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



avoid ambiguity and to prevent possible mis- 

 applications of the results of this study. "Mini- 

 mum size" may be viewed from two aspects: 

 absolute minimum size and effective minimum 

 size. Absolute minimum size is defined as the 

 smallest fish in the catch and is related to the 

 concept of knife-edged recruitment in defining 

 the size at recruitment to the fishery. Recruit- 

 ment is defined as the act of becoming vulner- 

 able to fishing. In the case of knife-edged re- 

 cruitment, no fish are vulnerable to fishing prior 

 to the size at recruitment. Fish that are larger 

 than the size at recruitment are full}^ vulner- 

 able to fishing. Since most recruitment is size 

 specific, hence sequential, the term effective 

 minimum size is also needed. Effective mini- 

 mum size is that size whose corresponding age 

 is used as the lower bound for integration of the 

 yield equation as if recruitment were knife- 

 edged, and which gives the same yield per re- 

 cruit as the sequential recruitment case. 



Approaches to Yield - Per-Recruit Analysis 



This paper examined several of the concepts 

 involved in yield-per-recruit analyses because 

 the question of what is the optimum minimum 

 size for a given rate of exploitation is usually 

 interpreted through such analyses. Both the 

 classical approach, in which fishing mortality 

 is constant with knife-edged reciiiitment. and 

 the more complex approach, in which fishing 

 mortality is size specific, are explored. 



Throughout the paper we have intentionally 

 kept mathematical notation to a bare minimum. 

 We believe that most of the equations used are 

 well known to readers actively involved in 

 stock assessment. Readers who are not familiar 

 with the equations can find excellent descrip- 

 tions in the cited literature. 



Employing the classical approach to yield- 

 per-recruit analysis involves: (1) estimating 

 the age or size at recruitment which represents 

 an approximation of the current state of the 

 fishery in terms of knife-edged recruitment; 

 (2) finding the age or size at recruitment which 

 maximizes the yield per recruit at a given level 

 of fishing mortality; (3) imposing some regula- 

 tion on the fishery such to achieve as its effec- 

 tive minimum size, the age or size at reci-uit- 

 , ment which maximizes the yield per recruit. 

 The advice from the yield-per-recruit isopleth 

 (in terms of the optimal age or size at recioiit- 



ment) may be interpreted as either a knife- 

 edged absolute minimum size or as an effective 

 minimum size. Since for the fishery under con- 

 sideration (and for many other fisheries as well) 

 recruitment is not knife-edged, then we are 

 talking about an effective minimum size. Now, 

 on the other hand, if we assume that the abso- 

 lute minimum size, the regulated size, and the 

 effective minimum size are all the same, then 

 we will have an inappropriate estimate of the 

 yield per recruit, and the optimum may not be 

 achieved. Somehow we need to determine the 

 relationship between the effective minimum 

 size and the regulated size; in some instances 

 they can roughly be the same; but this equality 

 will usually not obtain if the regulated size is 

 chosen to be the absolute minimum size in 

 the catch. 



The more complex approach, which estimates 

 size-specific fishing mortality, circumvents the 

 first difficulty encountered in the classical ap- 

 proach, i.e., determining a knife-edged approxi- 

 mation to the current state of the fishery. The 

 problem still remains, however, as to interpre- 

 tation of the advice from the yield-per-recruit 

 isopleth in terms of an effective minimum size. 

 Joseph and Tomlinson (1972, see footnote 4) 

 used the more complex approach in a recent 

 study on minimum size regulations for the At- 

 lantic yellowfin fishery. We have updated their 

 analysis by using data made available at the 

 Abidjan meeting and have also examined the 

 sensitivity of the methodology to various sources 

 of errors in the data. 



DATA, PARAMETERS, AND 

 COMPUTER PROGRAMS 



Data 



Catch- and length-frequency data for each 

 type of gear for the 1967-71 period were ob- 

 tained from the report of the meeting of the 

 special ICC AT working group (Tables 10, 11, 

 and 12 of ICCAT, 1972, see footnote 2) with 

 the exception of length-frequency data of the 

 1967-68 FIS fishery and 1971 Japanese long- 

 line fishery. Length frequencies for the 1967-68 

 FIS fishery were compiled from various 

 ORSTOM (Office de la Recherche Scientique et 

 Technique Outre-Mer) publications (Lenarz 

 and Sakagawa, 1972, see footnote 5). Length 



39 



