FISHERY BULLETIN: VOL. 76, NO. 2 



probabilities were adjusted. After adjusting the a 

 priori probabilities, we obtained the results given 

 in Table 1. The classification matrix was then es- 

 timated: 



C = 



0.800 0.040 0.167 

 0.080 0.740 0.208 

 0.120 0.220 0.625 



where the subscripts of the matrix elements ( c,^'s) 

 were 1, 2, and 3 for the Egegik, Kvichak, and 

 Naknek River classes, respectively. Seventy-two 

 percent of the fish in the test group were correctly 

 classified. The fish in the high seas sample were 

 then classified with the adjusted polynomial dis- 

 criminant method. 



Of the 101 sockeye salmon, 25 were classified as 

 Egegik River fish, 22 as Kvichak River fish, and 54 

 as Naknek River fish. The resultant vector was: 



Ru = 



0.267 

 0.222 

 0.511 



The estimated unknown vector was thus: 



C~' R.. = 



Based upon preliminary data for the 1977 Bristol 

 Bay sockeye salmon run from the Alaska Depart- 

 ment of Fish and Game, the actual unknown vec- 

 tor was: 



U 



0.325 

 0.061 

 0.614 



The classification matrix correction procedure 

 gave a slightly better estimate than the direct 

 results of the polynomial discriminant method. 

 The differences between the u, 's and the u , 's were 

 due to bias and variability. (We are presently 

 examining methods to reduce the variability of 

 our i/,'s.) 



A problem with the high seas sample is that 

 some of these sockeye salmon originate in rivers 

 other than those considered. Although the three 



Table l. — Results of the polynomial discriminant method on a 

 known test group of Bristol Bay sockeye salmon. The a priori 

 probabilities were 0.340, 0.332, and 0.328 for the Egegik, 

 Kvichak, and Naknek River classes, respectively. 



classes considered will account for nearly all of the 

 age 2.2 sockeye salmon bound for Bristol Bay, 

 some may be non-Bristol Bay fish. When the Bris- 

 tol Bay runs are at a low point in their cycle, up to 

 20% of the high seas sockeye salmon at Adak Is- 

 land may be non-Bristol Bay fish (Hartt et al. 

 1975). The possible bias from classifying the non- 

 Bristol Bay fish into the classes established should 

 be considered since 1977 is a low year in the sock- 

 eye salmon run cycle. 



In conclusion, the polynomial discriminant 

 method can be used to identify certain runs of 

 sockeye salmon on the high seas by differences in 

 freshwater scale growth patterns. Possibly the 

 relative proportions of sockeye salmon that will be 

 returning to inshore areas can be predicted. Even- 

 tually the method will be used to predict one year 

 in advance the relative run sizes to the major Bris- 

 tol Bay rivers by sampling these sockeye on the 

 high seas. 



Application to 

 Inshore Fishery Stock Separation 



A problem of interest to the Alaska Department 

 of Fish and Game is the separation of stocks in 

 commercial catches in inshore areas, particularly 

 the separation of Kvichak, Naknek, and Egegik 

 River sockeye salmon. The Division of Commer- 

 cial Fisheries is collecting data on scale measure- 

 ments for growth studies. They are interested in 

 how well these data and the polynomial discri- 

 minant method can separate Bristol Bay sockeye 

 salmon stocks. 



Scale data from samples of the 1973 spawning 

 escapement were examined. Each of two age- 

 classes was examined separately. Distance and 

 circuli counts to both the freshwater and saltwater 

 annuli were examined for use in the polynomial 

 discriminant method with the Kruskal-Wallis and 

 multiple comparison procedures. The accuracy of 

 classification for age 1.2 and age 2.2 sockeye salm- 



420 



