groups, B2 a.nd B3, which are assumed to be 

 the result of the growth of the same fish, can- 

 not be judged to be necessarily composed of 

 two groups. In other words, the former are 

 of the bimodal type while the latter are of the 

 unimodal type. With regard to this point the 

 following considerations may perhaps be 

 brought forward. 



First, looking at the form of B2 and B3, 

 they canhardly be considered bilaterally sym- 

 metrical, for in each case they are skewed to 

 the right. Furthermore, when we try compar- 

 ing A'b' and A"b", we see that in the forntier 

 the displacements of A' and b' are small, while 

 in the latter the displacements of A" and b" 

 are large, and it is possible to point out an 

 analogous relationship in the comparison be- 

 tween B2 and B3. That is, in B2 the degree 

 of skewnesB on the right is small whereas in 

 B3 it appears relatively large. The same sort 

 of relationship can be indicatedby making com- 

 parisons for each sea area separately (see 

 fig. 1). Second, let us consider what changes 

 in the course of their growth will affect two 

 groups which differ in the time at which they 

 were produced. When we examine the succes- 

 sive stages of existence of two groups defined 

 in terms of length composition, it may be 

 thought that perhaps with the passage of time 

 they may tend more and more to overlap. It 

 is thought that this is mainly due to the fact 

 that with the passage of time there is a rela- 

 tively greater increase in the growth rate dif- 

 ferential as between the individuals than in the 

 growth rate differential based on the difference 

 in the time of production, and it is imagined 

 that this effect also operates to some degree 

 in problem (b). 



If we think about the analogies pointed out 

 under consideration 1, taking account of the 

 effect of the process of growth as set forth 

 under consideration 2, there is probably no ob- 

 stacle to deciding that there is a fairly strong 

 relatedness between A'b' and B2 and A"b" and 

 B3. 



With regard to the assumptions 



(B2 *-C" »-D3) and (Bi »-C' ^D2), 



no points of essential disagreement can be de- 

 tected by a direct inspection of the form of the 

 modes. It is thought that the fact that the modes 

 gradually diminish in height is due to the effect 

 of the increasing mortality and the problem of 

 availability. 



Figure 5 shows how the displacements of 

 the modes look based onassumptions A, B, and 

 C. As is clear from the figure, the growth 

 rates based on these various assumptions are 

 in very good agreement. This fact may be 

 thought to strongly support the validity of 

 assumptions A, B, and C. 



As observed above, it must be said that 

 there is a considerable rational basis for the 

 establishment of assumptions A, B, and C, and 

 consequently it can be judged that there is a 

 strengthening of the validity of the hypothesis 

 that the variations in modes from year to year 

 arise from differences in the amount of repro- 

 duction or recruitment from year to year. 

 However, there is still a gap between the es- 

 tablishment of the assumptions A, B, and C and 

 the establishment of this hypothesis, so we 

 shall make a further consideration of this point 

 later. 



?o- 

 15 ■ 

 10 

 5 



•i 



is. 



AtiuMptlon (ft) 



si siii'i 5 9 1) Hi 5 9 911 lii 5 iiiin 111 5 i in'i MI a liii li s i '\>Vf'^ *•*? 



&•■<■) '■'■■J''' . 



Figure 5, --Mode transformation based on assumptions A, B, a.xsd C. 



30 



