each month the date on which the quota would 

 be reached. It included two procedural steps: 



1. A series of cumulative dolphin mortality esti- 

 mates for each future month was made by 

 summing the current total mortality, based 

 on kill-per-day statistics, and the projected 

 mortality for future months, based on kill- 

 per-ton statistics. 



To calculate the projected cumulative mortality 

 in future month m, we denote, at the end of month 

 h, 



T h = the estimated current total mortality 

 from the observed data by kill-per- 

 day method 

 T,„j, = the projected cumulative mortality 

 at the end of month m based upon 

 T„ 



U m = the tonnage of yellowfin tuna catch in 

 month m 



U m = the historical monthly tonnage aver- 

 age of yellowfin tuna catch 



Zw = observed kill-per-ton weighted by 

 number of vessels of two gear types. 



We then have 



1 m.h l z 1 m-\,h H" U „i ' ^W = 1 m-l.h "T U m ZiW 



Th +{ 



(! *) 



for m = h + l, h + 2 12 l<h<U 



and sfl 



*fj 



+ 



v=* +i 7 



sz£ + ZJ 



i=k+i 



where s, 2 is the sample variance of yellowfin tuna 

 catch for month i, and h refers to the month when 

 the up-to-date total mortality was estimated, 

 with the assumption that cov {Zw, XU f ) and cov 

 (Ui, U)) for i j* j are negligible, sf 2 k is an ap- 

 proximate sample variance of T mJl by the Delta 

 method (Seber 1973). s z ^, is the variance of 

 weighted kill-per-ton. Z w and Sz w are based on 

 the formulas of the ratio estimator (Equation 

 (D). 



2. For quota Q, the projection of closure date 

 was calculated as follows. If jQ<Ti 2 ,h, the 

 month g was chosen where T„-\.h<Q<T,,.h. 

 The projected date (V) in month g was then 

 obtained as: 



V = 



Q 



g-l.h 



Tg,k— Tg. 



V g 



\.h 



Q - (f h + Z w 2 u) 



v„ 



Ug " Z W 



where V g is the number of days in month g. 

 Kill-Per-Set Method 



The kill-per-set method was developed to esti- 

 mate the annual mortality at the end of the year. 

 It requires that all dolphin sets be stratified in 

 three ways: tonnage of yellowfin tuna catch dur- 

 ing dolphin set, vessel carrying capacity, and 

 fishing location (Table 1). Time of the year was 

 not a separate factor as it correlated closely with 

 fishing location. 



The kill-per-set method was formulated in the 

 same manner as the kill-per-day method (Equa- 

 tion (1)), except the auxiliary variable F#'s were 

 observed sets, r, was kill-per-set, and M; was 

 total number of sets. In addition, the estimated 

 total dolphin mortality was corrected for non- 

 reporting in IATTC logbooks, inside and outside 

 the CYRA, by a factor C, where C is the ratio of 

 tonnage of yellowfin tuna taken with dolphin 

 which were landed and weighed at port, to the 

 tonnage of yellowfin tuna recorded in the log- 

 books as an estimate at sea. The mortality for 

 strata without observed data was estimated with 

 the kill-per-set of adjacent vessel-class strata. 

 The resulting sample statistics are in Table 2. 



'r, = kill-per-set, S^, = sample variance of r,, X, = number of observed 

 dolphin sets, n, = number of observed trips. 



399 



