FISHERY BULLETIN: VOL. 74, NO. 3 



Although the single stage model used by 

 Kramer and Zweifel (1970) provides an adequate 

 grow^th curve, tM^o growth cycles are evident: one 

 extending from hatching to the depletion of the 

 yolk sac and the other a more rapid growth at the 

 onset of feeding. Thus, a two-stage model was 

 used to obtain the curves in Figure 2. The fitting 

 procedure is outlined in the Appendix. 



It is evident that early larval growth of this 

 species can be represented by a two-stage Laird 

 growth curve. The charcteristics of the growth 

 curves of feeding larvae, i.e., the second cycle, may 

 be related to several environmental factors of 

 which the two most important are probably food 

 ration and temperature. However, an examination 

 of data available on nonfeeding larvae (Figure 3) 

 indicated that even in food-limited situations, 

 change in size may be represented by the two- 

 stage Laird curve. 



Growth From Hatch to Depletion 

 of Yolk Sac 



The characteristics of the early posthatch 

 growth of larval fishes is more completely de- 

 scribed by Lasker (1964). In this series of exper- 

 iments, growth in length of the Pacific sardine, 

 Sardinops sagax, was measured for up to 10 days 

 following hatching at 12 temperatures in the 

 range 11°-21.3°C. The parameters of a single 

 stage Laird curve (Equation 2) were estimated for 

 each of these experiments. Data only up to the day 

 preceding the first decrease in size were used in 

 the calculations. 



Even though for such short time series, the 

 parameters are highly correlated due to near- 

 redundancy of one of the parameters, two obser- 

 vations were striking; there was a nearly constant 

 estimated hatching length of about 3.75 mm and 

 a nearly constant estimated maximum length of 

 about 6.1 mm. Accordingly, those experiments 

 with hatching lengths near 3.75 mm and a mea- 

 sured increase in size of at least 3 days were fitted 

 to the reparameterized model: 



L{t)T=Loe^^'-''"'"^ 



6.51- 



where 



K = Ao / a 



and the T subscript indicates temperature in °C. A 

 plot of a-p on temperature revealed another 

 Laird-Gompertz curve approaching an asymptote 

 at higher temperatures. 

 A five parameter model: 



o JACK MACKEREL 



A SENORITA 



• SQUARETAIL 



□ SARDINE 



2 4 6 8 10 12 



DAYS AFTER HATCHING 



Figure 3.-Change in length of yolk-sac and starving larvae; 

 curves are two-cycle Laird-Gompertz. 



where 





(5) 

 (5a) 



was used to fit the growth data from all exper- 

 iments and provided an excellent fit except at the 

 highest temperature where growth was always 

 overestimated. This suggested a temperature 

 optimum with growth rates decreasing as the 

 absolute difference | T - T^pi \ increases. Following 

 Stinner et al. (1974), who used a different temper- 

 ature function, we assumed symmetry around the 

 optimum. 



Using Equation (5a), the origin of the tempera- 

 ture scale may easily be shifted to the optimum 

 Topt by the relationships: 



«opt = «oe 



m(l-e'^^opt) 



and 



rw-opt = me'/^'^opt 



614 



