numbers of sampling units (baskets). This reduction is almost ex- 

 actly proportional to the reduction to be expected from the theoretical 

 relationship between cr and the nunnber of sampling units (fig, 5). 



The near identity of the empirical reduction in cr with the re- 

 duction calculated from the a- of the 18-basket subsets indicate that no 

 substantial new sources of variation were introduced when 2 con- 

 secutive days of fishing in the same area were considered as repli- 

 cates. Perhaps the close approximation also serves as a measure 

 of the suitability of the logarithmic transformation for this type of 

 longline catch„ 



In addition to the estimate of a for an 18-basket subset that 

 can be derived from the previous analysis, values were calculated 

 from three other series of 20-basket subsets. These latter were 

 from 40-basket stations fished as much as 90 miles apart, and were 

 obtained by pooling the catches of alternate baskets. The analysis of 

 these data is shown in table 4. Considering the 20-basket value deriv- 

 ed fronn table 3 with the three values from table 4, the range of the 

 logarithmic cr of a 20-basket set (. 191-.248) appears to represent 

 sampling variation. It follows that the best estimate of the cr of a 

 20-basket set of longline gear is obtained by averaging the four 

 empirically obtained variances and extracting the square root of the 

 mean variance, yielding a mean value of . 229. 



It does not follow that the estinaate of or obtained from our 

 carefully controlled experimental fishing can be applied to other 

 types of longline fishing, such as Japanese commercial fishing, in 

 which such variables as the length of time the gear is in the water 

 vary considerably from day to day„ As a test, two trial calculations 

 were made on series of data derived fronn Japanese commercial fishing 

 in which the sampling unit was about 2, 000 hooks fished per day in- 

 stead of the 240-400 hooks fished by POFI. The first series was ob- 

 tained by pairing consecutive days' fishing by one vessel. The second 

 series was obtained by selecting a block of ocean 60 miles square and 

 pairing catches that occurred in that block on the same date without 

 regard to vessel identity. As may be seen from table 5, these two 

 methods furnished nearly identical estimates of cr, but they are larger 

 than that obtained from our own fishing. 



Considering hook or basket number only, extrapolation of the 

 estimated (t of our experimental fishing (. 229 for a 20-basket set) to 



14 



