LENARZ ET AL.: YIELD PER RECRUIT OF ATLANTIC YELLOWFIN TUNA 



15 mo for F = 0.1 and 30 mo for F = 2.0. Since 

 estimator 1 requires size-selective data not fre- 

 quently available and does not respond to 

 changes in F, estimator 2 appears to be the 

 most attractive for knife-edged approximations. 

 The Atlantic yellowfin tuna fishery, however, 

 has a much more complex recruitment pattern 

 and size-specific F than this simple example 

 owing to the diverse gear types. The mix of 

 relative F among the various gear types makes 

 the determination of the appropriate current 

 t ' somewhat tenuous. 



r 

 Estimation of Constant Z 



The yield-per-recruit isopleths shown in Fig- 

 ures 1, 2, and 3 were calculated under the 

 assumption that fishing mortality and Z are 

 constant after the fish are recruited. The value 

 of Z was also estimated under the same assump- 

 tion. The section on size-specific fishing mortal- 

 ity will indicate that F is not a constant, but is 

 related to size. Thus our estimate of a constant 

 Z may not be realistic but may be a more 

 reasonable approach to estimating yield per 

 recruit than the size-specific F approach given 

 the quality of the data. It is the average of values 

 of Z estimated for the FIS bait boat and purse 

 seine fisheries (Lenarz and Sakagawa, 1972, 

 see footnote 5). The size-specific F section indi- 

 cates that F decreases with size for bait boats 

 and increases with size for purse seiners. Bever- 

 ton and Holt (1956) gave examples that indi- 

 cated that when F decreases with age, constant 

 Z will be overestimated and when F increases 

 with age, constant Z will be underestimated. 

 Hopefully we have obtained a reasonable esti- 

 mate by taking the average of Z's for the two 

 gears. 



Size-Specific I Approach 

 Estimates of Length Frequencies 



Length frequencies, numbers of yellowfin 

 caught by 5-cm intervals starting at 35 cm (32.5 

 cm ^ fork length <37.5 cm), were estimated for 

 each gear and the total fishery for two overlap- 

 ping periods, 1967-71 and 1969-71 (Figure 5). 

 The first period was used with the hope that 

 the effect caused by unequal strength of year 

 classes would be minimized by averaging. The 

 second period was used because it was felt that 



700r 



o 1969-71 

 • 1967 - 71 



40 



60 



80 100 120 



FORK LENGTH (cm.) 



140 



160 



180 



Figure 5. — Average length frequencies for the Atlantic 

 yellowfin tuna fisheries for two periods, 1967-71 and 

 1969-71. 



300 



Q 250 

 UJ 



o 



z 

 < 



-• 200 



z 

 li. 



3 150 



_) 



UJ 



>- 



\k 100 



o 

 o 

 o 



50 



OL 



o BAITBOAT 



• SMALL PURSE SEINE 

 A LARGE PURSE SEINE 

 A LONGLINE 



40 



60 



140 



80 100 120 



FORK LENGTH (cm) 



Figure 6. — Average length frequencies (1967-71) 

 tic yellowfin tuna caught by four gear types. 



160 



180 



of Atlan- 



the data are more accurate. Length frequencies 

 of the two periods are quite similar and produce 

 similar estimates of size-specific fishing mortal- 

 ity and estimates of yield per recruit. Thus, to 

 avoid redundancy, only the data for the 1967-71 

 period are used. Figure 6 and Table 2 show the 

 length frequencies for each gear. The curves are 

 as described earlier (see introductory section.) 



Estimates of Size-Specific Fishing Mortality 



Size-specific instantaneous coefficients of fish- 

 ing mortality were estimated with the method of 

 Gulland (1965) and Murphy (1965) as suggested 



45 



