RALSTON and POLOVINA: COMMERCIAL DEEP-SEA HANDLINE FISHERY 



son of the coefficients of determination obtained 

 from different levels of grouping. Thus it is 

 improper to compare the goodness of fit for the 

 grouped analysis to that for the total aggregate 

 without correcting for this bias. They suggest 

 that a more appropriate and direct way of 

 comparing the effect of these two levels is to 

 compare the proportion of variance in the total 

 catch explained by the predicted total catch 

 from the two levels of aggregation. We must use 

 catch rather than CPUE as the dependent vari- 

 able because the sum of the CPUE values pre- 

 dicted from each of the grouped models will not 

 predict total CPUE. 



When annual catch (C) rather than CPUE is 

 used the Schaefer model becomes 



annual catch explained by the sum of the three 

 species groups model is r 2 defined as: 



C = af-bf + E 



(2) 



where a and 6 are constants, /is fishing effort in 

 fisherman-days, and E is a normal random vari- 

 able with mean and finite variance. In the case 

 when catch and effort are aggregated into the 

 three species groups there will be three 

 equations of the form of Equation (2) based on the 

 grouped annual catch (C,) and grouped annual 

 effort (/) for i = 1, 2, 3. For the completely 

 aggregated TBSM there will be a single equa- 

 tion of the form of Equation (2) with total annual 

 catch {TC) and total annual effort (77). In all 

 four equations the nonlinear regression coeffi- 

 cients a and b can be estimated with the 20 yr of 

 annual data from 1959 to 1978. We can then use 

 these coefficients to obtain predicted group 

 annual catches (C l} ) for groups i = 1,2, 3 and years 

 j = 1, 2, ...,20, and the predicted total annual 

 catches (TQ) for years j = 1, 2, ...,20 given the 

 corresponding effort statistics. 



We now have two estimates of total annual 

 catch based on either TCj from the fully 

 aggregated TBSM or C v + C 2j + C 3j from the 

 three species groups regressions. We can 

 compare these two levels of aggregation based on 

 their accuracy in predicting TC. This is done by 

 defining SS g to be the sum of squares of TCj— &j 



— Ckj— Csj for j = 1, 2 20, or the deviations of 



the grouped predicted catch from the observed 

 total, and defining s g 2 — SS g /19. Let SS, be the 



sum of squares of TCj — TCj, j = 1, 2 20, or the 



deviations of the predicted total catch of the 

 completely aggregated TBSM from the observed 

 total catch. Finally let s 2 = SS,/19 and s T< 2 be 

 the sample variance of the total annual catch. 

 Then the proportion of the variance of the total 



2 _ 



1 -Sg/sre 



(3) 



and the proportion of the variance in the total 

 annual catch explained by the TBSM is r, 2 

 defined as: 



rf = 1 - s?/stc 2 



(4) 



For the MLKM bank we determine r 2 - 0.14 

 and r g 2 = 0.18. Thus the increased level of data 

 aggregation going from treating the fishery as 

 three separate groups to one total group does not 

 in fact improve the fit of the catch curve although 

 this appeared to be the case when the r 2 for the 

 TBSM applied to the total group was compared 

 to the r 2 values for the TBSM applied to each of 

 the three cluster groups (Table 4, Fig. 4). As 

 outlined previously these coefficients of deter- 

 mination, as calculated above, refer to the pre- 

 diction of catch from effort data, for which the fit 

 is substantially poorer than the fit of CPUE on 

 effort. 



A consideration of statistical aggregation 

 theory has shown that the classification of 

 bottom fish species into cluster groups results in 

 slightly better predictions of total bottom fish 

 catch than does analysis of the total aggregate. 

 Since superior performance is achieved at an 

 intermediate level of aggregation, it is possible to 

 discount the undesirable effects of "averaging" 

 which have troubled previous investigators 

 (FAO 1978; Pauly 1979; Pope 1979). Further- 

 more, the lack of significant interaction among 

 the species groups (Table 6) suggests that this 

 particular application of the TBSM to the 

 Hawaiian offshore handline fishery is appro- 

 priate. 



Even though the separation of data from the 

 MLKM bank into three species groups produced 

 only a marginally better fit than the total 

 aggregate model and the extra computations 

 which are necessary were extensive (e.g., 

 clustering), some advantage can be gained by 

 splitting the fishery up into the groups listed in 

 Table 3. Not only is the biological realism of the 

 stock-production analysis enhanced but interest- 

 ing patterns are also allowed to emerge. Notice, 

 for example, that while the estimate of MSY for 

 Group I from the MLKM bank is less than that 

 for Group III from the same bank (Table 5), the 

 fishing effort required to reach that figure is 



445 



