FISHERY BULLETIN: VOL. 80, NO. 4 



Dungeness crab 



Total salmon 



Silver salmon 



2 5 



Figure 6.— Total landings (kg) in the central California crab 

 and salmon fisheries for the years 1940-76. 



correlation functions of salmon and crab catch 

 are virtually the same as in northern California. 

 Salmon and crab fall to —0.37 and —0.59, respec- 

 tively, (the latter is significant at 0.05) at 4 yr, 

 then increase to +0.43 and +0.54, respectively, 

 (neither significant at 0.05) at 10 yr. First-dif- 

 ferencing decreases the strength of both the posi- 

 tive and negative peaks of auto-correlation in 

 both of these series. The estimated cross-correla- 

 tion between salmon and crab catch in the early 

 period is also similar to that in northern Califor- 

 nia except for a shift in the negative lag direction 

 near zero lag (Fig. 7). The correlation at zero lag 

 has a significant negative value in central Cali- 

 fornia whereas it is not significant in northern 



i o 



LlI 



rr 



rr 

 o 

 o 



CO 

 CO 



O 

 li 



o 



5- 



00 - 



-0 5 



•1.0 



-10 -5 5 



LAG ( years) 



10 



15 



Figure 7.— Estimates of cross-correlation functions between 

 central California Dungeness crab and total salmon catch, both 

 before and after the decline in 19(51. Outer significance levels 

 apply to the period after the decline. 



California. This shift would correspond to a 

 negative relationship between crab and salmon, 

 with salmon following crab more closely in cen- 

 tral than in northern California. After first- 

 differencing each series the positive correlation 

 peak at negative lag disappears but the negative 

 correlation at zero lag remains (Table 1). 



For the postdecline period (1962-76). the auto- 

 correlation function for crab catch appears 

 cyclic, as it was before the decline, but the period 

 of the cycles has apparently decreased (Fig. 8). 

 The auto-correlation function for salmon de- 

 creases to a significant negative value at 3 yr, but 

 shows no clear cyclic tendency for greater lags. 

 First-differencing decreases this first peak by 

 about 0.1 for both series. The cross-correlation 

 estimate for the postdecline period is similar to 

 the northern California relationship for negative 

 lags (i.e., crab following salmon), but is not simi- 

 lar for zero and positive lags (Fig. 7). Both of 

 these latter estimates are for a low number of 

 data points, hence interpretation for large lags is 

 risky (note that the outer significance levels in 

 Figure 7 are for the later period correlation). 

 After first-differencing only the positive correla- 

 tion at negative lag remains significant (Table 

 1). 



LAG (years) 



Figure 8.— An estimate of autocorrelation functions for cen- 

 tral California Dungeness crab and total salmon catch for the 

 years following the decline in crab catch (i.e., 1962-76). 



Switching Effort Between Species 



If the cyclic nature of salmon catch is caused 

 by fishermen fishing salmon only when crab are 

 not abundant, then cycles in salmon catch should 

 be determined by salmon catch in the part of the 



796 



