DISTRIBUTION OF EGGS AND LARVAE OF JACK MACKEREL 



251 



of subsequent modes is determined in the same 

 manner. 



Temperature data for the stations were supplied 

 by the Scripps Institution of Oceanography. If 

 the temperatures ^\athin the upper 30 meters of 

 water did not vary bj' more than 0.1° C, the data 

 from the station were used. 



The effect of temperature on rate of develop- 

 ment was shown by a regression of log hours of 

 development against temperature for each stage. 

 F= hours of development 

 X= temperature °C. 

 Log Y=a+bX 

 Separate regressions were made for three stages 

 (table 1) so that the regression statistics might be 

 compared. If a relation exists between rate of 

 development and temperature, the slopes for the 

 three regressions should be about the same. The 

 F-intercepts were not compared, since the lines 

 are almost parallel and occur at different levels; 

 the intercepts, as one would expect, are different. 



Table 1. — Temperature regression coefficients for the rate 

 of development of jack mackerel eggs 



The close correspondence of the slopes for the 

 three regressions indicates a uniform relation 

 between developmental rate and temperature. 

 By using the graph of the regression for the oldest 

 stage (stage IX), the incubation period to the 

 closest day could be predicted directly (fig. 3). 

 This regression was used in determining the num- 

 ber of whole days elapsing in the egg stage (d,) as 

 mentioned above. 



The incubation period (in hours) as predicted 

 by the regression for stage-IX eggs was compared 

 with the incubation period actually observed under 

 conditions of controlled temperature (see p. 250). 

 The close agreement between prediction, and ob- 

 servation is shown in the following table: 



20 



19 



9 I 7 



16 



o 



X 



I 5 



1.4 



126 



92 



84 

 75 ^j 



68^ 

 in 



61 fe 



t- 

 55 ? 



50 Q 



45, 

 40' 



o 



I 



12 13 14 15 16 17 18 



TEMPERATURE "C. 



Figure 3. — Relation between temperature and rate of 

 development for three stages of jack mackerel eggs. 



The close agreement between incubation period 

 predicted and actually observed lent confidence 

 to the reliability of the indirect method. 



The temperature-dependent incubation period 

 (di) is used to compute the average nimiber of eggs 

 spawned per day at the tth station(C() in the follow- 

 ing manner. 



The standard number of eggs at the ith station 

 (c'i) is divided by d,. 



After computing the estimate of the average 

 number of eggs spawned per day at the ith station 

 of 10 square meters, the number of eggs is inte- 

 grated over space to the siu-rounding stations by an 

 area factor (w,). The sample is then weighted 

 on the basis of the area it represents. The 

 boundaries of an area are formed by the perpen- 

 dicular bisectors of lines drawn to the stations 

 immediately surrounding the one under considera- 

 tion. 



The time factor (it) is derived by taking the 

 number of daj's from the previous occupancy of the 

 station to the occupancy of the station immedi- 

 ately succeeding the one under consideration and 

 dividing by 2. The products {ctWftt) are summed 



580553 O — 61- 



