VARIABILITY IN TRAWL CATCHES 



147 



TWO-TOW STATION DATA 



Since two tows were made at approximately 

 one-third of the stations in 1948, 1949, and 1950, 

 the series of paired observations furnishes a 

 measure of comparative variability between tows. 



As Winsor and Walford (1936) show, if the 

 basic distribution is Poisson the quantify 



ft ni + « 2 



should, in a number of random samples, have a 

 mean value of 1 and should be distributed in a 

 known manner. 



Table 1 shows the distribution of values of chi- 

 square for haddock, whiting, and the common 

 skate, and for total fish. The distribution is of 

 the same type as those found by Winsor and 

 Walford (1936) and Barnes (1949a) for plankton, 

 with an excess of large values of chi-square. 



In table 2, the totals of chi-square are classified 

 by sample size. Although there is some tendency 

 for the larger hauls to be associated with high 

 chi-square values, the values are generally high 

 for all levels of catch. While variability in samp- 

 ling is expected to arise from imperfections asso- 

 ciated with the sampling technique, it is clear that 

 if the data are taken from a population distrib- 

 uted at random these imperfections would have 

 to be of the grossest kind to account for the 

 variability observed. 



As a working hypothesis, the assumption of a 

 random distribution of plankton organisms does 

 not appear unreasonable, even though such an 

 assumption seems to have been suspect for some 

 time. A similar assumption for the distribution 

 of fish, however, appears quite unwarranted, since 

 trawl catches, fathometer records, and the obser- 

 vations and experience of fishermen indicate that 

 fish tend to congregate in schools. Trawl catches 

 show that these schools are heterogeneous and 

 that, while a particular species may predominate, 

 there is ordinarily a variety of species repre- 

 sented. These schools probably differ not only 

 in area but also in density within an area. 



In table 3, the catches of haddock in tow 1, 

 tow 2, and tows 1 and 2 combined are tabulated 

 for the two-tow stations. It is at once apparent 

 that the observed curve of distribution cannot 

 possibly be Poisson unless the mean is less than 1, 

 which it obviously is not. 



The observed distribution of frequencies of 

 catch per tow of haddock suggests the negative 

 binomial distribution (Greenwood and Yule 1920). 

 The combined data for the two-tow stations 

 (table 3) were therefore fitted by the negative- 

 binomial distribution. 2 Details concerning the 

 goodness of fit are summarized in table 4. 



This development suggested that the basic dis- 

 tribution of the catch-per-tow data might be the 

 negative binomial. It became necessary to ex- 

 amine not only the validity of this hypothesis in 

 the light of the data at hand but also any theo- 

 retical reasons why these data should be so 

 distributed. 



Xcgative binomial series were fitted to catches 

 of haddock per standard tow for each of three 

 depth zones: Depth zone 1, 0-30 fathoms; depth 

 zone II, 30-60 fathoms; and depth zone III, more 

 than 60 fathoms. While no particular signifi- 

 cance is thought to attach to these groupings, the 

 data were available in these classifications, and 

 these depth zones are presumed to represent a 

 certain homogeneity of conditions. The results 

 of these fittings are presented in table 5. The 

 catches for depth zone III are presented in figure 2. 

 Similar treatment was accorded the data for 

 the common skate (Raja erinacea), the whiting 

 (Merhicdus bilinearis), and the ocean perch 

 (Sebastes marinm). These data are presented in 

 tables 6, 7, and 8. The catches for common skate 

 and ocean perch are presented in figures 3 and 4. 

 The probabilities associated with the 2x 2 for 

 these data are summarized in table 9. They are 

 sufficiently high to retain the hypothesis that the 

 basic distribution is the negative binomial. This 

 hypothesis is strengthened, however, if theoretical 

 grounds, conforming to conditions known to 

 apply to the data, may be found. 



Let us first consider a Poisson distribution with 

 mean m. 3 Two essential conditions for a Poisson 

 distribution of items are that they be distributed 

 at random and independently of one another. If 

 the items are not distributed independently but 

 tend to cluster in groups, 4 the estimate of m will 

 tend to vary with sampling, and a Poisson dis- 

 tribution will no longer be obtained. 



' See appendix B. 



» The development follows in its essentials that demonstrated by Fisher 

 (1941). 



•Compare the "contagious" distributions of Polya, 1931; Neyman, 1939; 

 Cole, 1946; and Thomas, 1949. 



