LENARZ and ADAMS: SOME STATISTICAL CONSIDERATIONS OF TRAWL SURVEYS 



or 



Vj = {dS+(dSflk)lnS' 



V- = A + Jl 

 "^ nS nK 



(13) 

 (14) 



The standard error of the density is 



SEa = (^^-)V2 



\nS nK) 



(15) 

 (16) 



and the index of precision is 



Pj = id)l{dlnS + d^- /nkf' 

 = illdnS + llnky'^\ 



(17) 



From Equation (17), the precision of a density 

 estimate will decrease as the degree of aggrega- 

 tion increases (i.e., k -> 0). For the case when 

 k >> d, then the index approaches idnS)'' and 

 a unit increase in sample size and sample elemen_t 

 size are of equal importance. In the case of d 

 approximately equal to k then sample element 

 size has almost no effect on precision. When d >> 

 k, which is often the case for species that support 

 a commercial fishery, the index simplifies to 



Pa 



ink) 



1/2 



(18) 



In these cases, only sample size will affect 

 precision. 



More specific evaluation of sampling negative 

 binomial populations can be made by considering 

 the estimates of k for three rockfish species and 

 Equation (17). Since the limiting factor in these 

 surveys is usually ship time and not cost in a direct 

 sense, the evaluation is in terms of the most 

 efficient use of a ship day. The first two species 

 were the two target species in the Queen Charlotte 

 Sound survey: S. alutus, a high density, highly 

 aggregated species, and S. flavidus, a low density, 

 highly aggregated species. The third species was 

 S. aleutianus, a low density more randomly dis- 

 tributed species in Queen Charlotte Sound. 



The sampling plan in Queen Charlotte Sound 

 was to perform trawls of 0.5 h on the bottom which 

 covered an average of 2.80 km. The average 

 number of trawls per working day was 4.3. The 

 average working day was 13 h long. Assuming 0.5 

 h on the bottom per trawl and 4.3 trawls/d, then 

 the average nontrawling time per haul is 2.05 h. 

 The minimum nontrawling time per haul was 1.07 

 h. The current sampling plan calls for an average 

 of about 5 trawls/d. Using the above times, four 

 possible alternative strategies are: 1) 3 trawls/d 

 with gear at depth for 2.1 h, 2) 4 trawls/d with gear 

 at depth for 1.2 h, 3) 5 trawls/d with gear at depth 

 for 0.5 h, or 4) 6 trawls/d with gear at depth for 

 0.3 h. 



Using the four strategies, values for precision of 

 estimate of density were calculated for S. alutus, 

 S. flavidus, and S. aleutianus and are showm in 

 Figures 1, 2, and 3. The results of this analysis 

 follow directly from the result of the general 

 analysis. When the density to k ratio increases 

 above a critical level, precision is for all practical 

 purposes unaffected by changes in density. For the 

 more randomly distributed species (S. aleutianus) 

 the critical ratio occurs at higher density. For 

 more aggregated species (S. alutus, S. flavidus) 

 sample size (n) is not as effective in increasing 

 Pj in an absolute sense as in the less aggregated 

 species. Also, since sample size and sample ele- 

 ment size are inversely related and precision 

 increases with increased sample size except at 

 very low density, sample element size has little 

 effect on precision for these species except at very 

 low density Even for the less aggregated species, 

 sample element size has little effect on precision 

 except at low densities. 



For a fixed amount of sampling effort, the 

 precision of an estimate from a negative binomial 

 population is a result_of the interaction of popula- 

 tion factors, density ( d ) and degree of aggregation 

 ik); and sampling factors, sample size in) and 

 sample element size (S). Analysis of the results of 

 the Queen Charlotte Sound survey shows that 

 rockfish species have a wide range of possible 

 combinations of population factors. The analysis 

 of sampling strategies showed that the same 

 sampling plan could have been used for all three 

 species with no significant loss in precision. This is 

 due to the highly aggregated nature of rockfish 

 species. However, for other less aggregated species, 

 such as flatfishes, there would have been a greater 

 difference among sampling schemes. This empha- 

 sizes the importance of picking target species on 



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