454 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



associated with change in length of the fish; 

 but in the pink salmon this association is much 

 weaker, only about 12 to 16 percent. 



The two combined regression lines for number of 

 eggs on length and on weight of the fish in figures 

 3 and 4 of Foerster and Pritchard (1941, pp. 

 58, 59) obviously have much steeper slopes than 

 the regressions for the individual years, showing 

 that these lines do not represent the regressions 

 within years. Since the mean annual lengths of 

 the fish varied in the same direction as the average 

 number of eggs, these combined lines represent 

 chiefly regression between years and are therefore 

 of no utility in predicting egg number for various 

 fish lengths within any individual year. 



As the relation between egg number and fish 

 length within any year appears to be so weak in 

 pink salmon, it is of interest to determine what 

 factor is controlling egg number. One factor for 

 which measurements are available is sea tem- 

 perature at Ketchikan, Alaska, which is just 

 across Dixon Entrance from Masset Inlet and 

 slightly east of it. To determine the role of sea 

 temperature we have made a covariance analysis 

 using the pink salmon data from McClinton 

 Creek, Masset Inlet, B. C, prepared by Foerster 

 and Pritchard (1941), as follows: 



The results of the test are as follows: 



Number of eggs 

 (Y) 



Correlations of Y with X's 



Standard regressions of Y on X's. 



Fish length | Sea tempera- 

 ture 

 (-ST.) I (ATj) 



0. 7801 

 0. 0310 



-0. 8692* 

 -0.8314' 



i?=0.8593 (N. S.) 

 Y=3.834 A'l - 115.616A'2-)-7,954 

 Standard error of 3's=0.21536 



t for p,, ,=0.83138/0.21536=3.860 

 P of .05=3.182. 



The relation between the average number of 

 eggs in McClinton Creek pink-salmon females 

 and the summer sea temperature at Ketchikan, 



with fish length held constant, is shown in figure 

 2. The correlation, r,2, of .Yi with X^ is —0.9011 

 and is statistically significant. Obviously, both 

 annual mean fish length and annual mean egg 

 number are negatively correlated with sea tem- 

 perature. The annual differences in mean egg 

 count in pink salmon are a function of sea tem- 

 perature, because it is the principal factor con- 

 trolling average fish length. 



1900 



1500 



54 55 56 57 58 



MEAN SEA TEMPERATURE JULY-SEPT 



Figure 2. — Relation of annual mean egg number of 

 McClinton Creek pink salmon, O. gorbuscha, (body 

 length held constant) to mean July-September sea 

 temperature at Ketchikan. 



The above analysis does not mean that the 

 regression between egg number and fish length 

 within years is invalid, but that the within- 

 years regression for the combined samples can 

 only be obtamed by reanalysis of the original 

 data to eliminate the portion of the total regres- 

 sion accounted for by regression between years. 



The problem of the relative effects of mean 

 annual size and sea temperature on egg number 

 for the sockeye salmon is complicated by the 

 effect of varying age at maturity which will be 

 discussed later. 



In addition to the between-years difference in 

 egg number at any particular length, there is also 

 the difference between rivers mentioned previously 

 in the case of the king salmon populations of the 

 Klamath and Sacramento Rivers. A better il- 

 lustration of this is perhaps afforded by the data 

 from Eguchi, Hikita, and Nishida (1954) on chum 



