600 r 



1^00 



50 100 150 200 

 ESCAPEMENT (THOUSANDS OFFISH) 



2 50 



Figure 2. — Regression of return on escapement of Togiak 

 River sockeye salmon (brood years 1952-60) with fitted 

 birectilinear curve. Triangles indicate group means 

 within vertical broken lines; crosshatched area indi- 

 cates overlap of right-hand limb points with those used 

 in left-hand limb. Right-hand limb represents mean of 

 points to the right of indicated vertical line. Fitting 

 method is described in text. 



curve R = a E^'e""^ (where E is escapement; 

 R is return; a, b, and c are empirical con- 

 stants). In the present report, however, lam 

 proceeding on the simple assumption that lake 

 residence is the controlling point in the life 

 history of sockeye salmon and that control is 

 exerted as an upper asymptotic ceiling im- 

 posed by some factor related to lake size. 



Fitting the birectilinear curve by the group 

 mean method used herein had the undesirable 

 feature of being somewhat subjective; there- 

 fore it seemed useful to try an objective 

 method such as that of Quandt (1958), which 

 I applied to the Naknek River data. The "break" 

 occurred at about the same place as with the 

 group mean method. The slope of the right-hand 

 limb, when passed through the origin, was 

 3.47 compared with 3.80, and the difference 

 was not significant by the t test. Likewise 

 the slope of the right-hand limb did not differ 

 significantly from zero, and its mean (3126) 

 was not significantly different froin that of 

 the group mean fit (Z983). 



The Quandt method requires use of all pos- 

 sible "breakpoints" between the two straight 

 lines, which would involve calculating as many 

 as 24 separate regression lines for some 

 streams. In view of the lack of significantly 

 different results when I used this method on 



i/too 



o 800 



100 200 300 400 500 600 



ESCAPEMENT (THOUSANDS OF FISH) 



Figure 3.— Igushlk River, 1952-60 (see fig. 2). 



data from the Naknek River, I did not apply 

 the Quandt method to data from other streams. 



RETURN "HINDCASTS," 1958-67 



Some idea of the utility of the birectilinear 

 curves may be gained by comparing "hind- 

 casts" for a series of years with the recorded 

 returns for the same years. I have used data 

 from official documents to make this com- 

 parision for 10 recent years. 



Empirical Data 



I obtained data from a number of sources. 

 Escapements by stream system for 1944-63 

 were from Ossiander, 1967 (see footnote 2). 

 Returns by stream system for various brood 

 years in 1944-60 and total returns ("actual 

 runs") for 1958-67 were from Ossiander, 1966 

 (footnote 1), 1967 (footnote 2), and 1968.^ Esti- 

 mates of average age at return were from 

 Ossiander, 1966 (footnote 1). Published fore- 

 casts were from Royce (1961, 1962);"^'^ Tait 



Ossiander, Frank J. (editor). 1968. Bristol Bay red 

 salmon forecast of run for 1968. Alaska Dep. Fish Game, 

 Juneau, Inform. Leafl. 123, 14 pp. (Processed.) 



■^ Royce, William F. (editor). 1961. Forecast of Bristol 

 Bay red salmon run in 1961. Alaska Dep. Fish Game, 

 Memo. 1, 9 pp. + [12] pp. figs, and tables. (Processed.) 



' Royce, William F. (editor). 1962. Forecast of Bristol 

 Bay red salmon run in 1962. Alaska Dep. Fish Game, 

 Juneau, Inform. Leafl. 14, 23 pp. (Processed.) 



