Table 4.- Parameters for estimating incubation time / at 

 centigrade temperature T from the relationship Ir = 

 /oe"^' "' ° ' for several fishes where P is the same for all species. 



'Time from stage III eggs. 



2.2r 



2.0 



UJ 



P 1.8 



< 

 CD 



O 



o 



1.6 



1.4 



J- 



OBSERVED 



LAIRD -GOMPERTZ 

 — ARRHENIUS EQUATION 

 ® COINCIDENT POINTS 



A. 



0.00330 



0.00340 



0.00350 



0.00360 



^TEMPERATURE (°K) 



Figure 6.-A comparison of two methods of fitting the tempera- 

 ture-incubation time relationship in the northern anchovy. 



larval anchovy, on the average, hatch at about 2.9 

 mm. 



Prehatch growth curves were obtained by 

 fitting Equation (6) to hatch sizes of 2.85 at all 

 observed temperatures as shown in Figure 7. 



FISHERY BULLETIN: VOL. 74, NO. .3 



21° 19° 17° 15° 13° 11° 



0.8 



E 

 E 



I 

 h- 

 o 

 z 

 llJ 



2 4 6 8 10 12 



DAYS FROM FERTILIZATION 



Figure 7. -Prehatch growth curves estimated from Equations (5) 

 and (5a) for the northern anchovy. 



Comparison with the sardine curves indicate that 

 similar events (i.e., stages of development) occur 

 relatively later for the anchovy. Observed and 

 estimated event times are shown in Table 5. 



Except for size at hatch, development data for 

 the prehatch stage was not available for any other 

 species. The curves may, if desired, be easily 

 constructed from the parameters as shown in 

 Table 6. 



DISCUSSION 



Nothing seems more true than the statement of 

 Thompson (1942:158), "Every growth-problem 

 becomes at last a specific one, running its own 

 course for its own reasons. Our curves of growth 

 are all alike-but no two are ever the same. Growth 

 keeps calling our attention to its own complexity. 

 . . . not least in those composite populations whose 

 own parts aid or hamper one another, in any form 

 or aspect of the struggle for existence." 



The truth of this statement has been realized in 

 the disappointing search for growth models de- 

 rived from physiochemical processes. While it is 

 true that the mathematical form of some equa- 

 tions arrived at from metabolic considerations are 

 the same as those derived in other ways, more 



618 



