INTRODUCTION 



A fundamental problem in inferring the density of a popula- 

 tion fronn a sample or series of samples is the estimation of the 

 magnitude and sources of variability inherent in the sanriples. 

 Variability may arise from the way the population is distributed in 

 space and from imperfections in the sannpling methodo The purpose 

 of this paper is to provide a method of estimating the reliability with 

 which longlinel/ catches of yellowfin tunaZ/ represent the relative 

 abundance of the population. 



As a prelude to estimating the variability of the longline catches 

 we will first examine the way in which yellowfin are distributed in space. 

 This will be followed by an empirical examination of the distribution 

 of the catches in order to ascertain a transformation that will permit 

 the application of conventional statistical methods. Finally, the variance 

 will be estimated as a basis for establishing fiducial limits, 



SOURCES OF DATA 



The catch data used in this study of variability are from two 

 sources: records of Japanese commercial fishing in the western 

 equatorial Pacific in 1950 and 1951, and records of fishing conducted 

 by U, S. Fish and Wildlife Service research vessels in the central 

 Pacific in 1951 and 1952. The principal differences between the two 

 types of data are: (1) The commercial vessels fished around 2, 000 

 hooks along 50 miles of line while the research vessels fished only 

 240-480 hooks along 5-10 nniles of line, (2) The commercial vessels, 

 fishing in fleets, made n^any sets in particular areas while the research 

 vessels, operating singly, made single sets of gear at stations spaced as 

 much as 90 nniles apart. (3) The records of the commercial fishery con- 

 tain only total catch and total amount of gear for each set, whereas the re- 

 cords of the research operation include these data and other details in- 

 cluding the catch of each hook along the line. 



1/ The longline is used commercially to catch tunas and marlins in the 

 Pacific Ocean by Japanese fishermen (Shapiro 1950) and by American 

 fishermen in Hawaii (June 1950). It is also used by American fishery 

 research organizations such as the Pacific Oceanic Fishery Investi- 

 gations of the U. S. Fish and Wildlife Service to ascertain the abundance 

 of deep swimming tunas and marlins in areas not supporting commercial 

 fisheries. 



2/ Neothunnus macropterus (Temminck and Schlegel) 



1 



