DISTRIBUTION OF EGGS AND LARVAE OF JACK MACKEREL 



271 



with field observations, it was assumed that the 

 extrapolation could be made for jack mackerel, too. 

 An analysis of successive length-frequency 

 diagrams has not been used because the time 

 interval between successive cruises is too great 

 for the estimation of a rapid growth rate. Sec- 

 ondly, any changes in the survival of larvae 

 between cruises would influence the length fre- 

 quencies; hence the changes would alter the 

 estimation of the growth parameter and thereby 

 alter the estimates of annual survival. A growth 

 rate derived from direct observation has the 

 advantage of being independent of variation in 

 survival. 



T.\BLE 27. — Estimates of abundance of young sardine, using 

 single phase and double phase growth curoes, 1950 



(Single phase after Ahlstrom (1954b)) 



Category 



Single phase: 



Egg - - 



Yolk-sac larvae. 

 Larvae: 



4.75 mm 



5.75 mm 



6.75 mm 



7.75 mm 



8.75 mm 



9.75 mm 



10.75 mm 



Double phase: 



Egg 



Yolk-sac larvae: 



3.25 mm 



4.75 mm 



Larvae: 



5.75 mm 



6.75 mm 



7.75 mm 



8.75 mm 



9.75 mm 



10.75 mm 



Size range 

 (mm.) 



2. 26- 4. 25 



4.2&- 5.25 

 5. 26- 6. 25 

 6.26- 7.25 

 7. 26- 8. 25 

 8. 26- 9. 25 

 9. 26-10. 25 

 10.26-11.25 



2. 26- 4. 25 

 4. 26- 5. 25 



5.26- 6.25 

 6.26- 7.25 

 7. 26- 8. 25 

 8. 26- 9. 25 

 9. 26-10. 25 

 10.26-11.25 



Duration 

 (days) 



3.0 

 3.5 



4.8 

 3.9 

 3.3 

 2.9 

 2.6 

 2.3 

 2.1 



3.0 



1.9 

 6.1 



4.2 

 3.5 

 3.1 

 2.7 

 2.4 

 2.2 



Average 

 age (days) 



1.5 

 4.8 



13.2 

 16.8 

 20.0 

 22.7 

 25.1 

 27.3 



1.5 



3.9 



7.5 



12.1 

 15.9 

 19.2 

 22.1 

 24.7 

 27.0 



Estimated 

 abundance 



285, 676 

 11,850 



10. 778 

 5,590 

 6.197 

 5,931 

 4,834 

 3,738 

 2,880 



285, 676 



21,829 

 10,144 



5,191 

 5.843 

 5. 648 

 4.655 

 3,582 

 2,749 



The regression statistics of section A (table 26) 

 were used to estimate the duration of the various 

 size categories of jack mackerel through the 

 3.0-nim. size class and the regression statistics 

 of section B for all size classes thereafter. The 

 duration of the size category (in days) through 

 the 3,0-mm. size category is given by — 



\ogl"-\ogl' 

 0,067 



where /" is the upper boundary' of the size class, 

 and /' is the lower l)oundarv. 



The duration of the size category (in days) for 

 all remaining size categories is given by — 



\ogl"-\ogl' 

 0.013 



The average age for any size category is given 

 by summing the duration of size class for shorter 

 size classes and adding one-half the duration of 

 the size category under consideration. For ex- 

 ample, the average age of the 4.5-mm. size cate- 

 gory is obtained hy summing the durations for 

 categories, eggs through 4.0 (15.6) and adding 

 one half of 3.7. The average age is 17.4 days. 



The coincidence of the absorption of the yolk- 

 sac and the inflection of the survival curve is 

 tentatively interpreted as follows : 



Basic mortality rates of pelagic fish eggs and 

 yolk-sac larvae are high owing to factors intrinsic 

 to the eggs and inherent in the species; most of 

 those which are unfit have died before absorbing 

 their yolk or die shortly thereafter; the survivors 

 beyond the critical stage now survive at a higher 

 rate because they have successfully negotiated 

 the change in nutrition (i.e., from yolk to copepod 

 eggs and nauplii). A more comprehensive expo- 

 sition of this hypothesis is given by Farris (1960). 



SOURCES OF ERROR AND BIAS IN 

 SAMPLING LARVAE 



In the section on sources of error in egg 

 sampling, some of the more obvious sources of 

 error and bias were examined. These same 

 sources of error were examined in sampling pro- 

 cedures for larvae. In addition, the avoidance of 

 the net by the larvae might be added as a source 

 of error. 



RETENTION OF LARVAE BY THE NETS 



Incomplete retention by the net of some small 

 size classes of larvae becomes a serious problem. 

 Estimates of abundance were made for the 2.0- 

 and 2.5-ram. size classes of larvae in 1952 (table 

 25). These estimates are lower than the estimated 

 abundance of the 3.0-mm. size-class larvae, indicat- 

 ing that the smaller size classes were undersampled. 

 Larvae less than 3.0 mm. in length, meeting the 

 mesh head on, are able to pass through and do not 

 appear in our collections in proportion to their 

 true abundance. Estimates for these size classes 

 were not made in 1953 and 1954. 



Figure 4, from Ahlstrom and Ball (1954) suggests 

 that the head depth may be 10 to 20 percent 

 greater tlinn the body deptii at the pectoral. If 

 this is so, the maximum depth of the 3.0-mm. 

 larvae is greater than the maxinuini mesh opening 

 of tlie sampling net (0.55 mm. after shrinking 



