ZWEIFEL and LASKER: PREHATCH AND POSTHATCH GROWTH OF FISHES 



be identified as a fixed percentage point in Figure 

 5 or the estimated value 



t,^ = In 



( 



K 



K - In {Lt/Lo) 



) 



/a, 



(7) 



as shown in Table 3. 



Lasker (1964) found that the functional jaw did 

 not develop at the lowest two temperatures in 

 agreement with the result that the critical size 

 would not be reached until well after yolk 

 absorption. 



^° 'I°=.6.I3 

 5.97 



E 

 E 



I 



2 4 6 8 10 12 14 



DAYS FROM FERTILIZATION 



Figure 5.-Prehatch growth curves estimated from Equations (5) 

 and (5a) for the Pacific sardine. 



Incubation Times 



Incubation times were available for several 

 other species. The fitting of Equation (5a) for each 

 species showed no clear bias at any point along the 

 curve (Figure 4). As for the sardine, no evidence of 

 a temperature optimum appeared for any of the 

 species in the temperature ranges used in the 

 experiments. However, it was observed that the 

 decay parameter was relatively constant varying 

 from 0.03 to 0.09 with a mean value of 0.05. When 

 Equation (5a) was fitted with the temperature 

 decay parameter, /?, the same for all species, 

 incubation times were closely approximated by 

 Equation (5a) with parameters as shown in Table 

 4. 



The incubation curves used here differ sig- 

 nificantly from those calculated from the classical 

 Arrhenius equation: log (incubation time) = a + 

 6/absolute temperature. Using this method, near- 

 ly all species showed a characteristic under- 

 estimate at the temperature extremes and over- 

 estimates in the middle range as shown for the 

 northern anchovy, Engraulis mordax (Figure 6). 



Prehatch Growth Curves for 

 Other Species 



In addition to incubation times for the northern 

 anchovy, Kramer'' recorded time to several 

 developmental egg stages. Also, Lasker (1964) 

 provided time to hatch from stage IV^ (Table 5). 

 Further, Hunter (pers. commun.) indicates that 



•■^Unpublished data available at SWFC. 



''Stages of embryological development are those described by 

 Ahlstrom (1943). 



Table 3.-0bserved (Obs.) and estimated (Est.)' time in hours to developmental egg stages^, hatch, and appearance of the functional jaw 



of the Pacific sardine. 



'/.^ = 0.0341, K = 5.20, a„ = 0.0317, m = 6.19, and /? 

 ^Egg stages are defined in Ahlstrom (1943). 



0.0489. 



617 



