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



5.0 



4.0 



10 20 



FISHING EFFORT 



30 



Figure 19. — Annual equilibrium yield as a function of 

 fishing effort at two different ages at recruitment, t^'. 



The above result of singular action on the 

 minimum size regulation resulted in a fortuitous 

 increase in total yield and MSAY. This result 

 may not always occur, however. Consider that if 

 the fishery were operating with t ' at 27 mo and 

 F = 0.2. then the yield per recruit would be 

 2.77. The optimal yield per recruit is 3.02 at a 

 t ' of 19 mo. If singular action were taken to 

 lower the ^ ' to 19 mo, a slight loss of total yield 

 would occur even with the improved yield per 

 recruit. Even more disconcerting would be the 

 loss in potential MSAY of 28%. The fishery 

 would be suboptimized in a sense. Since the 

 MSAY is usually estimated from a time series 

 of catch and effort data, the actual potential 

 which could have been realized had t ' remain- 

 ed at 27 mo would likely be underestimated. 

 It is likely that yield per recruit studies would 

 continue as the fishery developed effort beyond 

 F = 0.2, such that eventually the upper curve 

 might be attained; this is because the optimal 

 age at recruitment increases asymptotically as 

 F increases. The low initial forecasts of MSAY, 

 however, could hamper development of the 

 fishery. 



An even worse consequence of singular action 

 on yield per recruit is illustrated in Figure 20. 

 Assume the fishery is operating at about 0.6 

 unit of effort with an age at recruitment such 

 'to obtain curve A, but the yield per recruit is 

 adjusted to maximal for the age at recruitment 

 giving curve B. The actual MSAY of curve A 



1,0 2,0 



FISHING EFFORT 



3,0 



Figure 20. — Annual equilibrium yield as a function of fish- 

 ing effort at two different ages at recruitment (see text). 



might never be realized since the maximum 

 equilibrium yield in curve B is also at 0.6 unit 

 of fishing effort. This case represents true sub- 

 optimization. 



CONCLUSIONS 



Although there are some uncertainties in our 

 knowledge of the parameters that enter into 

 calculations of yield per recruit of yellowfin in 

 the Atlantic, it is possible to come to some con- 

 clusions from our results. 



The least amount of data and assumptions 

 is involved in the simplified Beverton and Holt 

 method. Results from this method (Table 1) 

 show that, in all but a few extreme cases in a 

 wide range of growth and mortality parameter 

 values, an increase in the effective minimum 

 size would result in an increase in yield per 

 recruit. However, our most reasonable estimates 

 of the parameters indicated that at the current 

 level of fishing, an increase in the effective mini- 

 mum size could only result in about an 8% 

 increase in yield per recruit. We conclude that 

 even if the quality of our data is poor an increase, 

 probably minor, in yield per recruit of Atlantic 

 yellowfin would occur if the effective minimum 

 size is increased and if it is assumed that small 

 yellowfin tuna were not dumped. 



We next assumed that our most reasonable 

 estimate of growth, constant Z, and effective 

 minimum size are correct and constructed yield- 

 per-recruit isopleths with the Ricker method for 



59 



