method is applied to the unknown mixed sample. 

 This is done with the classification matrix correc- 

 tion procedure. 



First, the fish in the unknown mixed sample are 

 classified with the polynomial discriminant 

 method (using the adjusted a priori probabilities). 

 The proportions resulting for each subpopulation 

 and the decision matrix allow simple algebraic 

 solution for the estimated true proportions of the 

 various subpopulations in the zones of interming- 

 ling. 



Estimates of this type are often needed in par- 

 ticular management situations involving Pacific 

 salmon. By using scale samples and the polyno- 

 mial discriminant method, the proportions of the 

 major classes present in areas where the subpopu- 

 lations mix can be estimated. We have considered 

 only two possible applications in this paper: high 

 seas monitoring for predictive purposes and the 

 analysis of catch samples. Many other possibilities 

 exist for other situations and other salmon species: 

 the timing of inshore runs could be examined in 

 estuarine areas or in river systems, the continent 

 of origin of salmon on the high seas could be 

 examined (for those species or areas not already 

 analyzed), or the intermingling of hatchery and 

 native populations could be analyzed for certain 

 fisheries. Since scale samples are relatively easy 

 to collect and exchange and since computers are 

 readily available to do the necessary calculations, 

 the polynomial discriminant method is a flexible 

 and practical tool for the racial analysis of Pacific 

 salmon, particularly sockeye salmon. 



ACKNOWLEDGMENTS 



Many thanks are due to Colin Harris, Allan C. 

 Hartt, and Robert L. Burgner for their editorial 

 advice and guidance. We also wish to thank James 

 B. Scott for his meticulous work with the scale 

 data. Many others providing services to the deep 

 sea tagging project at the Fisheries Research In- 

 stitute deserve thanks. The scale samples and 

 data from the Bristol Bay river systems were col- 

 lected by the Alaska Department of Fish and 

 Game. We are grateful to Paul Krasnowski and 

 other Alaska Department of Fish and Game per- 

 sonnel for providing these vital samples. This re- 

 search was primarily supported by NOAA, Na- 

 tional Marine Fisheries Service, under Contract 

 No. 03-6-208-35470. The inshore stock separation 

 project was supported by the Alaska Department 

 of Fish and Game. 



FISHERY BULLETIN: VOL. 76, NO. 2 



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422 



