7. Repeat cycle to end of study period, starting 

 each cj'cle with step No. 5. 



EXAMPLE OF APPLICATION 



Since hypothetical data are seldom satisfactory 

 to demonstrate the application of a technique, the 

 following example of application to the fishery for 

 Atlantic cod (Cad us morhua) is included. It has 

 been used to achieve concreteness, not to make new 

 discoveries about the cod. Catch data were summed 

 for International Commission for the Northwest 

 Atlantic Fisheries Divisions 5Y and 5Z, and the 

 following parameters were assemblcfl for analog 

 computation: 



1. The central value of F = 0.35 used in Bever- 

 ton and Hodder (19G2) was assumed to be 

 the average {F) for the entire study period 

 1932-1958. From this figure, values were 

 calculated for eight periods, from the relation 

 F= qf, where/ was value of fishing effort from 

 Beverton and Hodder and q = F/f: 



2. The central value .l/ = 0.2 given by Beverton 

 and Hodder was assume(^l to be in effect dur- 

 ing the entire stud}' period. 



3. Lengths-at-age were oh'' ' iied from Schroedcr 

 (1930) and convert'- 'ghts-at-age witii 

 a length-weight cu. to data given in 

 Bigelow and Schroeder (1953). A Gompertz 

 curve was fitted to tlie weights-at-age with 

 constants G= 1.47, g = 0.340, and uv = 5.9 lb. 



4. No empirical data were available as the basis 

 of a stock-recruitment curve, .\fter some 

 preliminary experimentation, a hypothetical 

 curve (fig. 5A), with mode at an arbitrary 

 /?«■( = 32,000 metric tons, was ado])te<I for the 

 first formal trial. Tiio concavity of the left 

 hand limb was based only on experience from 



other species. From data on age composi- 

 tion in Beverton and Hodder it was estimated 

 that lr = -i years. 

 5. From data in Beverton and Hodder (1962) 

 and Silliman and Wise (19(il), it was esti- 

 mated that if lr = tr before the change in cod- 

 end mesh size from 2% to 4' 2 inches in 1954, 

 then /c = 'r+0.25 year for 1954 and there- 

 after. This change was accomplished by the 

 comparator (fig. 2), a device which actuates 

 a switch when the input (t in this application) 

 reaches a predetermined value (1^ here). The 

 comparator delayed application of F for one 

 <iuarter of a year, for j-ear classes entering 

 in 1954-58. 



The initial tiial simulation, based on the parame- 

 ters just listed, produced a poor fit of calculated 

 (Yu:) to actual (}'„,) catches (r=— 0.17). On the 

 basis of this trial, the shape of the recruitment curve 

 was altered .somewhat (fig. 5B) for the .second trial. 

 All other ])arameters remained the same. After the 

 recruitment relation was revised, a second trial pro- 

 duced a considerably improved fit (r = 0.59). Finally, 

 the value of M was changed to 0.25 and mean /'' to 



200 



P , 1,000s OF METRIC TONS, YEAR n 

 to 



FiGunK 5. — Hypothetical recruitment curves for .New Kng- 

 l.and cod. Vertical hrokcn lines indicitc range of values 

 used in computation.-J. 



40 



U.S. FI.SH A.ND WILDLIFK SERVICE 



