tuations in the percentages of smolts migrating 

 at age II, although the escapement levels vary 

 somewhat independently. The proportions of age 

 II smolts were at or below average for the 

 escapement years 1954, 1956, and 1958 in the 

 Naknek and Kvichak systems and for 1956 and 

 1958 in the Ugashik system (no data are avail- 

 able for Ugashik in 1954 and 1955). The per- 

 centages were above average in the three sys- 

 tems for the escapement years 1959 and 1960 

 (fig. 21). These concurrent fluctuations suggest 

 the influence of general climatic factors. 



RELATION BETWEEN RETURN AND ESCAPEMENT 

 FOR THE NUSHAGAK FISHING DISTRICT 



The relation between the numbers of adults 

 returning (catch plus escapement) and the 

 numbers in the parent escapement is of gen- 

 eral interest, though frequently the intermediate 

 statistic — numbers of smolts produced — is now 

 available. The longest series of return-escape- 

 ment data available is for the Nushagak fishing 

 district (Igushik, Snake, V^ood, and Nuyakuk 

 Rivers combined) for the escapements of 1946- 

 57 and the resulting returns (table 31 ) . 



Table 31. — Number of sockeye salmon in parent escapements 

 and resulting returns, Nushaaak district, 19i6-57 



Year of spawning 



Fish in parent 

 escapement 



Fish in 

 resulting return 



1946. 

 1947- 

 1948_ 

 1949. 

 1950. 

 1951. 

 1952. 

 1953. 

 1954. 

 1955. 

 1956. 

 1957. 



The return-escapement data from the Nusha- 

 gak district were used to calculate the recruit- 

 spawner relation (reproductive curves) of 

 Schaefer (1954), Beverton and Holt (1957), and 

 Ricker (1958). When the weighted sums of 

 squared deviations of the observed data from 

 each of the predicted curves were calculated, the 

 deviations were least from the curve derived 

 from Ricker's formula : 



R = aEe "^ 



where R = number of sockeye salmon in the re- 



z 

 o 



,55 

 REPLACEMENT LINE- 



STANDARDIZED RICKER 

 REPRODUCTION CURVE 



MODIFIED RICKER 

 REPRODUCTION CURVE 



I 2 3 4 5 6 



FISH IN PARENT ESCAPEMENT (MILLIONS) 



Figure 22. — Kelation between number of sockeye salmon 

 in return (catch plus escapement) and number in par- 

 ent escapement, Nushagak fishing district, 1946-57. 

 The number beside each point indicates the parent 

 escapement year. 



turn, E = number in the parent escapement, and 

 a and b are constants. For the Nushagak district 

 return-escapement data, a = 3.951 and b = 

 0.6269. The calculated curve and original data 

 for the Nushagak system are presented in figure 

 22. The estimated maximum yield is at the point 

 where a line parallel to the replacement line is 

 tangent to the curve — for the Nushagak district 

 this point corresponds to an escapement of about 

 900,000 fish. 



Addition of another parameter (n) to Ricker's 

 formula as follows 



R = aEe '•^" 



gives greater fle.xibility in fitting the data. This 

 modified version of Ricker's curve permits more 

 exact fitting of a reproduction curve to observed 

 data. 



For the Nushagak data the relation was 



R = 4.191Ee-° «''^''°'"° 



The modification also gives an estimated opti- 

 mum escapement of about 900,000. This curve is 

 essentially the same as the standardized curve 

 produced by the unmodified Ricker formula. 



Ricker's formula can also be used to study the 

 relation of return to potential egg deposition. 



448 



U.S. FISH AND WILDLIFE SERVICE 



