ZWEIFEL and LASKER: PREHATCH AND POSTHATCH GROWTH OF FISHES 



Table 5.-0bserved (Obs.) and estimated (Est.y time in hours to developmental egg stages^, hatch, and appearance of the functional jaw 



of the northern anchovy. 



'Estimates obtained from Equation (7) with parameters as shown in Table 6. 

 'Egg stages are defined by Ahlstrom (1943). 



Table 6.-Mathematical parameters for prehatch growth curves of six fishes. See text for 



notation. 



often than not no meaningful biological interpre- 

 tation of the metabolic parameters can be made. 

 The essence of the growth equation used here is 

 genetically programmed processes of exponential 

 growth and of exponential decay of the specific 

 growth rate. The most probable source of expo- 

 nential growth is, of course, self-multiplication of 

 cells, the causes of decay are many but not well 

 understood. Laird (1964, 1965a, b, i966a, b, 1967) 

 has shown that this kind of relationship offers a 

 practical means of analyzing growth of all tumors, 

 as well as embryonic and postnatal growth of a 

 number of avian and mammalian species. We have 

 shown that at least the early stages of the growth 

 of fishes follows a similar pattern. 



As with other organisms, several growth cycles 

 exist in fishes. The number of such cycles which 

 will be recognized is determined by the time scale 

 of measurements. We have used three cycles: 1) 

 from fertilization to hatching, 2) from hatch to 

 onset of feeding, and 3) feeding larvae. 



In addition, we have observed that the temper- 

 ature specific growth follows a similar pattern, i.e., 

 exponential increase with an exponential decay of 

 the temperature specific growth rate. In some 

 instances a temperature optimum exists beyond 

 which the specific growth rate begins to decline, 

 although this may be related to food requirements 

 at onset. of feeding. Further, we have observed 



that for the same spawn 1) the asymptotic limit of 

 each growth cycle is independent of temperature 

 and 2) the biological events such as developmental 

 egg stages, hatching, functional jaw development, 

 etc., occur at the same size at all temperatures. 



Figure 8 shows posthatch growth curves of the 

 sardine as 1) extrapolated from the prehatch 

 curves and 2) obtained from posthatch data. Al- 

 though the curves are quite similar at higher 

 temperatures, differences in the lower tempera- 

 ture range are large. Nevertheless, the time to 

 development of the functional jaw is much more 

 accurately determined from the extrapolated 

 curve, indicating an intrinsic process independent 



5.97 



E 



s 



I 

 I- 

 o 



z 



UJ 



3.73 



2 4 6 8 10 12 



DAYS FROM FERTILIZATION 



Figure 8.-Posthatch growth curves of the northern anchovy. 

 Solid lines are extrapolated from prehatch curve. Broken lines 

 are fitted to actual growth data. 



619 



