COOK and LORD: IDENTIFICATION OF STOCKS OF SOCKEYE SALMON 



on was examined for each age-group with known 

 test groups. 



The degree of separation for age 1.2 sockeye 

 salmon is shown in Table 2. (Egegik River fish are 

 historically insignificant in this age-class.) The 

 scale characters providing this separation were: 1) 

 the circuli count to the first annulus, 2) the dis- 

 tance to the first annulus, 3) the distance from the 

 first to the second annulus, 4) the distance from 

 the second to the third annulus, 5) the circuli count 

 from the third annulus to the edge of the scale, and 

 6) the distance from the third annulus to the edge 

 of the scale. Ninety-five percent of the fish in the 

 test group were correctly classified. 



The degree of separation for age 2.2 sockeye 

 salmon is shown in Table 3. The scale characters 

 providing this separation were: 1) the circuli count 

 to the first annulus, 2) the distance to the first 

 annulus, 3) the circuli count from the first to the 

 second annulus, 4) the distance from the second to 

 the third annulus, 5) the distance from the third to 

 the fourth annulus, and 6) the circuli count from 

 the fourth annulus to the edge of the scale. 

 Seventy-seven percent of the fish in the test group 

 were correctly classified. 



Thus, the polynomial discriminant method can 

 provide adequate separation with a given data 

 base. The data collected for growth studies provide 

 good separation in some cases. Sockeye salmon 

 from the Egegik, Kvichak, and Naknek Rivers are 

 distinguishable in terms of these scale measure- 

 ments and it should be possible to estimate their 

 relative proportions in catch samples. 



Table 2 . — Results of the polynomial discriminant method on 1 . 2 

 age Bristol Bay sockeye salmon from 1973. The a priori prob- 

 abilities were 0.52 and 0.48 for the Kvichak and Naknek River 

 classes, respectively. 



T.\BLE 3. — Results of the polynomial discriminant method on 2.2 

 age Bristol Bay sockeye salmon from 1973. The a priori prob- 

 abilities were 0.342, 0.330, and 0.328 for the Egegik, Kvichak, 

 and Naknek River classes, respectively. 



COMMENTS AND CONCLUSIONS 



The key to successful implementation of the 

 polynomial discriminant method is the choice of 

 scale characters that reflect differences between 

 the subpopulations of concern. The scale charac- 

 ters that are most likely different are those that 

 are formed when the populations are geographi- 

 cally separated. Genetic and environmental 

 influences on scale formation probably interact to 

 create these differences. Although it is likely that 

 no single characteristic will provide the required 

 separation, a group of characteristics analyzed 

 with multivariate techniques ( e.g. , the polynomial 

 discriminant method) will often provide this re- 

 quired separation. The polynomial discriminant 

 function technique requires no consideration of 

 the underlying probability density functions for 

 these scale characters because these density func- 

 tions are estimated nonparametrically. Once the 

 characters that provide the best separation are 

 determined (by rank order comparison procedures 

 in this paper) the discriminant function analysis 

 may be implemented. 



A learning sample is needed to calculate the 

 discriminant function for each subpopulation. 

 These fish comprising these samples must be col- 

 lected before or after the populations intermingle 

 (either as smolts or returning adults in the respec- 

 tive rivers). Learning samples must be taken from 

 the same year class and freshwater age-group as 

 the unknown (mixed) population if the scale 

 characters are known or thought to vary from year 

 to year. Using Specht's (1966) algorithm and the 

 data from these learning samples, the coefficients 

 in the discriminant functions are calculated. The 

 next step is to appraise the effectiveness of these 

 polynomial discriminant functions. 



By classifying a group of test samples the pro- 

 portion of correctly identified fish and the clas- 

 sification error rates can be determined. The pro- 

 portion of correctly identified fish will likely be low 

 until a good set of a priori probabilities is deter- 

 mined. As the a priori probabilities are adjusted to 

 balance the classification error rates, the propor- 

 tion of correctly identified fish will generally in- 

 crease. The proportion of correctly identified fish, 

 when the classification error rates are satisfactor- 

 ily balanced, gives an indicator of the effectiveness 

 of the polynomial discriminant method. The clas- 

 sification error rates specific to these final a priori 

 probabilities are now estimated so that they may 

 be corrected for when the polynomial discriminant 



421 



