LENARZ and ADAMS: SOME STATISTICAL CONSIDERATIONS OF TRAWL SURVEYS 



Table 7. — Estimates of mean densities id) (in numbers per kilometer), k, standard errors, with chi-square 

 goodness of fit tests for trawl catches by depth strata in the Queen Charlotte survey. 



Insufficient nonzero elements to perform chi-square test. 

 ^Randomly distributed, fc -*^. 



P<0.01). Although the rockfish species tended to 

 be aggregated, the group covers a wide range of 

 spatial patterns. 



In sampling from a negative binomial distribu- 

 tion, the precision of a density estimate for any 

 given population depends both on the properties of 

 the population, its density id) and degree of 

 aggregation ik), and on the characteristics of 

 sampling, sample size (n) and the sample ele- 

 ment size (S) (tow length). By modifying the 

 sample characteristics, one can modify the preci- 

 sion of estimates. 



Taylor (1953) showed in his Appendix E that 

 reducing sample element size ( length of the trawl ) 

 was the optimal sampling strategy under the 

 condition that the total sampling area remained 

 constant. That is, if A = area of strata (which is 

 constant over all strata, i.e., Aj = A 2 = A3 ...), 



a = area of the sampling element, and n = the 

 number of samples taken in each stratum, then 

 the value (a/A )n is fixed. Therefore, by reducing 

 the length of tow, there must be a corresponding 

 increase in the number of tows. However, in the 

 body of his paper, Taylor implies that it would be 

 advantageous to reduce sample element size even 

 with a constant number of samples. His argument 

 is based on the relationship between the mean and 

 variance for a negative binomial population ( Vnb^ ) 



Y 



nb-i 



m + m' Ik. 



The argument is that as m is reduced by some 

 factor 176, then Vnbg would only be 



V. 



nbf 



mlb + {mlbf Ik. 



669 



