming P. vetulus re- 

 vealed an allometric relationship (Fig. 6). A dis- 

 tinctive feature of this plot was the apparent con- 

 tinued, even accelerated growth of sagittae as P. 

 vetulus larvae reached the size of transforma- 

 tion, 18-20 mm SL, when rate of growth in body 

 length slows down. Physical evidence of acceler- 

 ated growth in otolith diameter relative to body 

 length can be seen by the increased width of the 

 outermost increments on otoliths of larvae older 

 than 30 d (e.g., outer 9-10 increments on sagitta 

 in Fig. 2c). The otolith diameter to standard 

 length relationship, once a mathematical formu- 

 lation has been computed, can be used to back- 

 calculate individual growth histories of larvae 

 and juveniles (Rosenberg 1980; Methot in press), 

 as has been done for adult fishes (Tesch 1968; 

 Ricker 1969). 



DISCUSSION 



As in numerous other temperate and some 

 tropical species of fishes, growth increments on 

 the otoliths of P. vetulus larvae appear to be 

 formed daily after yolk-sac absorption when 

 larvae become capable of exogenous feeding. 



Counts of these increments provide more pre- 

 cise and accurate estimates of larval age and 

 growth rates throughout the larval period than 

 have previously been available. This informa- 

 tion, when combined with abundance data, 

 allows computation of age-dependent mortality 

 rates resulting in more accurate estimates of 

 larval mortality in the sea. 



Empirically, both the Gompertz and von 

 Bertalanffy growth models fit the larval P. 

 vetulus data well. Both yielded similar values for 

 length at age and growth rates from which age- 

 dependent mortality estimates can be made. 

 There has been much disagreement, on theoreti- 

 cal grounds, as to the appropriateness of either 

 model for describing growth in fishes, although 

 they are mathematically quite similar (e.g., 

 Zweifel and Lasker 1976; Ricker 1979). Despite 

 numerous attempts to attribute biological signif- 

 icance to mathematical models of growth, the 

 best criterion available for choosing a particular 

 model is still goodness of fit to the data (Ricker 

 1979). In that respect, both models were appro- 

 priate to this data set. 



A practical measure of the appropriateness of 

 mathematical models is the relative accuracy 

 and stability of pertinent parameter estimates 

 (Gallucci and Quinn 1979). In the Gompertz 



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