VARIABILITY IN TRAWL CATCHES 



149 



The trawl-catch data were classified by the 

 same depth zones as were used above. The 

 number of species, S, and the number of in- 

 dividuals, N, were determined for each depth 

 zone in each year, and also for each depth zone 

 for the 3 years combined, 1948-50. Logarithmic 

 series were fitted to each grouping. Goodness of 

 fit was determined in the usual way. The data 

 were grouped so that the number of expected 

 observations was close to five. After the first 

 few terms, the interval of grouping necessary to 

 obtain five expected observations increases rapidly 

 so that in general it is not feasible, or necessary, 



to compute the series beyond the first four or five 

 groupings, these groupings usually including the 

 first 150 to 200 terms. 



The results of fitting logarithmic series to the 

 distribution of species and numbers of fish 

 represented by each are presented in tables 12 

 (a, b, and c) and 13 (a, b, and c), together with the 

 chi-square for each grouping and the probability 

 of obtaining a worse fit by chance for the total 

 chi-square. It is apparent that the hypothesis of 

 logarithmic distribution cannot be rejected. 6 



• The relationship of the logarithmic series to the negative binomial is 

 discussed (p. 155 and appendix A). Derivation of the logarithmic series 

 and some of its mathematical properties are presented in appendix C. 



NUMBER OF SKATE 

 Figure 3. — Number of tows, number of common skate, and the fitted binomial distribution. 



