COOK and LORD: IDENTIFICATION OF STOCKS OF SOCKEYE SALMON 



-1 



U = C" R 



or 



Generally 



Since 



substitution yields u^ = 



Cii 



which is the correction formula of Worlund and 

 Fredin (1962) (except for differences in notation 

 and terminology) that has been used in many 

 two-class Pacific salmon stock identification 

 studies. 



Application to Sockeye Salmon Samples 

 Taken in High Seas Sampling 



A problem of interest to the nations bordering 

 the North Pacific Ocean is the origin of sockeye 

 salmon taken on the high seas. The rivers of origin 

 of sockeye salmon south of the central Aleutian 

 Islands in summer are of particular interest to the 

 United States since an index of their overall rela- 

 tive abundance is used to forecast the numbers of 

 mature fish returning to Bristol Bay in the follow- 

 ing year (Rogers 1975). These fish are primarily of 

 Bristol Bay origin (Hartt 1962, 1966; Hartt et al. 

 1975). Knowledge of the relative abundance of the 

 various runs of the Bristol Bay stock south of the 

 central Aleutians would be useful for forecast pur- 

 poses and might provide insight into the high seas 

 life history of the various runs. 



In order to recognize age 2.2 immature sockeye 

 salmon on the high seas in 1976, the freshwater 

 growth patterns of scales from three of the major 

 rivers in Bristol Bay were examined.® Scales from 

 the smolt outmigrations of 1974 for the Kvichak 

 and Naknek Rivers were used as learning and 



*Age designation indicates fish which migrated to sea after 

 two winters in freshwater and have spent two winters at sea. 

 They are expected to return from the ocean primarily at age 2.3, 

 or after sf)ending three winters at sea. 



testing samples. For the Egegik River scales from 

 age 2.2 adult fish returning to spawn in 1976 were 

 used as learning and testing samples because 

 smolt scales were unavailable. The freshwater 

 scale patterns offish from these runs were used to 

 classify the sockeye salmon captured south of 

 Adak Island during summer 1976 after having 

 spent two winters in the ocean. 



The scale patterns were examined under a mi- 

 croprojector of the type described by Dahlberg and 

 Phinney (1968). The widths of the summer, 

 winter, and plus growth zones were measured in 

 terms of circuli counts and distance. The width of 

 the widest circulus was also measured. Each scale 

 character was then ranked over all classes (rivers) 

 and the Kruskal-Wallis statistic (Kruskal and 

 Wallis 1952) calculated. The difference between 

 the average sum of ranks for each pairwise class 

 combination was also calculated. On the basis of 

 these statistics the scale characters providing the 

 best univariate separation were selected for use in 

 the polynomial discriminant method. Highly de- 

 pendent scale characters were not used. 



By examining the learning samples, six scale 

 characteristics were chosen for use in the polyno- 

 mial discriminant method: 1) The number of the 

 circuli in the first winter growth zone, 2) the 

 number of circuli in the second summer growth 

 zone, 3) the number of circuli in the plus growth 

 zone, 4) the width of the first summer growth zone, 



5) the width of the second winter growth zone, and 



6) the width of the widest circulus.® Learning 

 sample sizes of 25, 25, and 24 for the Egegik, 

 Kvichak, and Naknek River classes, respectively, 

 were used to calculate the coefficients in the 

 polynomial function for each class. The classi- 

 ficatory ability of these functions was then tested. 



The relative test sample sizes for each class were 

 determined by examining run size data. According 

 to the average run sizes of age 2.3 salmon for the 

 last 8 yr approximately equal numbers offish from 

 each class were expected to occur in the unknown 

 sample. However, since the Kvichak River test 

 sample size was twice that of the Egegik or Nak- 

 nek River sample size, the fish in the latter test 

 samples were given a weight of 2 when the a priori 



'It should be mentioned that all data points were "nor- 

 malized." That is, the mean and standard deviation for each scale 

 character were calculated from the learning samples (all 

 categories combined). All data points were then transformed by 

 subtracting off" the mean and dividing by the standard deviation 

 for the appropriate scale character. This is done for numerical 

 purposes. 



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