FISHERY BULLETIN: VOL. 80, NO. 4 



LAG (years) 



Figure 2.— An estimate of the autocorrelation functions for 

 northern California total salmon and crab catch data (Fig. 1). 

 Dotted lines are 0.05 error limits (see text). 



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Northern Salmon 

 i salmon catch lags 

 1 crab catch 

 . ! 1940-1976 



■10 



-5 



LAG (years) 



10 



Figure 3.— An estimate of the cross-correlation function be- 

 tween northern California total salmon and crab catch data 

 (Fig. 1). A positive lag corresponds to salmon following crab. 



but is essentially the same as the auto-correlation 

 of catch (i.e., decreases to significant negative 

 values at 4 and 5 yr, then increases to significant 

 positive values at 10 yr). 



The auto-correlation functions computed from 

 first-differenced crab and salmon catch series 

 have the same form but are lower in absolute 

 values. The first negative peak is just barely sig- 

 nificant in both, whereas the positive peak of 

 about 10 yr is significant only for the crab catch 

 series. 



An estimate of the cross-correlation between 

 total northern California salmon and crab catch 

 is of the form that would arise from two cyclic, 

 covarying processes with a period of 9 or 10 yr 

 and a constant lag of about 4 yr (salmon leading 

 crab) (Fig. 3). Decreasing amplitude of the cor- 

 relation function with increasing lag is caused by 

 the increasing amplitude of crab catch. The im- 

 plications of Figure 3 are that crab catch is nega- 

 tively correlated with salmon catch 1 or 2 yr later 

 and salmon catch is positively correlated with 

 crab catch 3, 4, and 5 yr later. 



The same cross-correlation computed for the 

 years for which crab abundance estimates are 

 available (1952-76) is essentially the same as Fig- 

 ure 3. The cross-correlation computed using pre- 

 season abundance instead of catch also is quite 

 similar. First-differencing all three cross-cor- 

 relation functions reduces the amplitude of the 

 function somewhat. The correlation at positive 

 lag is no longer significant and correlation at 

 negative lag is significant only at a lag of —5 yr 

 (except for first-differenced preseason abun- 

 dance which is not quite significant). The values 



of cross-correlation for the various versions of 

 these time series are summarized in Table 1. 



Northern California Catch by 

 Salmon Species 



Because of differences in life history between 

 the two species and the fact that increasing num- 

 bers of silver salmon originate in hatcheries, 

 comparison of the relative contributions of each 

 species to the cyclic covariation with crab could 

 provide a clue to the underlying cause. Neither of 

 the estimated auto-correlation functions for king 

 and silver salmon appear as cyclic as the auto- 

 correlation of combined salmon catch (Fig. 4). 

 From this figure king salmon appears somewhat 



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5 



00 



•0 5 



10 



4 6 



LAG (years) 



10 



Figure 4.— An estimate of the autocorrelation functions for 

 northern California king salmon and silver salmon catch data 

 (Fig. 1) for the years 1952-76. 



794 



