FISHERY BULLETIN: VOL. 80, NO. 4 



catch record is still not known and research in 

 this area is continuing. 



In contrast to the considerable research atten- 

 tion attracted by cyclic fluctuations in crab 

 catch, fluctuations in the salmon catch record 

 have, to our knowledge, not been previously iden- 

 tified as cyclic. Yet, as seen in Figure 1, these 

 apparently periodic fluctuations in salmon catch 

 have a peak amplitude of about ±0.5 of the mean 

 value. While abundance is predicted each year as 

 part of the management process, these predic- 

 tions have not taken advantage of this regular 

 pattern that accounts for about two-thirds of the 

 peak catch. An understanding of the underlying 

 cause of cycles in salmon catch has great poten- 

 tial for improved predictive ability and better 

 salmon management. 



There are many possible causes of the observed 

 similar cycles in the salmon and crab fisheries. 

 There may be a direct biological interaction be- 

 tween the two species that by itself gives rise to 

 cycles. Alternatively, one may vary cyclically 

 and a direct biological interaction may cause the 

 other to follow it. As another class of possibilities 

 the two processes need not necessarily be directly 

 related but may both be under the influence of a 

 third process (e.g., environmental factors). A 

 third class of possible causes of the observed co- 

 variation is some sort of economic linkage be- 

 tween the two fisheries. Since many fishermen 

 fish both species, abundance and effort in one 

 could affect effort in the other. 



METHODS AND DATA 



Our approach to eliminating unlikely causes of 

 the observed covariation from the many possible 

 causes is based on interpretation of estimated 

 auto- and cross-correlation functions (also called 

 correlograms). This statistical technique has 

 been useful in interpretation of cycles in wildlife 

 populations (Moran 1949; Finerty 1980) and is a 

 recommended initial step in time series analysis 

 (Jenkins and Watts 1968; Box and Jenkins 1970). 

 However, there are few useful results on statisti- 

 cal significance of estimated correlation func- 

 tions. We use a simple form of a method described 

 by Bartlett (1946). If individual points in a time 

 series are independent and identically distrib- 

 uted, an estimate of the correlation between 

 them is Gaussian with mean zero and variance 

 1/N where N is the total number of samples on 

 which the estimate is based. In the following 

 analysis we show 5% error limits on plots of cor- 



relation functions. The occurrence of values of 

 correlation greater in magnitude than this limit 

 more frequently than 1 in 20 indicates a "non- 

 random" process. This approach is somewhat 

 limited in that it focuses on single points rather 

 than the pattern of the estimated correlation 

 function as a whole. 



If samples in each series are not independent, 

 the significance of both cross- and auto-correla- 

 tion functions will be overestimated (Granger 

 and Newbold 1974). A suggested solution to this 

 problem in estimating cross-correlations is to 

 prewhiten (i.e., remove correlation between sam- 

 ples) each series by fitting an ARM A model (Box 

 and Jenkins 1970) to the series, then compute 

 cross-correlations between the residuals. We 

 have not taken this approach for two reasons: 

 1) Computed correlations based on the residuals 

 actually underestimate significance of results 

 (Box and Pierce 1970; Durbin 1970) and 2) pre- 

 whitening may actually remove correlations of 

 real interest. With regard to the latter, some 

 auto-correlation within each series exists be- 

 cause of known physical processes (e.g., the fact 

 that catch is the result of fishing several age 

 classes causes intraseries correlation). Removal 

 of this intraseries correlation would reduce the 

 chance of detecting real interseries correlation 

 (e.g., correlation stemming from a causal mech- 

 anism that involved catch). Removal of intraser- 

 ies correlation on the basis of known physical 

 mechanisms will provide more meaningful re- 

 sults; however, it will require further studies of 

 effort dynamics and life histories in both the 

 salmon and crab fisheries. In the meantime, as a 

 simple exploration of the possibility of "spurious" 

 results, we also present correlograms computed 

 from first-differenced data (first-differencing is 

 the process of replacing the data point x t at time 

 t with the difference x t — .r ( _i). First-differencing 

 reduces intraseries correlation and has been 

 shown to greatly reduce the incidence of spurious 

 interseries correlation (Granger and Newbold 

 1974). Correlation results of first-differenced 

 data can be interpreted as the correlation be- 

 tween changes in each series. Also, in all correla- 

 tions presented, a linear trend has been removed 

 from the series. 



Salmon data for these analyses are from month- 

 ly catch records collected and published by the 

 California Department of Fish and Game (1954- 

 78). The northern California salmon catch con- 

 sists of landings at Crescent City, Eureka, and 

 Fort Bragg. The central California catch is from 



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