the fouvth-year class, the ratio between sniall and medium fish 18 * qc^ =. 



This ^iveo 2^s 1.4.5 so p s .83» Averaging these figures p s ,74. 

 235 



''*In the same way the ratio between large (over 15 kan ) and medium (15-10 kan) 



.53p^-^ 

 fish is 1-p . This gives 3.9 which means that p r .70. The ratio be- 



,19+.47p .95p*t_Ei 



tween larj;^ (over 20 kan) and medium ^20-10 kan ) fish is 1-p or I.48 



.19+P+-.05P*' 

 which gives the value p r .655. 



^ Fish taken in their first year are represented by f© , those which become 

 second-year fish by po, those taken in their second year by f; , those which sur- 

 vive into the third year by pi , and those taken in their third year by fx. If 

 the proportion of each of these year classes rtiich is captured is related to the 

 length of time during which the fish are present on the fishing grounds, we get 

 fotfi :fa.« ^:1::^. Therefore the proportions of fish of the year, second-year fish, 

 and third-year fish which are taken are ^:pc:^oPi. This gives 49:47:4 so 



n - 42 X i s .48 and p s ^ x 4. s .34.» Therefore the percentage iriiich live an 

 4-9 2 » **i 



additional year, that is the survival rate, is (.48) z .23 for fish of the year 

 and .34 for second-year fish, 



■'^Since small adult tuna weigh 3-10 kan they include l*'^lZ^''2 = '78 of the 

 third-year fish, and J;9'q'§^Z| s .81 of the fourth-year fish. Medium fish weigh 

 10-40 kan and include 1-.81 r,19 of the fourth-year class, all of the fifth-^ 

 sixth-, and esventh-year classes, and /q^/^^|^| = •13 of the eighth-year class. 

 Large fish weigh over 40 kan and include 1 - .13 z "S? of the eighth-year class 

 and all fish of the ninth-year class and older. Accordingly if p represents the 

 survival rate thon small: medium: large s .78f,Slp:.19pfp''+p^+p'*"+.13p'' : .87p-f ^^ , 

 In both the Japan Sea and the Pacific the ratio between medium and small fish is 

 1,61 so p s ,90, and the ratio of large and medium is .87 so p x .78. 



If the catch rate for young tuna is represented by f and the catch rate of 



