BOTSFORD ET AL.: CYCLIC COVARIATION IN CALIFORNIA FISHERIES 



season that overlaps the crab season. In other 

 words, salmon catch should appear to be much 

 more cyclic early in the season than late in the 

 season. Salmon catch for the months of April 

 through June and the period from July through 

 September are shown in Figure 9. 6 The only 

 readily apparent feature of this plot is the in- 

 creasing trend of early season catch. 



Estimates of the auto-correlation functions of 

 early and late season salmon catch are shown in 

 Figure 10. Neither of these appears as smoothly 



*The same analysis as that presented here was performed 

 with a bisecting; date of 31 May rather than 30 June with no dif- 

 ference in the results. 



20 



I 5 - 



x 



I- 



< 



° I 



z 

 o 



< 



CO 



-i 0.5 - 



< 



00 



1 



Northern California 

  April - June 

 July- September 



I I 



50 



55 



60 



65 

 YEAR 



70 



75 



80 



Figure 9.— Total salmon catch (kg) in northern California in 

 the early part of the season (April-June) and the late part of the 

 season (July-September) for the years 1952-76. 



Northern California 

 Salmon Catch 



April - June 



July- September. _ 



-1.0 



10 



12 



LAG (years) 



Figure 10.— Estimates of the autocorrelation functions for the 

 early (April-June) and late (July-September) parts of the sea- 

 son. 



cyclic as the total catch. However, since they both 

 decrease to negative values then increase to ap- 

 proximately the same positive value at a 10-yr 

 lag, one does not appear more cyclic than the 

 other. 



Estimates of the cross-correlation between 

 total crab catch and early salmon catch and be- 

 tween total crab catch and late salmon catch are 

 shown in Figure 11. There is very little differ- 

 ence between these functions for each time peri- 

 od and they are quite similar to the same function 

 for total annual catch. The only difference be- 

 tween the two species is a slightly more pro- 

 nounced pattern of correlation for early rather 

 than late season to the right of the origin (i.e., 

 where salmon follows crab). After first-differ- 

 encing only the positive correlation at a lag of —5 

 remains (Table 1). 



From Figures 10 and 11 we can conclude that 

 the cyclic nature of salmon catch is not contained 

 entirely in the early, overlapping part of the sea- 

 son. 



A second, though not independent, means of 

 testing the proposed hypothetical mechanism is 

 to examine the mean data of salmon catch. If 

 crab abundance determined salmon catch early 

 in the salmon season, mean date of the salmon 

 catch would increase with crab catch. The cor- 

 relation between mean date of salmon catch and 

 total crab catch was not significant (r — —0.022 

 with linear trend subtracted from mean date of 

 salmon catch). Thus this test also yields a nega- 

 tive result. 



A third consequence of the proposed mecha- 



o 



h- 

 < 



or 

 or 

 o 

 <_> 



CO 



co 

 O 



rr 



<_> 



5 



00 - 



-0 5 



-1.0 



Northern California 

 salmon catch logs crab 



April - June 



July- September 



•15 



-5 



LAG (years) 



15 



Figure 11.— Estimates of the cross-correlation functions be- 

 tween Dungeness crab catch and total salmon catch early in the 

 season (April-June) or total salmon catch late in the season 

 (July-September). 



797 



