Jagielo et al.: Demersal groundfish densities in trawlable and untrawlable habitats off Washington 



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that it is relatively more difficult (i.e. more dive sites are 

 required) to detect density differences between habitats for 

 tiger rockfish, as compared to flatfish. The associated power 

 curves for these two values of cf are illustrated in Figure 6. 

 Figure 6 suggests that, given our observations (for values 

 of c? as low as 1.1), a sample size guideline of approximately 

 15 submersible dive sites in each habitat type would yield 

 approximately an 80% chance of detecting a difference in 

 mean density at least as large as the random noise esti- 

 mated in the data for a similarly designed study. 



Our statistical power analysis also indicated that, when 

 the relative proportions of untrawlable and trawlable habi- 

 tat, as well as the variability in the trawl survey estimates 

 of abundance, are taken into consideration, the problem of 

 estimating the trawl survey habitat bias can require sub- 

 stantially more samples than would be required simply 

 to compare the density differences between two habitat 

 types. Values of the trawl-survey habitat-bias effect size- 

 index (c?^), calculated for a range of untrawlable habitat 

 proportions with empirical trawl and submersible survey 

 data, are given in Table 10 and are plotted for rockfish and 

 flatfish in Figure 7. Using the calculated values of d^ from 

 Table 10, we derived sample size guidelines for rockfish and 

 fiatfish (at power=0.80, a=0.05). The resulting relationship 

 between the sample size required to estimate the trawl 

 survey habitat bias (the «=number of submersible dive 

 sites in each habitat type) and the proportion of untraw- 



lable habitat in a management area (A^/A) is illustrated 

 in Figure 8. If, for example, the area of untrawlable habitat 

 represented 20% of a management unit. Figure 8 indicates 

 that the sample size required to estimate the trawl survey 

 habitat bias would be « = 31 for rockfish (d^=0.73), and n = 

 9 for flatfish (c/^=1.41). Sample sizes for lingcod were much 

 higher (n>100), owing to the comparatively small detectible 

 effect size required (d(,=0.13). 



Discussion 



Our study successfully obtained a first look at the variabil- 

 ity in groundfish densities in trawlable and untrawlable 

 habitats for a study area off Washington. We also developed 

 a framework to use these types of observations to derive 

 sample size guidelines for designing larger-scale studies 

 to estimate the trawl survey habitat bias. The limited geo- 

 graphic scope of our study precludes extrapolation of our 

 specific results to the west coast at large. However, we dem- 

 onstrated an approach that can be used to establish sample 

 size guidelines for future work by illustrating the interplay 

 between statistical sampling power and 1) habitat-specific 

 density differences, 2 ) variance of density estimates, and 3) 

 the proportion of untrawlable area in a habitat. 



In our study area, we observed striking differences in 

 species composition and fish density between the traw- 



