FISHERY BULLETIN: VOL. 84, NO. 1 



Table 3. — Numbers of purse seine sets involving dolphins 

 in the eastern Pacific Ocean, from 1959 to 1972, for small 

 (<600 tons) and large (>600 tons) vessels, and for successful 

 (> 1 /» tons tuna) and unsuccessful (< 1 /4 tons) sets, modified 

 from Punsly (1983). 



developed on one vessel in 1959-60 (Barham et al. 

 1977) and used by at least three vessels in 1961 

 (Anonymous 1962). If 79% of the sets in 1964-65 

 were made using this procedure, as suggested by the 

 very limited available data, a rather rapid increase 

 in usage must have occurred in 1962 and 1963. This 

 is possible because, if properly used, the procedure 

 reduces the amount of handling time of dead 

 dolphins, thus speeding up the fishing operation. As 

 an approximation, we assume that usage increased 

 from to 0.79 linearly from 1959 to 1964-65, and 

 was 0.89 for 1966-71 and 0.96 for 1972. 



Denoting the interpolated and extrapolated esti- 

 mates of the proportion of successful sets using the 

 backdown dolphin release procedure by P t gives 



Xtill - Pistil, 



X t ii2 = (1 - Pt) Xti\»- 



Substituting these relationships into Equation (3), 

 with the assumption that the estimated numbers of 

 sets given by Punsley (1983) are constants, the 

 following equations result when the terms are 

 rearranged: 



T t = X {P'in[ x tii*Pt + C(l - PtV^tii'] + P'i2»Xti2»} 



i 



= Z \R'illXtil»[Pt + C(l - PJ\ + P'i2'X t i2.\. 



i 



(4) 



The time series of estimated annual kill (t t ) from 

 1959 to 1972 was obtained by pooling the available 

 data over years and strata, resulting in estimates that 

 are not statistically independent. Thus in order to 

 estimate the variance of the total kill of dolphins for 

 the period in addition to the variances it is necessary 

 to determine the covariances among the annual 

 estimates. 



We denote the estimates of the total kill of dolphins 

 (f t ) for each year from 1959 to 1972 by the vector 

 f, and denote the estimates of the variances of the 

 elements of f by the symmetric matrix If. The 

 estimate of the kill in each year (Equation (4)) can 

 be expressed in matrix form as the product of a vec- 

 tor of the numbers of sets in each of the four com- 

 binations of the vessel size and fishing success 

 classifications (X t ), and a vector of the four corre- 

 sponding kill rates (Q f ). Each element of T then can 

 be expressed as a matrix product 



Tt = X\ Q t 



(5) 



where X' t = (X tn „ X m „ X nz „ X tZ2 .) 



Qt = 



Qn 



Qt2 

 Qt3 



Qa 



R. in [P t (i -Q + C] 

 R. 2n [P t (l -Q + C] 



R»\2» 

 R. 22. 



P'inft 



P»21lft 



K*\2* 



R*22* 



and /, = P,(l - 6) + C. 



Then the variance-covariance matrix of T is 



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