70 



60 



- 50 



X 

 10 



40 - 



z 

 o 



- 30 - 



3 



20 - 



10 > 



ACTUAL RETURN 

 "hindcast;' BI-RECTILINEAR 

 PUBLISHED FORECASTS 



_L 



J_ 



_L 



_L 



1958 



1959 



I960 



1961 



1962 



1963 



1964 



1965 



1966 



1967 



Figure 13. — Comparison of "hindcast" values and published forecasts with actual 

 Bristol Bay returns, 1958-67. 



SUMMARY 



1. A close relation between return and lake 

 size can be demonstrated for Bristol Bay 

 sockeye salmon runs. 



Z. A birectilinear recruitment curve can 

 be used to express the dependence of returns 

 on escapement size for small escapements 

 and on nursery lake capacity for large escape- 

 ments. 



3. The subjective features in fitting the 

 birectilinear curve can be eliminated by using 

 the Quandt "all possible breakpoint" approach. 

 This method is extremely laborious and pro- 

 duced results for the Naknek River not sig- 

 nificantly different from those obtained with 

 the fitting method used herein. 



4. Utility of the birectilinear curve in fore- 

 casting was studied by comparing "hindcasts" 

 with published forecasts and actual runs. The 

 coefficients of determination for hindcasts and 

 published forecasts were about the same (0.46 

 for the birectilinear; 0.39 for the published 

 forecasts). Recent improvements in published 

 forecasts have overcome the advantage of the 

 birectilinear approach for the small runs of 



1967-69; the issue remains unresolved for 

 larger runs such as those of 1960 and 1965. 



5. Use of estimated returns from the bi- 

 rectilinear curves with the "probability tree" 

 age allocations of Ossiander might provide a 

 valuable composite method. 



ACKNOWLEDGMENTS 



Reynold A. Fredin, Donald D. Worlund, 

 Richard C. Hennemuth, and Frank J. Ossiander 

 of the Bureau of Commercial Fisheries, and 

 Robert L. Burgner and Donald Rogers of the 

 Fisheries Research Institute of the University 

 of Washington reviewed my manuscript. Their 

 suggestions have resulted in substantial revi- 

 sions but they cannot be held responsible for 

 any errors of fact or interpretation. 



LITERATURE CITED 



BURGNER, ROBERT L. 



1964. Factors i n fl u e n c i n g production of 

 sockeye salnnon ( Oncorhynchus nerka ) 

 in lakes of southwestern Alaska. Verh. 

 Int. Ver. Limnol. 15: 504-513. 



