Ti A; 



TfrX-T-XCQ 



An underlying feature of this simple index (A, /A,,) 

 is that while catches should rise and fall with 

 effort (T/s), they should also increase and decrease 

 with abundance. Consequently, abundance is a 

 factor influencing output or capacity when the 

 other inputs, except for effort (GRTi, are fixed. 



Example Problem 



An example problem is presented below utiliz- 

 ing the model formulations in the previous sec- 

 tion. In this problem it is assumed that there are: 

 1)11 species, 2) 1 vessel category (all otter trawl- 

 ers), 3) 1 time period (1 yr), and 4) 1 area. The 

 objective of the problem is to maximize the gross 

 revenues to the otter trawl fleet assuming the 

 1977 catch restrictions, the most recent bycatch 

 ratios, and an estimated U.S. deflated harvesting 

 capacity as developed in the previous section." 



The species that were used and their associated 

 bycatch ratios are in Table 3. The interpretation of 

 the entries in the table is as follows: when a pound 

 of cod is sought in a directed fishery for cod, 1 lb of 

 cod, 0.0.59 lb of haddock, 0.012 lb of redfish, etc., 

 are caught.'" The total pounds caught when seek- 



^For the purpose of this problem, gross revenues were used in 

 the objective function since the separable costs of catching these 

 species has not yet been determined. The costs of traveling to and 

 from the fishing grounds should also be included in the objective, 

 but these are not available at present. 



"The bycatch ratios used in the LP problem were not con- 

 verted from pounds to metric tons. The basic data for the compu- 

 tations in the LP problem were specified in pounds. 



FISHERY BULLETIN: VOL. 77. NO 2 



ing to catch a pound of cod in a directed fishery for 

 cod is 1.344. 



Table 4 presents the total gross revenue realized 

 for each species when attempting to catch that 

 species in a directed fishery. For example, when 

 attempting to catch a pound of cod in a directed 

 fishery, the total of 1.344 lb offish actually caught 

 is worth a total of 35.2 cents and includes the value 

 of the cod and the value of the bycatch. Table 5 

 presents the amount of processing capacity re- 

 quired per pound of each species caught in a di- 

 rected fishery and includes the bycatch require- 

 ment. Cod, haddock, and pollock are the only 

 species of those listed that are landed drawn and a 

 loss of 15% by weight is assumed. A total pro- 

 cessing capacity of 500 million pounds (226,796 t) 

 was assumed. 



Estimates i)f Landings Adjusted 

 for Abundance 



Estimates of adjusted landings (incorporating 

 cost factors) were made (Table 2) using the ap- 



Table 4. — Gross revenue per pound in a directed fishery. 

 (Source: U.S. Department of Commerce 1976.) 



Total revenue per pound 

 caught in a directed fishery 

 (includes value o( bycatch) 

 Species (c'lb) 



Atlantic cod 

 Haddock 

 Redlish 

 Silver hake 

 Red hake 

 Pollock 



Yellowtail flounder 

 Other flounders 

 Other finfish 

 Atlantic mackerel 

 Squid 



35.2 

 52.7 

 16.G 

 16.2 

 20.3 

 22.6 

 46.4 

 55.6 

 28.7 

 13.3 

 10.0 



T.^BLE 3.- 



-United States otter trawl bycatch ratios in 1974 for ICNAF areas. (Source: Northeast Fisheries Center. National Marine 

 Fisheries Service, NOAA. Woods Hole, Mass.) 



430 



