size of alewife runs and area of lakes ac- 

 cessible to them. 



The large sockeye salmon run of I960 to 

 Bristol Bay (Ossiander, 1966,^ table 2) led to 

 extensive studies by the Bureau of Commer- 

 cial Fisheries and the Fisheries Research 

 Institute (University of Washington, Seattle) to 

 study the relation of the I960 escapennent to 

 its fresh- water environnnent. Data reported by 

 Burgner, DiCostanzo, Ellis, Harry, Hartman, 

 Kerns, Mathisen, and Royce (1969) indicate 

 that for three of the major stream-lake sys- 

 tems (Wood River, Kvichak River, Naknek 

 River), the spawners seldom if ever fully use 

 all of the available gravel. The limiting factor 

 to survival is thus most likely the capacity of 

 nursery lakes for juvenile salnnon; this idea is 

 supported by a comparison of lake areas and 

 average sockeye salmon runs (table 1). No sta- 

 tistical analysis is required to see the close 

 relation; the ranks of areas and runs are iden- 

 tical for all except the two sn-iallest systems. 



The above data support the idea that the 

 size, or area, of nursery lakes limits the 

 capacity of each stream-lake system to pro- 

 duce sockeye salmon smolts (the direct linnit- 

 ing factor is probably something related to 

 area, such as food supply, rather than space 

 itself). Under such circumstances one would 



TABLE 1. — Bristol Bay lake systems, ranked by 

 total lake area, and mean returns of sockeye 

 salmon, 1959-58. Areas from Burgner et al. 

 (1969); returns from Fred in et al. (1968)^ 



Lake system 



Area 



Return 



Sq. km. Thousands of fish 



Kvichak 2, 889 9, 867 



ifeegik 1,132 2,394 



Naknek 790 1, 884 



Wood 425 1,680 



Ugashik 385 1,016 



Branch or Alagnak. 297 585 



Nuyakak 279 194 



Igushik 74 456 



^ Fredin, R. A., S. Pennoyer, K. R. Middle- 

 ton, R. S. Roys, S. C. Smedley, and A. S. 

 Davis. 1968. Information on recent changes in 

 the salmon fisheries of Alaska and the condi- 

 tion of the stocks. U.S. Bur. Commer. Fish, 

 and Alaska Dep. Fish Game, 151 pp.; App. 1-9 

 pp. text, [55] pp. tables; App. II-[l] p.; 

 App. III-[4] pp. figs.; [2] pp. refs. 



""^ Ossiander, Frank J. (editor). 1966. Bristol Bay red 

 salmon forecast of run for 1966. Alaska Dep, Fish Game, 

 Juneau, Inform. Leafl. 82, 44 pp. (Processed.) A manu- 

 script version of Informational Leaflet 82 (showing per- 

 centage age compositions omitted from the processed 

 version) also was used in preparing the present report. 



expect a curvilinear relation between escape- 

 ment and return numbers to approach some 

 asymptote related to nursery lake capacity. 

 The actual points of such regression, how- 

 ever, are affected by so n-iuch extraneous 

 variability that no specific type of curve can 

 be discerned. As a first approximation, I de- 

 cided to use a relation consisting of two 

 straight lines. This type of curve is included 

 in Ricker's (1954) general treatment of repro- 

 duction curves, and he later suggested its 

 possible use for sockeye salmon (Ricker, 1958). 

 Data from the Naknek River demonstrate the 

 birectilinear regression systenn (fig. I). One 

 straight line, to the left of the regression dia- 

 gram, has a slope depending on the dennon- 

 strated relation between escapement and re- 

 turn for the smaller escapements. The other 

 is a horizontal line representing the capacity 

 of the nursery lake(s). Several of the regres- 

 sion plots for stream-lake systenns of Bristol 

 Bay confornn reasonably well with the birecti- 

 linear relation (figs. 2-11). 



COMPARISON WITH OTHER TYPES OF 

 CURVES AND METHODS OF CURVE FITTING 



The right-hand limb of the escapement- 

 return curve may possibly decline after reach- 

 ing a maximum, as in the recruitment curves 

 of some marine fishes. Ossiander (1967) 

 made this assumption in the modified Ricker 



spoOr 



u. 4000 



in 3,000 



o 



X 



<^ 2.000 



1,000 - 



500 1,000 1.500 2,000 2,500 



ESCAPEMENT ( THOUSANDS OF FISH) 



Figure 1. — Regression' of return on escapement. Data on 

 Naknek River sockeye salmon are used to show the parts 

 of the curves (fitting methods are described later in the 

 text) where return might be limited by size of escape- 

 ment and by lake capacity. 



Ossiander, Frank J. (editor). 1967. Bristol Bay red 

 salmon forecast of run for 1967. Alaska Dep. Fish Game, 

 Juneau, Inform. Leafl. 105, 51 pp. (Processed.) 



