Figure 2. --Length frequency of the albacore caught in the northwestern 

 Pacific during the longline season (indicated by permillage). 

 Solid line -length frequency curve indicatedby lapped mean 

 between three length classes. Broken line - length groups 

 estinnated by fitting normal curves. 



at the same time or appearing to fuse together. 

 Consequently, this is interpreted as the ap- 

 pearance at the sanne time of a number of 

 different size groups. In figure 2 the solid 

 line shows in permillages the results of 

 smoothing the actual measured values with a 

 moving average of 3 cm. The dotted lines are 

 the result of an attempt to analyze this into a 

 number of normal distributions.—' According 

 to this, for each year we can detect six size 

 groups. In view of the fact that there is gen- 

 eral correspondence among the positions of 

 each size group, we set up the assumption that 

 "six size groups which correspond from year 



3/ 



— Nornnal distributions with various 



average sizes, standard deviations, and total 

 numbers have been get up, and those whose 

 sunns best fit the results of the treatment with 

 a moving average have been taken up. The 

 goodness of the fit for each year has been ex- 

 amined by the chi-square test. With the length 

 classes 2 centinneters, and decreasing the de- 

 grees of freedom each year (3X6+ 1), each 

 case gave a fit of P > 0.9. (1 degree of free- 

 dom for each determination of the number of 

 normal distributions, and since 6 normal dis- 

 tributions were fitted each year and for each 

 of them 3 parameters were determined, the 

 degrees of freedom were decreased by 18 or a 

 total of 19.) 



to year appear in the albacore captured in the 

 North Pacific. Some degree of variation in 

 their nnodal length from year to year can be 

 seen." On the basis of this assumption we shall 

 try to bring out some of the characteristics of 

 these size groups. 



Results - I. Positional Relationships 

 of Each Size Group 



Table 1 shows the modal lengths for each 

 age group, the groups having been designated 

 as I to VI from the smallest fish to the largest. 

 Tables 2 and 3 show respectively the direct 

 difference of the modal lengthl/ and the lagged 

 difference ^' . The following statements can be 

 made on the basis of tables 1 to 3: 



1. The average modal lengths of each 

 group for the 5 years from 1948 to 1952 are 

 approximately 57 cm. for group I, 67 cm. for 

 group II, 78 cm. for group III, 89 cm. for 

 group IV, 100 cm. for group V, and 111 cm. 

 for group VI. 



4/ 



— Difference in modal length for group N 



and group N + 1 in the same year. 



5/ 



— Difference in modal length between 



group N for a given year and group N + 1 of the 

 following year. 



8 



