Dressel and Norcross: Using poststrafication to improve abundance estimates from multispecies surveys 



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Because this study is an observational study 

 with haphazard sampling, the precision and 

 bias cannot be directly assessed. Instead, we 

 estimated and compared the precision by using 

 unstratified and poststratified estimators. We 

 qualitatively estimated the relative amount of 

 design bias (i.e., how representative the esti- 

 mates are) with the use of habitat. In previ- 

 ous studies (Norcross et al., 1995; 1997; 1999), 

 depth and sediment were identified as habitat 

 characteristics closely associated with the dis- 

 tribution of the four species in this study. From 

 depth, sediment, and fish abundance data col- 

 lected in this study we were able to identify 

 ranges of habitat characteristics associated 

 with areas of high, low, and no fish density. 

 By estimating the proportion of area (km 2 ) in 

 the study area characterized by the ranges of 

 depth and sediment, it was possible to estimate 

 the proportion of the survey area with high, 

 low, and no fish density. Because samples in 

 our study were not randomly allocated, the 

 probability of selection was not equal among all 

 samples in the survey area. The resulting num- 

 bers of samples taken in areas of high, low, and 

 no fish density were not in proportion to the 

 size (km 2 ) of those areas as it would have been 

 with repeated simple random sampling. There- 

 fore, by comparing the relative size of high, low 

 and no fish-density areas in the survey area 

 with the relative number of samples in those 

 areas, we made qualitative estimates of the design bias 

 associated with the estimators. Although an assessment 

 of the relative amount of design bias made in this way is 

 only an approximation, it is helpful when using haphaz- 

 ardly collected data in order to provide some indication 

 of the amount of design bias based on the disproportion 

 of samples in an area to the size of that area. 



Because of the complexities of statistically testing the 

 annual stratified data, the second goal of our study was 

 to develop indices of abundance that closely approximat- 

 ed the annual differences of poststratified estimates and 

 that could easily be tested for statistically significant 

 changes between years. To achieve the second objective, 

 three indices of annual relative abundance were con- 

 structed and compared with respect to their estimated 

 relative precision and design bias: one from all sites in 

 the survey area, one from all sites within the species' 

 habitat, and one from all sites within an area of high 

 fish density within the species' habitat. 



The data for this study were obtained from six years 

 of juvenile groundfish surveys conducted in Kalsin Bay 

 and Middle Bay, Kodiak Island, Alaska. The four spe- 

 cies studied were age-0 rock sole (Lepidopsetta spp.), 

 age-1 yellowfin sole (Pleuronectes asper), age-0 Pacific 

 halibut (Hippoglossus stenolepis), and age-0 flathead 

 sole (Hippoglossoides elassodon). The survey data were 

 collected during the six-year survey under three dif- 

 ferent survey designs, none of which were strictly ran- 

 domized, but each involved some degree of haphazard 



Study area 

 Alaska. 



Figure 1 



(in black) in Middle and Kalsin Bays, Kodiak Island, 



sampling due to weather, sediment structure, and other 

 logistical restrictions for beam trawling in small bays 

 off the Gulf of Alaska (Norcross et al. 3 ). Although many 

 trawl survey data sets to which these methods could be 

 applied are collected under a probability sampling de- 

 sign where the estimator is unbiased, the haphazardly 

 collected data set used in our study was chosen to show 

 how poststratification can be applied when both the pre- 

 cision and the bias of the estimator are unknown. 



Methods 



Sampling 



Middle and Kalsin Bays are part of Chiniak Bay, 10 nmi 

 south of the town of Kodiak, Alaska. The total size of 

 the study area, 87 km 2 , included the combined areas of 

 both bays and the areas directly outside the mouths of 

 the bays (Fig. 1). Middle Bay is 8 km long and has depths 

 of 50 m at the mouth of the bay and an area of 21 km 2 . 

 Kalsin Bay is 8 km long, has depths greater than 100 m 



3 Norcross, B. L., B. A. Holladay, A. A. Abookire, and S. C. 

 Dressel. 1998. Defining habitats for juvenile groundfishes 

 in Southcentral Alaska with emphasis on flatfishes. Vol. I, 

 Final Study Report, OCS Study MMS 97-0046, 131 p. Coastal 

 Marine Institute, Univ. Alaska Fairbanks, Fairbanks, AK 

 99775. 



