In conclusion, there is considerable evidence that yellowfin tuna 

 are not randomly distributed in space but rather are aggregated. This 

 is indicated by the distribution of hooked yellowfin along a longline., and 

 by the great variability of longline yellowfin catches when contrasted 

 with longline black marlin catches. This apparent tendency to aggregate 

 must be taken into consideration when approaching a statistical treat- 

 ment of yellowfin tuna catches made by the longline. 



TRANSFORMATION OF THE CATCHES FOR ROUTINE 



STATISTICAL TESTS 



In order to apply routine statistical procedures, such as analysis 

 of variance, to enumeration data of the type obtained by longline fish- 

 ing for yellowfin tuna, several conditions must be met (Barnes 1952). 

 The most important of these are normality of the distribution and in- 

 dependence of the mean and standard deviation. These conditions obtain 

 if the event under study (catching a yellowfin) has a high enough probabil- 

 ity of occurrence and a random distribution. The catch rates of yellow- 

 fin tuna are of a magnitude to suggest a Poisson distribution, but the 

 presence of schooling or aggregation, previously demonstrated, results 

 in too many extremely low or extremely high values to fit a Poisson 

 distribution (Quenouille 1949, Barnes and Marshall 1951). Under these 

 circumstances a distribution such as the negative binomial more nearly 

 fits the data, and the catches must be transformed prior to the applica- 

 tion of statistical tests. 



The need for transformation of longline yellowfin catches is indi- 

 cated graphically in figure 2. These catches show a linear relation be- 

 tween the mean and the standard deviation. In order to overcome this 

 difficulty two seemingly appropriate transformations were tested on 

 these data. The first transformation was based on the assumption that 

 the catch rates fit a negative binomial in which the distribution of schools 

 follows a Poisson form and that of the catches from schools a logarithmic 

 form (Quenouille 1949)o Our procedure follows the methods described 

 by Anscombe (1949). This requires estimating a value of k common to 

 the eight distributions by fitting successive values of k into the formula: 



T = (N -l)s^ - (N - 1-1 /k) 7(1 +7 1/k) 

 (FTW~ 



(N - number of items; s^ = sample variance; r" = average catch 

 per set). This trial and error process is continued until the sum of T 



