Age groups 

 Odd-numbered years 



Even-numbered years 



one 

 year 



one 

 year 



one_ 

 year 



one 

 year 



a A B C D 



large — Ismail— ->■ large— ^ small— -^large 



small ^ large ^ small ^ large >-Bnnall 



and D, while to those which appear 

 conspicuously in odd-numbered years A and C 

 correspond. Consequently if we assume re- 

 lationships attendant upon growth based on as- 

 sunnptions A, B, and C, we can postulate the 

 above diagram of the mechanism. 



In this diagram of the mechanism, the 

 words "large" and "small" indicate the rela- 

 tive abundance of each age group as between 

 the different years, the solid lines show the 

 relationship accompanying growth, and the 

 dotted lines indicate the existence of the even- 

 numbered year type and the odd-numbered year 

 type. As is clear from the figure, this mech- 

 anism diagram satisfies the existence of the 

 alternate-year cycle from the point of view of 

 relative abundance, and it can be understood 

 that the essential factors are marked variation 

 every other year in the amount of the schools 

 considered as separate age groups, and that the 

 age group a is taken as a starting point. Con- 

 sequently, if we think that Dj which appears in 

 1948 and D2 which appears in 1950 have come 

 through the same procesa as D3 appearing in 

 1952, we can consider that the elements of the 

 alternate-year cycle for 1948 and 1950 

 originated 5 years before those years. 



(b) Concerning the displacements of the modes: 



The only direct comparison which can be 

 made on this point is of age groups A and B, 

 and as already stated in (2) and (3), a tendency 

 can be detected for the nnode for age group A to 

 be displaced to the left in even-numbered years 

 and to the right in odd-numbered years, and for 

 age group B contrariwise to the right in even- 

 nunnbered years and to the left in odd-numbered 

 years (fig. 3). If we consider this to be direct- 

 ly linked to the nnagnitude of the amount of fish 

 in these groups in the years referred to, it can 

 be said that for both age groups A and B the 

 mode is displaced to the right in years when 

 fish are abundant and to the left in years when 

 they are scarce. However, considerable dis- 

 crepancies in the location of the modes can be 

 detected annong abundant years and among 

 scarce years, and we can also cite the example 



of age group A, which in 1949, when the fish 

 were plentiful, and in 1952, when the fish were 

 scarce, had its mode appear at almost the sanne 

 position. Consequently, even though we assume 

 that the displacement of the modes is a factor in 

 the alternate -year cycle, it is obvious that it 

 does not appear as such a clear-cut difference 

 as did factor (a). At the present we cannot de- 

 cide whether or not it is a factor in the alternate- 

 year cycle, but it can be said that there is a 

 possibility that it is, and in such case we may 

 think that it is organically linked with factor (a) 

 and we may expect that it will give important 

 indications for a consideration of the mechanism 

 giving rise to the alternate-year cycle. 



IV. Considerations of the Mechanism by Which 

 the Alternate-year Cycle Arises 



In the preceding section it was shown 

 clearly that a controlling factor in the alternate- 

 year cycle is the marked difference in the 

 amount of fish of different ages insofar as as- 

 sumptions A, B, and C are used as a basis, and 

 it was ascertained that it was possible to explain 

 the mechanism rationally by relating it to the 

 processes accompanying growth. We cannot say 

 definitely whether or not the phenomenon of the 

 alternate -year cycle will continue hereaiter. 

 But assuming that it will continue, we shall 

 attempt to consider the mechanism which gives 

 rise to it chiefly from the standpoint of pushing 

 ahead these studies in the future. 



From the diagram of this mechanism it is 

 possible to interpret the source of the phenome- 

 non as something which arose in age group a 

 prior to its development. To put it concretely, 

 we are dealing with the fact that the amount of 

 fish in age group a is great in even-numbered 

 years and small in odd-numbered years and that 

 these phenomena are alternately repeated. Con- 

 sequently, with regard to the nnechanism giving 

 rise to phenomena of this sort, it is thought that 

 the following two ideas nnay be established: 



(a) They arise as a result of gradual 

 addition during the process of growth of age 

 group a. 



33 



