152 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



large number of tows containing a small number 

 of species in these years. 



The improvement in agreement of the observa- 

 tions with hypothesis which occurs when the first 

 three tows are eliminated suggests that a dry net 

 does not fish efficiently. This may be true but, 

 on the other hand, the elimination of these tows 

 in the 1950 data makes practically no change at 

 all in the species-per-tow distribution. The trawl 

 data are being studied in an effort to find an ade- 

 quate explanation of the departure of species-per- 

 tow distribution from theory. 



It is evident that if we accept the hypothesis of 

 a Poisson distribution of species per tow, we have 

 a useful method of gauging the efficiency of the 

 sampling procedure. The data presented in tables 

 15 and 16 suggest that tows are present in the 

 data which ought to be rejected for purposes of 

 further analysis, provided an objective basis for 

 their rejection can be discovered. A Poisson dis- 

 tribution of the occurrence of species in tows also 

 provides means for further study of differences 

 between bottom types, depth zones, or other 

 environmental factors. 



USE OF CATCH DATA IN THE ANALYSIS OF VARI- 

 ANCE 



When the program for sampling fish popula- 

 tions on the fishing grounds was planned it was 

 anticipated that the technique of analysis of 

 variance could be applied to extract as much in- 

 formation as possible from the body of data to be 

 collected, and the sampling program was designed 

 with this technique in mind. A necessary condi- 

 tion, however, for a valid analysis of variance is 

 that there be a constant residual variance. If the 

 variance changes with the mean level, a suitable 

 transformation is necessary to stabilize the 

 variance. 



If the variance can be expressed as a function 

 of the mean m, it has been shown (Curtis 1943) 

 that the appropriate transformation may be 

 determined. 



In the early stages of the present analysis, it 

 was found that the standard deviation of the 

 catches per tow was approximately proportional 

 to the mean for many species. Typical examples 

 are presented in tables 10 and 11 and figures 5 

 and 6 for haddock and whiting catches. The 



O 10 20 30 40 50 60 70 80 90 100 

 MEAN 



Figure 5. — The mean and standard deviation of haddock 

 catches for the subareas and depth zones of Georges 

 Bank. 



relation between the standard deviation and the 

 mean may be expressed 



c =km. 



(4) 



where a x is the standard deviation of catches x 

 with the mean of x equal to m. 



It is shown by Bartlett (1947) that for any func- 

 tion g(x), we have approximately 



c g 2 =(dg/dm) 2 f(m) (5) 



so that if a 2 is to be constant, K 2 say, we must 

 have 



Kdm 



g(m)=j 



(6) 



From equations 4 and 6 we have: 



j(m) = a 2 =k 2 m 2 

 , , N C Kdm 



and 9{m n^m 



or g( m ) = {K/k) log m+C (7) 



where C is a constant introduced by integration. 



