FISHERY BULLETIN: VOL. 80, NO. 4 



nism is a relationship between catch per delivery 

 of crab and salmon catch. If fishermen continue 

 to fish crab when crab is abundant, then there 

 would be a relationship between catch per crab 

 delivery and salmon effort in months of overlap 

 between the two fisheries. This relationship 

 would show up in salmon catch provided it was 

 not occluded by fluctuations in salmon abun- 

 dance. The value (v) per delivery of crab catch 

 was computed for the months of May and June 

 each year as follows: 



PW 



CPID 



where 



P 



W 



CPI 



D 



market price 



total weight landed in the months 



of May and June 

 consumer price index 

 number of deliveries in the 



months of May and June. 



For the years 1952 to 1976 there is no significant 

 relationship between salmon catch during May 

 and June and value of each crab delivery (r = 

 0.31). 



DISCUSSION 



Interpretation of the correlation functions 

 computed here is somewhat subjective. Since, as 

 described earlier, significance levels do not hold 

 rigorously, they can be interpreted only in a rela- 

 tive sense. Correlations from the first-differenced 

 data can supplement interpretations of the raw 

 (except for detrending) data. First-differencing 

 removes intraseries correlation, hence empha- 

 sizes changes between adjacent points in a series. 

 Cross-correlations computed from first-differ- 

 enced series are more sensitive to the timing of 

 changes, and less sensitive to sustained high and 

 low values. The lag between recurring changes 

 in specific directions in each series must remain 

 constant in order to produce a high cross-correla- 

 tion. Significant correlations that do not remain 

 high following first-differencing should not 

 necessarily be regarded as spurious, rather they 

 may stem from variables that are highly auto- 

 correlated (e.g., abundance or catch as compared 

 with age-class sizes). On the other hand signifi- 

 cant correlations that remain high following 

 first-differencing probably stem from variables 

 with less intraseries correlation. 



Computed cross- and auto-correlations sup- 



port the existence of cyclic covariation between 

 crab and salmon catch in northern California. 

 The fact that the negative correlation at a lag of 

 +2 (Fig. 3) is no longer significant after first-dif- 

 ferencing (Table 1) implies that it probably arose 

 from the extended periods of high constant crab 

 catch and low constant salmon catch (Fig. 1). 



These same characteristics appear to be pres- 

 ent when each salmon species is considered indi- 

 vidually. They are, however, weaker in the king 

 salmon and weaker still in silver salmon. The 

 shorter length of the silver salmon time series 

 may be responsible for the latter. 



The analysis of central California data is more 

 informative, although it too is constrained by 

 shorter series. Early catch records in central 

 California resemble northern California records 

 in some respects. The auto-correlations of both 

 salmon and crab are the same and the cross-cor- 

 relation function has the same general shape 

 except that the peak at negative lag is at —3 yr 

 and the peak at positive lag in northern Califor- 

 nia is at a lag of zero (Figs. 3, 7). This negative 

 correlation at lag is quite apparent in Figure 6. 

 The most striking departure from the northern 

 California situation is the substantial decline of 

 the positive peak at negative lag and the persis- 

 tence of the negative peak at lag following first- 

 differencing (Table 1). This implies that changes 

 in crab and salmon that are in the same direction 

 are less regular than changes in the opposite di- 

 rection. 



Following the decline in crab catch in central 

 California the auto-correlation functions show 

 weaker cycles of shorter period for the crab and 

 the existence of a cyclic pattern for salmon is 

 questionable. The cross-correlation function is 

 similar to the predecline case but shifted to more 

 negative lags. This could occur, for example, if 

 two cyclic processes retained their shape but 

 were shifted in time with respect to each other. 

 After first-differencing the positive peak at 

 negative lags persists yet the negative peak is 

 diminished in magnitude by half. The postde- 

 cline period is similar to northern California in 

 this respect but differs in having a negative cor- 

 relation at a lag of —2. 



The observed differences in lag value of points 

 of significant correlation raise the question of 

 whether the northern California crab or salmon 

 fishery lags its central California counterpart. 

 The cross-correlation between northern Califor- 

 nia and central California salmon catch for the 

 period 1940 to 1976 has a significant positive 



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