The values of k were used in the probability distribution function, 



P = ( B + x - 1)! R* m 



X x! (2- 1)1 * -& (2) 



where R = p/q 

 P = x/B 



q = 1 + p 



to calculate the expected frequency of samples containing x organisms 

 (P ) . A chi-square statistic: 



X 2 = (Fx - P y ) 2 (3) 



P x 

 where F x = actual frequency of x organisms 



was used to test the fit of the actual catch distribution against a 

 negative binomial. 



The adequacy of the trawl program was determined by transforming 

 the catch (ln(catch + k/2)) and using the pooled variances to determine 

 the number of samples required to detect specified changes in the means. 

 Typically, testing for differences between arithmetic means requires a 

 simple subtraction: 



Ho: ul-u2=0 vs Ha: yl-p2=d 



For In transformed data this specified difference (d) is the ratio of 



the geometric means (R) or d=ln(R). The following analysis of variance 



model: 



log e (catch + £/2) = X + YR + MO + YR*MO + STA +YR*STA + (4) 

 STA*MO + YR*MO*STA + e 



was used to estimate the variances associated with each main and crossed 

 effect. These were pooled to produce an estimate of the underlying variance, 



