BOTSFORD and WICKHAM: UPWELLING INDEX AND DUNGENESS CRAB CATCH 



exists for all three locations at a lag of 1 yr. For 

 greater time lags no significant characteristics 

 appear. 



The auto-correlation of crab catch is plotted in 

 Figure 5. The correlation function for each loca- 

 tion decreases to a point of significant negative 

 correlation. This is a characteristic of a cyclic 

 process with a period of twice the lag value at that 

 point. For California the period of the cycle would 

 be 9 yr, and for Washington and Oregon it would 

 be 12 to 13 yr. A subsequent increase to a positive 

 correlation at a lag of twice that of the negative 

 peak is further indication of a cyclic process. 

 However a lag of that length is greater than 30% 

 of the total length of the data. 



DISCUSSION 



These results must be interpreted in light of the 

 general implications and limitations of statistical 

 correlation. The correlation coefficient is used to 

 measure the intensity of association between two 

 variables and determine whether or not it is 

 greater than that expected by chance alone. A high 

 correlation coefficient serves only as an indication 

 that a causal relationship may exist. The nature of 

 the causal mechanism may take several forms. A 

 high value of the correlation coefficient between 



two variables may be caused by one variable 

 directly influencing the other. It may also be 

 caused by a third variable influencing them both. 

 Other possible alternative forms are more 

 complicated combinations of these two. The causal 

 mechanism may be very complex and indirect. 

 Conclusions from the results obtained must, 

 therefore, serve only as indications of areas of 

 possibly fruitful investigation. 



The results in Figure 3 indicate a possible rela- 

 tionship between upwelling and catch. The posi- 

 tive correlation at 0.5 yr lag which continues for 

 several years could result from increased crab 

 growth or survival due to increased food which 

 may be due to nutrients provided by upwelling. 

 The correlation at low lag time indicates 

 agreement with Peterson's (1973) contention that 

 adults are affected. The maximum correlation, 

 however, appears at a shorter lag time in Califor- 

 nia than in Washington or Oregon. The fact that a 

 significant correlation continues for an additional 

 year may also be due to the same cause with the 

 longer lag being the sum of the time required for 

 the effect of nutrients to be felt at a point in the 

 food chain in which the crab feeds plus the time 

 required for that crab to reach a catchable size. 



The cause of the apparent periodic nature of 

 catch data indicated by Figure 5 is of primary 



l.O-r 



California 



0.5-- 





O 

 § 



o 



u 



-0.5 ■- 



Figure 5.-Auto-correlation of crab catch for Washington, Oregon, and California. 



905 



