Hypothesis 2 - Differences in the growth rate 

 from year to year 



This is a consideration of a case where 

 hypothesis (2) is the controlling factor in the 

 variations in the modes from year to year. In 

 this case: (a) the amount of growth during the 

 year assumed in hypothesis (1) should be taken 

 as the difference between years in the amount 

 of growth; (b) the differences in the amount of 

 growth between years are small by comparison 

 with the amount of growth within the year. 

 These two conditions are postulated in this case. 

 We shall see whether or not it is possible to 

 form a rational postulate to account for the dis- 

 placement of the modes accompanying growth 

 while satisfying the conditions of hypothesis (2) 

 and conditions (a) and (b). If, on the basis of 

 figure 4, we attempt to form an assumption for 

 the sort of relationship that will satisfy condi- 

 tions (a) and (b), the following relationships 

 may be thought of. 



aiAi (1948) »-C' (1949) (D) 



A'b' (1949) ^D2 (1950) (E) 



a2A2 (1950) »► C" (1951) (F) 



a"A" (1951)- 



■D3 (1952) 



(G) 



However, these assumptions are basically 

 in conflict on the following points. First, when 

 the amount of growth within the year based on 

 the assumptions is made to correspond to as- 

 sumptions A, B, and C, there exists in all 

 cases between the amounts of growth of the two 

 a discrepancy of approximately 3:1, and this 

 relationship stands in opposition to the first 

 proposition, which was that the rate of growth 

 varies from year to year. 



Secondly, when the amount of growth in the 

 year based on this assumption and the discrep- 

 ancies among the length frequency groups ap- 

 pearing in the same year (which are handled as 

 independent units in the assumption) are made 

 to correspond with assumptions A, B, and C 

 and are compared, there is in every case a 

 discrepancy between the two averaging 3 : 2. 

 If this sort of relationship is considered in di- 

 rect connection with growth, it is thought to be 

 clearly inconsistent. 



In conclusion, assumptions (D) to (G) do 

 not satisfy hypothesis (2), and it is also appar- 

 ent that the assumptions themselves do not sat- 

 isfy the relationship accompanying growth. In 

 short, as long as we postulate that schools of 

 the same stock return repeatedly into the fishing 



grounds, we cannot establish any assumptions 

 that would satisfy both hypothesis (2) and condi- 

 tions (a) and (b) at the same time, and conse- 

 quently it can be decided that hypothesis (2) 

 cannot at least be the dominant factor in the 

 variations in the modes from year to year. 



Hypothesis 3 - Differences in migratory 

 phenomena from year to year 



Concretely, this hypothesis is based on the 

 idea that the migrations of the schools as dif- 

 ferentiated by length groups differ from year to 

 year. What is meant in this case is that the 

 schools which come into the fishing grounds in a 

 given year and those which come into the fishing 

 grounds in the following year do not have any 

 direct relationship. However, it is anticipated 

 that in order to link up hypothesis (3) rationally 

 with the alternate-year cyclical phenomena al- 

 ready described, we must bring into hypothesis 

 (3) in some form or another a cyclical migra- 

 tional phenomenon which occurs in units of 2 

 years. Let us assume a displacement of the 

 modes attendant upon growth based upon this 

 sort of assumption, and examine the validity of 

 the results. If we postulate the existence of 

 migrational phenomena with aperiodof 2 years, 

 the schools which come into the fishing grounds 

 in a certain year may be thought to return again 

 to the grounds 2 years later, so it is to be ex- 

 pected that any direct relationship will be be- 

 tween the schools in odd-numbered years and 

 between those of even-numbered years and 

 would not exist between those of successive 

 years. Consequently we will assume the 

 following relationships from figure 4. 



Even-numbered years: 



aiAi (1948) »>B2 (1950) ^ D3 



(1952) (H) 



Bi (1948) ^D2 (1950) (I) 



a2A2 (1950) »- B3 (1952) (J) 



Odd-numbered years: 



A'b- (1949) ^C" (1951) (K) 



If we attempt t o examine the validity of 

 these assumptions as seen through the phenom- 

 ena, it will be understood that as regards their 

 relatedness fronn the point of view of the inter- 

 nal structure of the several length groups, it 

 can be established under postulates similar to 

 those considered for assumptions A, B, and C, 

 while as far as growth rate is concerned there 

 is general agreement among the several 



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