469 



Abstract— Population assessments 

 seldom incorporate habitat informa- 

 tion or use previously observed dis- 

 tributions of fish density. Because 

 habitat affects the spatial distribution 

 offish density and overall abundance, 

 the use of habitat information and 

 previous estimates offish density can 

 produce more precise and less biased 

 population estimates. In this study, 

 we describe how poststratification can 

 be applied as an unbiased estimator 

 to data sets that were collected under 

 a probability sampling design, typi- 

 cal of many multispecies trawl sur- 

 veys. With data from a multispecies 

 survey of juvenile flatfish, we show 

 how poststratification can be applied 

 to a data set that was not collected 

 under a probability sampling design, 

 where both the precision and the bias 

 are unknown. For each of four spe- 

 cies, three estimates of total abun- 

 dance were compared: 1) unstratified; 

 2) poststratified by habitat; and 3) 

 poststratified by habitat and fish den- 

 sity (high fish density and low fish 

 density) in nearby years. Poststrati- 

 fication by habitat gave more precise 

 and (or) less design-biased estimates 

 than an unstratified estimator for all 

 species in all years. Poststratification 

 by habitat and fish density produced 

 the most precise and representative 

 estimates when the sample size in the 

 high fish-density and low fish-density 

 strata were sufficient (in this study, 

 Ha20 in the high fish-density stratum, 

 na9 in the low fish-density stratum). 

 Because of the complexities of statis- 

 tically testing the annual stratified 

 data, we compared three indices of 

 abundance for determining statisti- 

 cally significant changes in annual 

 abundance. Each of the indices closely 

 approximated the annual differences 

 of the poststratified estimates. Selec- 

 tion of the most appropriate index was 

 dependent upon the species' density 

 distribution within habitat and the 

 sample size in the different habitat 

 areas. The methods used in this study 

 are particularly useful for estimating 

 individual species abundance from 

 multispecies surveys and for retro- 

 spective studies. 



Manuscript submitted 28 December 2001 

 to the Scientific Editor's Office. 



Manuscript approved for publication 

 31 March 2005 by the Scientific Editor. 



Fish. Bull. 103:469-488 (2005). 



Using poststratification to improve 



abundance estimates from multispecies surveys: 



a study of juvenile flatfishes 



Sherri C. Dressel 



Brenda L. Norcross 



Institute of Marine Science 



School of Fisheries and Ocean Sciences 



University of Alaska Fairbanks 



245 O'Neill Building 



Fairbanks, Alaska 99775-7220 



Present Address (for S C Dressel): Alaska Department of Fish and Game 



Commercial Fisheries Division 



802 3rd Street 



P.O. Box 240020 



Douglas, Alaska 99824-0020 

 E-mail address (for S C. Dressel): shern_dressel(S ) fishgame. state. ak. us 



Scientists must be able to assess popu- 

 lation abundance with a high degree 

 of confidence to achieve the goals of 

 fishery management (Quinn, 1985). 

 To do this, survey designs and esti- 

 mation methods that minimize the 

 variance in estimates of abundance 

 are needed. Recently, the National 

 Research Council (NRC, 2000) rec- 

 ommended incorporating habitat 

 information and commercial fisher- 

 ies data in population assessments. 

 Both of these data may result in lower 

 variances in estimates of abundance. 

 Habitat type and habitat quality 

 are becoming more widely recognized 

 as primary determinants for the dis- 

 tribution and survival of marine fish 

 species (Murawski and Finn, 1988; 

 Gadomski and Caddell, 1991; Reichert 

 and van der Veer, 1991; Norcross et 

 al., 1999). Until recently, however, 

 few studies have been directed to- 

 ward defining fish habitat or using 

 habitat associations to help decrease 

 the variability in abundance estima- 

 tion (Scott, 1995). In response to the 

 growing recognition of the importance 

 of habitat, the Magnuson-Stevens 

 Fishery Conservation and Manage- 

 ment Act was amended in 1996 (Pub- 

 lic Law 104-297) so that the National 

 Marine Fisheries Service (NMFS) and 

 regional fishery management councils 

 must describe and identify essential 



fish habitat (EFH) for managed spe- 

 cies. Similarly, a recent report from 

 the NRC calls for methods that link 

 environmental data to stock assess- 

 ments (NRC, 2000). 



Poststratification can be used in a 

 number of different ways to address 

 the NRC recommendations. Although 

 poststratification is not a new statisti- 

 cal method, it is one that is not com- 

 monly used for estimating ground- 

 fish population abundance and can 

 be used to meet these newly defined 

 challenges. In contrast to a stratified 

 sampling design, poststratification 

 is a method that allocates samples 

 to strata after they have been col- 

 lected. As a result, habitat data col- 

 lected during a survey can be used 

 for stratification. When poststratifi- 

 cation is applied to data that have 

 been collected under a simple random 

 sampling design, the poststratifica- 

 tion estimator is unbiased and may 

 produce more precise estimates than 

 those from a simple random sampling 

 estimator. Poststratified estimates 

 will be nearly as precise as strati- 

 fied sampling with proportional al- 

 location, in which the sample sizes 

 in each stratum are proportional to 

 stratum sizes, if stratum sample sizes 

 are large (rc>20) and errors in esti- 

 mates of strata areas are negligible 

 (Cochran, 1977; Pollock et al., 1994; 



