Lehodey et al.: Modelling the distribution of Beryx splendens 



755 



satisfactory; in particular, the residuals are centered 

 on zero, are not correlated with the length and depth 

 variables, and have a constant variance (Table 4; Fig. 

 6). These characteristics indicate a good fit of the 

 bivariate normal model to the data as demonstrated 

 by comparison of actual and predicted CPUE (Fig. 4). 

 Extrapolation of the model to the data not used in 

 the modelling exercise is unsatisfactory because the 

 mean value of the residuals is not centered on zero 

 for the Fukuju Maru data and because the residuals 

 are correlated with the length variable for the RV 

 Alls data and with the depth variable for the Hokko 

 Maru data (Table 4; Fig. 6). This suggests the exist- 

 ence of factors affecting the population's distribution 

 not accounted for by the model. 



Recursive model 



The parameters of the recursive model were esti- 

 mated separately for seamounts B and J. The deter- 



Table 3 



Bivariate normal model: predicted parameters for 

 seamounts B and J. SD=Standard deviation. 



Seamount and number offish measured 



B 

 1,557 



J 



1,957 



Parameters Estimation SD Estimation 



SD 



X 



V-i 



V-d 

 °; 



P 2 



3.66xl0 6 0.85xl0 6 0.5xl0 9 4.5xl0 9 



A=theoretical cumulative CPUE. 

 ^=mean length (cm). 

 p^=mean depth (m). 

 <7,=standard deviation oflength. 

 <7j=standard deviation of depth. 

 p 2 =regression coefficient of length on depth. 



Table 4 



Bivariate normal model: results of analysis of residuals (e) for fit control and temporal validation of the model for 

 seamounts B and J. 



H : e = . The mean value of the deviations between estimated and observed CPUE is 0. If a, is <0.05, H u is rejected. 

 p,= regression coefficient oft on length. 

 p 2 =regression coefficient of e on depth. 

 // :p, = 0. If ct,is< 5%, H is rejected. 

 H :p 2 = 0. If a 3 is < 5%, H is rejected. 



