IDENTIFICATION OF STOCKS OF BRISTOL BAY SOCKEYE SALMON, 



ONCORHYNCHUS NERKA, BY EVALUATING SCALE PATTERNS 



WITH A POLYNOMIAL DISCRIMINANT METHOD^ 



Rodney C. Cook^ and Gary E. Lord^ 



ABSTRACT 



A polynomial discriminant method is developed for the racial classification of stocks of sockeye salmon. 

 The method is based upon the nonparametric estimation of the multivariate probability densities of the 

 scale characteristics for each stock considered. Errors in classification are examined and a correction 

 procedure is extended to the n-class case. As an example, sockeye salmon of age 2.2 sampled on the high 

 seas are classified to river of origin based on freshwater scale growth patterns. Also, freshwater and 

 marine scale characters are evaluated for stock identification purposes involving certain Bristol Bay 

 runs. 



Racial analysis of high-seas salmon has important 

 applications both in life history studies of various 

 stocks and in management considerations of these 

 stocks. As a result, many have examined the 

 characteristics of scale structure to differentiate 

 salmon subpopulations. Konovalov (1971) notes 

 that some investigators were ignoring many 

 characteristics in scale structure which arise 

 under the effects of ecological factors in specific 

 bodies of water. When the ecological conditions 

 affecting scale characters are seriously consid- 

 ered, statistically significant differences between 

 subpopulations can often be found. The ability to 

 recognize salmon subpopulations depends upon 

 the differences between the stocks in terms of 

 examined characteristics and the accuracy of the 

 analytic technique. Various discriminant function 

 analyses have been traditionally used. 



Fukuhara et al. ( 1962), Amos et al. ( 1963), and 

 Dark and Landrum (1964) used linear discrimi- 

 nant functions based upon morphological charac- 

 teristics to identify the continent of origin of 

 Pacific salmon. Scale characteristics and linear 

 discriminant functions were used by Anas (1964) 

 and Mason (1966). Anas and Murai (1969) used 

 linear and quadratic discriminant functions. Re- 

 cent investigations by Major et al. ( 1975) and Bil- 

 ton and Messinger (1975) used unspecified dis- 



'Contribution No. 478, College of Fisheries, University of 

 Washington, Seattle, Wash. 



^Fisheries Research Institute, University of Washington, 

 Seattle, WA 98195. 



^Applied Physics Laboratory, University of Washington, Seat- 

 tle, WA 98195. 



criminant function techniques, probably similar 

 to those of Anas and Murai ( 1969). These and other 

 studies show the utility of discriminant function 

 methodology for identifying races of Pacific salm- 

 on. 



Salmon managers need a flexible and easily im- 

 plemented stock identification technique. This 

 paper applies a generalized discriminant function 

 technique to measurements of sockeye salmon 

 scales to attempt to fulfill this need. 



DISCRIMINANT FUNCTION 



ANALYSES OR 

 PATTERN RECOGNITION'' 



Discriminant function analysis depends on the 

 recognition of underlying patterns differing 

 among classes of objects. In this case, scale pat- 

 terns characterize a sockeye salmon of a particular 

 origin. A set of p-scale characters (a p-tuple or 

 vector in p-space) measured on an individual 

 salmon provides a description of that salmon. A 

 sample of p-tuples for a number of salmon from one 

 origin (the learning sample) establishes a region 

 in p-space characteristic of that class of sockeye. 

 Samples from salmon of different and known ori- 

 gins establish regions in p-space which may be 

 separated by decision surfaces. A sockeye salmon 

 of unknown origin may be classified according to 

 which region its p-tuple occupies. The accuracy of 

 classification depends upon the precision with 



Manuscript accepted November 1977. 

 FISHERY BULLETIN: VOL. 76. NO. 2. 1978. 



"A good text on pattern recognition is given by Patrick ( 1972). 

 A review of the literature is given by Das Gupta (1973). 



415 



