754 



Fishery Bulletin 92(4). 1994 



group will move down to zone D- +1 with a probability 

 1-p (Fig. 5). Thus, it is possible to determine the 

 CPUE (X- k ) for the population of a depth zone D r 

 on a seamount j, for a size class k in terms of the 

 subpopulations of zones D i and D l _ l on the higher- 

 level seamount j—1. This is expressed as follows: 



P X lllM+ (l-p)X, 



1J L,* 



(3) 



Specifically, if p=0, CPUE is distributed solely ac- 

 cording to the depth of the top of the seamount and 

 if p=l, it is distributed solely according to the abso- 

 lute depth. If the parameters X^ p,, o p p rf , o d , p, and 

 p. estimated from a known seamount length-depth 

 distribution are known, it is possible to calculate all 

 the CPUE (X i]k ) values for any seamount j (deeper 

 or shallower), depth zone D i and size class k. The 

 foregoing seven parameters can be estimated by mini- 

 mizing the SSE between the CPUE recorded on one 

 of the best sampled seamounts (B or J) and the CPUE 

 estimated by Equation 3. This estimation is per- 

 formed by a nonlinear regression (SAS, 1988). 



Results 



Bivariate normal model 



Application of a bivariate normal model implies that 

 mean length can be deduced from depth by a linear 

 regression weighted by the CPUE x, = ax d + b where 

 a and b are constants). The results of this regression 

 for seamounts B and J show mean length and depth 

 to be significantly correlated ( Table 2). Consequently, 

 the bivariate normal model can be tested for each of 

 these seamounts. 



The parameters of the bivariate normal model were 

 calculated separately for seamounts B and J (Table 

 3). The determination coefficient, 9 R 2 , for seamounts 

 B and J respectively equals 0.87 and 0.93. The re- 

 sidual analysis was carried out to test the fit of the 

 model to the data from the Humboldt cruise on sea- 

 mounts B and J. The results show the residuals are 



fl 2 = 



h- 



(Y. - Y) 



7i 



(V, 



with Y = CPUE. 



