FISHERY BULLETIN: VOL. 76, NO. 4 







(3) 



where d,^ = catch of species j taken in directed 

 fishery for species //catch of 

 species i in directed fishery for 

 species i 

 bi = constraint on total catch of speciesj, 

 for J = 1 . . . m. 



The estimates of d^ for each country for 1973 are 

 presented in Appendix Table 1. Analogous tables 

 for the 1971 data are in Brown et al. (1973). 



The solution used in this paper was devised by 

 using the Simplex Algorithm (Hadley 1963: 132f) 

 which was computed by using a Honeywell^ com- 

 puter program LINPRO; a description of this use 

 of linear programming is given in appendix II of 

 Brown et al. (1973). In this analysis the linear 

 constraints were that no country would exceed its 

 national allocation for any species (6,). The output 

 of the LINPRO program includes the vector X of 

 directed catches of the species along with the re- 

 sultant total catches of the species and the overall 

 total catch. 



RESULTS AND DISCUSSION 



The results of each country's simulation are 

 given in Appendix Table 2. In each case the sum of 

 the species quota allocations exceeded the coun- 

 try's maximum possible catch (without violating 

 single species constraints) as determined by the 

 linear programming model. Table 2 lists the ratios 

 of the simulated catches to the TAC's using 1973 

 and 1971 bycatch ratios. For 4 countries (Bul- 

 garia, Canada, G.D.R., and Japan) of the 11, the 

 percentages derived from 1971 bycatch ratios dif- 

 fered from those derived from 1973 fishing pat- 

 terns by at least 0.20. More detailed reporting of 

 catches (i.e., by species rather than groups) in 

 1973 than in 1971 and, therefore, in the analysis 

 contributed to this change. Poland, United States, 

 France, and Federal Republic of Germany (F.R.G.) 

 were the only countries which could have taken 

 >80'^ of the sum of their species TAC's based on 

 1971 or 1973 bycatch rates. The United States, 

 however, has a significant discard of fish which is 

 not taken into consideration in this analysis. Of 

 the other countries considered, the effect of unre- 



TABLE 2. — Comparison of maximum catches from linear pro- 

 gramming simulation using 1971 and 1973 bycatch ratios, with 

 sum of species "quotas" for the ICNAF area. 



Maximum catch — sum of 

 species quota using: 



ported discard would be expected to be greatest in 

 the Spanish squid fisheries. 



Closer inspection of Appendix Tables 2 and 3 

 reveals the species which were the limiting factors 

 in a country's inability to take the sum of its 

 species quotas at present. These are the species 

 which were caught in significant amounts as 

 bycatch and directed catch and for which a species 

 quota was met. The species whose catch was most 

 frequently limiting was herring, when either 1971 

 or 1973 bycatch ratios was used. The next major 

 species using 1973 ratios were pollock and "other 

 pelagic" and using 1971 ratios were "other fish," 

 "other pelagic," and haddock. Pollock was less 

 limiting when 1971 ratios were used because it 

 was combined with the "other groundfish" cate- 

 gory, which had not been limiting. 



The sum of the linear programming estimates 

 over countries using 1971 and 1973 data are pre- 

 sented in Tables 3 and 4, respectively. In each case 

 the sum of the expected maximum catches deter- 

 mined by the linear programming runs was only 

 about 60^^ of the sum of the species quota. The 

 simulated directed fisheries catch levels composed 

 only 707c using 1971 bycatch ratios and 73% of the 



Table 3. — Sum of individual country's linear programming 

 simulation of 1975 catches in the ICNAF area, maximizing total 

 catch (1,000 t) and using 1971 bycatch ratios. Catches of France 

 assumed to be those using 1973 bycatch ratios. 



^Reference to trade names does not imply endorsement by the 

 National Marine Fisheries Service, NOAA. 



854 



