270 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



.2- 



DINE 



ANCHOVY 



JACK MACKEREL 



2 

 DAYS 



3 



PAST 



HATCHING 



Figure 12. — Growth curves of jack mackerel, Pacific 

 sardine, and northern anchovy. (Open circles indicate 

 complete absorption of the yolk.) 



from the line. The comparison of the two slopes 

 indicated that the initial relative growth rate is 

 about five times that of the later relative growth 

 rate. 



Table 26. — Regression statistics for the relative growth rate 

 of jack mackerel larvae 



Section A: days 1 

 through 3 



Section B: days 4 

 through 8 --- 



0.328 

 .486 



0.0C7 

 .013 



0. 0091 

 .0017 



Syh 



0.01)10 

 .0184 



1.3 

 3.1 



0.614 

 .687 



The relative growth rates of the other two 

 species (Pacific sardine, Sardinops caerulea, and 

 northern anchovy, Engraulis mordax) illustrated 

 in figure 12 are similar to the growth rate shown 

 for jack mackerel. In addition, the relative 

 growth rate of the sardine as determined by direct 

 observation (6 = 0.018) is in good agreement with 

 the relative growth rate (6 = 0.019) determined by 

 Ahlstrom (1954b) using an indirect method 

 (Farris, 1959: p. 33). Ahlstrom, working with 

 preserved material, was able to follow length- 

 frequency modes through time. 



Although growth has been described by two log 

 curves instead of one, either would have served as 



well for estimating survival. The abundance of 

 a size class is given by the following equation : 



C= 



i=l 



c'tWftt 



where 



C= estimate of total abundance of larvae 

 of size class 



C(=standard number of larvae belonging to 



the size class at the ith station 

 ■W(=area factor proportional to area of the 

 t'th station 



<(=time factor equal to one-half the time 

 from preceding ocupancy plus one-half 

 the time to succeeding occupancy 



d<= duration of size category in days, i.e., 

 the number of days used by larvae to 

 grow from the lower-size boundary to 

 the upper-size boundary of the size 

 class 



71 = number of stations considered. 



The effects of 1- and 2-phase growth on mortal- 

 ity estimates were compared by recomputing 

 estimates of abundance for sardines given by 

 Ahlstrom (1954b: p. 133). In recomputing abun- 

 dance of yolk-sac larvae, the fonnula used was — 

 Duration of size category (days) = 



log r'-log V 

 0.081 ' 



where 0.081 is the log increase in length per day 

 of the larvae, I' is the lower boundary of the 

 size-class interval, and I" is the upper boundary 

 of the size-class interval. The duration of size 

 category for the remaining size categories of 

 larvae is given by — 



logZ"-logr 

 0.018 



The results of the recomputation are given in 

 table 27 under the heading "double phase," and 

 may be compared with Ahlstrom's figures. The 

 slight differences in average age for given size 

 may be due to shrinkage of the larvae upon 

 preservation in formalin. 



Since relative growth rates derived from labo- 

 ratory observations on the first 5 days in the life 

 of a sardine could be extrapolated and reconciled 



