FISHERY BULLETIN. VOL 72. NO. 1 



Table \. — Optimal values of .size at recruitment (cm) as a function of the rate of 

 exploitation (E) and the ratio of M to K (Q) for three estimates of L^..' 



E 

 Q 0.1 0.2 0.3 0.4 0.5 0.6 0.7 



= 175.2 cm 



= 194.8 cm 



= 223.0 cm 



115.8 

 102.8 

 92,5 

 84.1 

 77,1 

 71.1 



128.8 



114,4 



102,8 



93.5 



85.7 



79.1 



147,4 

 130,9 

 117,7 

 107,0 

 98,1 

 90.5 



' Dashed lines encompass our reasonable range of values; 

 our most reasonable estimate. 



underlined value is 



reasonable range of estimates (deleting the un- 

 reasonably low E — 0.12), and the underlined 

 value in the center of Table 1 is our most reason- 

 able estimate. One can see in Table 1 that the 

 values are all greater than the approximate 

 absolute minimum size of 32.5 cm'^ for the At- 

 lantic yellowfin tuna fishery over the range of 

 the estimates of L^ . 



For the moment let us assume that recruit- 

 ment is knife-edged at 32.5 cm (0.67 kg) and 

 that the fishery can be regulated such to obtain 

 a knife-edged recinaitment at any desired size. 

 Therefore, the maximum possible increases in 

 yield per recruit may be computed. Our smallest 

 reasonable values for optimal size at recruit- 

 ment are 47.1 cm (2.0 kg), 52.4 cm (2.8 kg), or 

 60.0 cm (4.1 kg) depending on L^. The respec- 

 tive predicted values of yield per recruit are 

 2.0% , 3.1% , and 4.3% higher than when size at 

 recruitment is 32.5 cm. Our largest reasonable 

 estimates of optimal size at recruitment are 97.1 

 cm (17 kg), 107.9 cm (24 kg), or 123.5 cm (36 

 kg). The respective predicted increases in yield 



" The value of 32.5 cm represents our selection for an 

 approximate absolute minimum size for the Atlantic 

 yellowfin tuna fishery, which also agrees with that chosen 

 by Joseph and Tomlinson ( 1972, see footnote 4). 



per recruit are 65% , 73% , and 82% . The predict- 

 ed increase in yield per recruit using all of our 

 most reasonable parameter estimates, i.e., rais- 

 ing 32.5 cm to 83.2 cm (11 kg), is 23%. The 

 bounds on an increase in yield per recruit, 2% 

 to 82% , and the most likely value of 23% , are 

 estimated under the assumptions of knife-edged 

 recruitment, and that size at recruitment rep- 

 resents an absolute minimum size. The Atlantic 

 yellowfin tuna fishery, however, does not have 

 knife-edged recruitment. 



We used equation lb of this paper to obtain 

 our most reasonable estimate of the 1967-71 

 average effective minimum size for the Atlantic 

 yellowfin tuna fishery from average lengths 

 given in Table 15 of Lenarz and Sakagawa 

 (1972, see footnote 5). The estimate of average 

 effective minimum size is about 55 cm (3.2 kg). 

 Nearly all the values within the dashed lines in 

 Table 1, however, are greater than 55. The only 

 smallest reasonable estimate of optimal effective 

 minimum size greater than 55 cm is 60.0 cm 

 with Lqo — 223.0 cm. An increase from 55 to 

 60.0 cm would give an increase in yield per re- 

 cruit < 0.2% . The large.st reasonable estimates of 

 optimal effective minimum size predict increases 

 in yield per recruit of 28% , 36% , or 45% with in- 



42 



