I^KIK'HK KT AL.: AGE AND GROWTH OF PAROPHRYS VETULUS 



final, "best" count was reached. Successive 

 counts and verification counts which were made 

 by the original reader at a later time usually did 

 not vary by more than ±2. Age estimates could 

 not be obtained for 10% of the field-caught larvae 

 because increments were faint and indistinct or 

 the otoliths were misshapen. Maximum otolith 

 and nucleus diameters were measured to the 

 nearest micron. Photomicrographs were taken 

 at 500 X or 1,000 X magnification under a light 

 microscope. 



Shrinkage of larvae preserved in 80% ethanol 

 was compared with shrinkage after preservation 

 in 10% seawater-diluted Formalin, the fixative 

 most commonly used to preserve plankton 

 samples. Thirty 7-day-old reared larvae were 

 measured alive and immediately preserved in 

 either 80% ethanol (15) or 10% Formalin ( 15). The 

 live, mean standard lengths of the two groups of 

 larvae were 4.34 and 4.42 mm. After 4 mo in 

 preservative the mean standard length of the 

 ethanol-preserved group was 4.20 mm and of the 

 Formalin-preserved group, 4.196 mm. Mean 

 percent shrinkage or 100(original SL — pre- 

 served SL/original SL) was 3.2% in the ethanol- 

 preserved group and 5.1% in the Formalin- 

 preserved group. The difference in amount of 

 shrinkage between the two groups was highly 

 significant (ANOVA, P<0.01). Care must be 

 taken, therefore, when comparing estimates of 

 size at age based on measurements of larvae pre- 

 served in different fixatives. From this limited 

 investigation it became apparent that Formalin- 

 preserved P. vetulus larvae appear to be some- 

 what smaller at age than ethanol-preserved fish. 



Statistical Procedures 



Gompertz and von Bertalanffy growth models 

 were fitted to larval P. vetulus data because the 

 form of the length-age plot was nonlinear with 

 a distinct upper asymptote. A detailed discussion 

 of the Gompertz function, which is the primary 

 model used in this paper, and methods for ob- 

 taining initial parameter estimates are pre- 

 sented by Zweifel and Lasker (1976). The gen- 

 eralized equation of this model is: 



L, = Loexp[x(l-e- Q ')j, 



where L, = length at age f; Lo = length at t = 

 (i.e., where the curve intercepts the y-axis); and 



K= — > or the specific growth rate at t = 



divided by the rate of exponential decay. Un- 

 transformed data were used in this model be- 

 cause the standard deviation of larval lengths at 

 age remained relatively constant and did not in- 

 crease with age, indicating variance homogene- 

 ity within the data set. The Gallucci and Quinn 

 (1979) version of the von Bertalanffy equation 

 was employed, utilizing the new parameter, w = 

 kL x , where k is the growth constant, and L x , the 

 asymptotic maximum size, which for P. vetulus 

 larvae is the maximum size attained in the 

 plankton prior to transformation into benthic 

 juveniles. The general form of this equation is: 



L t = f (l - exp [- kit - *>)] I . 



where t is the time when Lo = (i.e., where the 

 curve intercepts the x-axis). 



The SPSS NONLINEAR 4 program employ- 

 ing Marquardt's algorithm was used to fit both 

 models. A measure of goodness of fit was pro- 

 vided by the residual sums of squares (RSS), 

 the standard error of the regression (or standard 

 deviation of the residuals), and approximate 95% 

 confidence limits for each parameter assuming 

 linearity. Linear confidence theory can be ap- 

 plied here because the assumption of linearity at 

 the final (least squares) parameter values is a 

 reasonable one (Conway et al. 1970; Kimura 

 1980). A comparison of the RSS at the final pa- 

 rameter values to the linear estimate RSS pro- 

 vides a measure of the linearity of the sum of 

 squares (SS) function (SPSS NONLINEAR pro- 

 gram). 



Absolute growth rate or 



k-U 



expressed in 



millimeters per day and specific growth rate or 

 In La — In L\ 



k-U 



X 100 expressed as percent per 



day of length were calculated (Ricker 1979). 



RESULTS 

 Increment Formation 



Parophrys vetulus larvae survived and grew in 

 the laboratory for over 35 d after hatching, with 

 some individuals eventually transforming into 

 juveniles. However, growth after yolk-sac ab- 

 sorption, between days 4 and 5, was retarded and 



4 SPSS NONLINEAR. Statistical Package for the Social 

 Sciences, Vogelback Computing Center, Northwestern Uni- 

 versity, Evanston, IL 60201. 



95 



