756 



Fishery Bulletin 92(4). 1994 



BIVARIATE NORMAL MODEL 



SI AM' UNI II 



9 S 

 SI 2 



32 40 48 



Ft (cm) 



St AMOUNT B 



570 620 



DEPTH (m) 



< g 

 9 2 



• • 



I I 



9 5 



tr I -1000 j- 1 

 o" 

 ?• 2000 i— 



H-h- 



630 670 710 750 

 DEPTH (m) 



RECURSIVE MODEL 



1000 2000 3000 4000 



ACTUAL CPUE 

 (No.SSnV100.000 hooks) 



SEAMOUNTB 



y8 



3000 t 



2000 *• 



1000 +J 



1000  

 ■2000- 

 3000- 



t-t-t 



520 540 560 560 600 620 

 DEPTH (m) 



1000 2000 3000 4000 



ACTUAL CPUE 

 {No. lsh/100.000 hooks) 



2000 

 1000- 

 0- 

 1000- 

 2000 

 -3000 





24 



Figure 6 



Bivariate normal model and recursive model for seamounts B and J: distribution of predicted CPUE of alfonsino, 

 Beryx splendens, in relation to actual CPUE and distributions of residuals in relation to length (cm) and depth (m). 

 Dotted lines delimit the confidence interval at cx=0.05. 



Table 5 



Recursive model: estimated parameters of the dis- 

 tribution of CPUE on the hypothetical original sea- 

 mount calculated from seamount J data. SD = stan- 

 dard deviation. 



Li;=mean length (cm). 



H,/=mean depth (m), 



0/=standard deviation oi Length 



(^standard deviation of depth. 



p 2 =regression coefficient of length on depth. 



p=probability that fish will redistribute according to absolute depth 



A„=theoretical cumulative CPUE. 



mination coefficient, R 2 , calculated for seamount J 

 equals 0.82, while for seamount B it equals 0.69. 

 Therefore, the parameters estimated for seamount 

 J were used in the model (Table 5). The residuals 

 resulting from fitting the model to data from the 

 Humboldt cruise on seamount J are satisfactory; in 

 particular, they are centered on zero and are not cor- 

 related with the studied variables (Table 6; Fig. 6). 

 These features indicate a good fit of the recursive 

 model to the data as demonstrated by comparison of 

 actual and predicted CPUE for seamount J (Fig. 4). 

 It is interesting to note the low value of p (close to 

 0.1 as shown in Table 5), which indicates that the 

 seamount top depth parameter has greater impact 

 on the length distribution than does the absolute 

 depth parameter. 



Spatial validation was carried out for seamount B 

 from the data collected during the Humboldt cruise 

 (Table 6). The residuals are centered on zero and not 

 correlated with the length and depth variables. How- 

 ever, since their variance is not constant (Fig. 6) and 



