FISHERY BULLETIN: VOL. 80. NO. 3 



Table 5.— Significant applications of the total biomass Schaefer model to the Hawaii 

 Division of Fish and Game data set where species have been aggregated according to 

 cluster analysis species groupings. 



'MLKM = Maui-Lanai-Kahoolawe-Molokai 

 KNK = Kauai, Niihau, and Kaula Rock. 

 2 MSY = maximum sustainable yield. 



Y = aiN\ + CU2N2 - 

 + (d + c 2 )NiN 2 



6i7vV 



62M 2 



(1) 



where M and N2 refer to the population sizes of 

 species one and two and a\, c^, 61, 62, Ci, and C2 

 are model parameters (Pope 1979). This model is 

 the sum of two single-species surplus production 

 models with the additional term (ci + c 2 )NiN2 to 

 account for the interaction between the two 

 species. Depending upon the signs of c\ and C2 the 

 equation models predation, competition, or 

 mutualism. More importantly, the sum of these 

 two parameters determines the impact of the 

 interaction on the sustainable yield of the system. 



The question of whether significant interac- 

 tion occurs among the cluster-analysis species 

 groups was examined by considering the MLKM 

 bank alone. The regressions of all three cluster 

 groups were highly significant from this region 

 and further treatment of these data is therefore 

 considered appropriate. 



In the three-species version of Equation (1) 

 there are three terms involving the sum of c 

 parameters. In this analysis a species group (I, 

 II, or III) is treated as though it were a single 

 species and the a and b parameters necessary to 

 evaluate the equation were taken from the 

 independently calculated regressions of Table 5. 

 A nonlinear regression routine (SAS Institute 

 1979, program NLIN) was employed to estimate 

 the sums of the various c parameters for the 

 MLKM bank (Table 6). It is apparent that these 

 sums do not differ significantly from zero and 

 hence there is no evidence for. significant inter- 

 action among groups. This result further 



Table 6.— Tests of whether interaction between cluster 

 analysis species groups have a significant effect on total bottom 

 fish yield from the Maui-Lanai-Kahoolawe-Molokai bank. 



Term 



Parameters 



Evaluated 

 value 



95% confidence 

 limits 



(c, + c 2 ) N,fV 2 

 (c 2 + c 3 ) N 2 N 3 

 (c, + c 3 ) /v,N 3 



(C1 + c 2 ) 

 (c 2 + c 3 ) 

 (c + c 3 ) 



0.242 



0.185 



-0 868 



(-0.244, 0.728) 

 (-0 284. 0.654) 

 (-2.365. 0.629) 



supports the classification of species into 

 independent assemblages for use in an aggre- 

 gated treatment of the data. 



In the final analysis all species were treated as 

 a single group and the TBSM was applied to the 

 total aggregate. Of the four possible regressions 

 of CPUE on /, both the MLKM and Oahu banks 

 yielded significant results (Table 7). Similar 

 computations were performed for these sites as 

 had been done previously. In addition the regres- 

 sion of total bottom fish CPUE on / for the 

 MLKM bank and the corresponding catch curve 

 (catch versus effort) were plotted (Fig. 3). It is 

 reassuring to note that the sum of the three- 

 species group MSY's from this bank, calculated 

 from the preceding analysis, amounts to 103,700 

 kg/yr. This estimate compares favorably with the 

 present result (a difference of about 2%) though 

 the two figures were computed somewhat inde- 

 pendently. A comparison of MSY/nmi 100- 

 fathom isobath between these two banks reveals 

 the Oahu value to be substantially less than the 

 MLKM value. Although this may in actuality 

 represent differences in habitat quality and pro- 

 ductivity between these banks, there is the pos- 

 sibility that the difference is at least partially 

 due to a difference in the extent of unreported 

 recreational fishing pressure between the banks. 



The results of the stock-production analysis for 

 the MLKM bank provide statistically acceptable 

 regressions, yet the estimates of production are 



Table 7. — Significant applications of the total biomass 

 Schaefer model to the Hawaii Division of Fish and Game data 

 set where all species have been grouped into one total 

 aggregate. 



Bank 



MSY 2 (kg/yr) 



Optimum effort (fisherman-days) 



MSY/nmi, 100-fathom isobath 



Catchability coefficient 



t value (df = 18) 



'MLKM = Maui-Lanai-Kahoolawe-Molokai. 

 2 MSY = maximum sustainable yield. 



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