Shimada and Kimura: Seasonal movements of Gadus macrocephalus 



809 



ods, Pacific cod have presumably returned to the feed- 

 ing grounds on which they were originally tagged. 

 The absence of any definitive within-season pattern 

 is further illustrated in Figure 6. Pacific cod released 

 and recaptured during the same three-month period 

 (i.e. within the same season, perhaps in different 

 years) showed only random movement and little di- 

 rectional bearing. This is in marked contrast to the 

 strong interseasonal movements traced between 

 fall-winter and winter-spring quarter tag recaptures. 



Multiway contingency analysis 



Results from a multiway contingency table analysis 

 (Table 2) indicated that month of recovery most 

 strongly influenced the area of recovery. Although 

 area of tagging also had a significant affect on the 

 area of recovery, the month of tagging was seen to 

 have only a relatively small affect on the area of re- 

 covery. Thus season of recovery appeared as the 

 strongest correlate to area of recovery, which further 

 supports our finding of strong seasonal migrations 

 in Pacific cod. 



Seasonal-areal population dynamics 

 modeling and catch distribution 



A histogram of residuals from predicted tag recover- 

 ies indicates that the 13-parameter population dy- 

 namics model of the tagged population fit the data 

 quite well (Fig. 7). The parameter estimates from the 

 tagging model (Table 3) show strong movement from 



Table 2 



Multiway contingency table analysis of tag recovery 

 data for Pacific cod, Gadus macrocephalus, in the 

 eastern Bering Sea. The model examined all two- 

 factor interactions (i.e. no factor deletions). Each two- 

 factor interaction was tested for significance by de- 

 leting it from the model. Factor 1 = season of release 

 (4 levels), 2 = area of release (3 levels), 3 = season of 

 recovery (4 levels), 4 = area of recovery (3 levels). 



' Interaction large but fixed by design. Z-statistic is a standard 



normalization of the hierarchical chi-square test. 

 *** Interactions were significant; a=0.0001. 



Table 3 



Estimates of parameters (and coefficients of varia- 

 tion measured as proportions) for the population 

 dynamics model for tagged Pacific cod, Gadus macro- 

 cephalus, in the eastern Bering Sea. Areas are shown 

 in Figure 3. 



1 Quarterly instantaneous natural mortality rate: 

 M= 0.235(0.109). 



2 Seasonal instantaneous fishing mortality rates: 



F =0.01389(0.149), F =0.0082(0.176). 

 F su =0.0075(0.152), F f =0.0087(0.141) 



3 Seasonal distribution over (Area 1, Area 2, Area 3): 



a p u = [0.0246 (0.570), 0.1884 (0.188), 0.7870 (0.047)] 

 b p sp = [0.4849 (0.148), 0.3937 (0.175), 0.1214 (0.371)] 

 c p su = [0.5830 (0.122), 0.2330 (0.255), 0.1840 (0.318)] 

 d p f = [0.1103 (0.304), 0.5167 (0.105), 0.3730 (0.143)] 



the major spawning area (Area 3) in spring, further 

 movement onto the shelf (Area 1) in summer, move- 

 ment off the shelf in fall, and movement to the spawn- 

 ing areas in winter. Furthermore, the model results 

 confirm strong seasonal movement between areas in 

 a manner consistent with our previously described 

 pattern of seasonal Pacific cod movements. 



The apparent high annual instantaneous natural 

 mortality rate ( M = 0.96 ) and low annual fishing 

 mortality rate ( F = 0.038 ) of the tagged population 

 can be noted. This is probably due to tag loss, tag- 

 ging mortality, or the under-reporting of tag recov- 

 eries as previously discussed. Multiplying releases 

 by 1/3, or multiplying recoveries by 3 would lower M 

 and increase F nearer to expected levels 

 ( M = 0.87, F = 0. 1 1 ). However, the model fit and es- 

 timated seasonal distribution of the tagged popula- 

 tion were not affected by this scaling of observed re- 

 leases or recoveries. Therefore, the population dy- 

 namics model estimates of seasonal distribution ap- 

 pear to be robust to tag loss, tag mortality, or 

 under-reporting of recoveries. 



The estimated areal distributions (within seasons) 

 of the tagged population largely reflect the areal dis- 

 tribution of tag recoveries. Also, although no catch 

 data were used in the population dynamics model, 

 the results coincide well with the estimated seasonal 

 distribution of the commercial catches (Table 4). The 

 main difference appears to be that the hypothesized 

 fall season off-shelf movement, and subsequent move- 

 ment into the winter spawning area (Fig. 4, C and 

 D), is more pronounced in the commercial catch data 



