In any trial-and-error approach involving several 

 variables, the question of uniqueness must be faced. 

 It is fair to ask, if one set of parameters has produced 

 a reasonable result, may not another set produce one 

 that is equally reasonable'? 



Although it is not possible to answer the above 

 question for the general case, some light may appear 

 from a further examination of the trials on cod 

 reported above. In assessing goodness of fit, I took 

 account of the ratio of mean heights of the calculated 

 and actual catch curves, as well as the correlation 

 between them. Thus I had two criteria of "good- 

 ness of fit": Yu^/Y,,, and r. To provide some idea 

 of the discriminative value of these criteria, I made 

 additional simulations in which only F or M was 

 ^'aried and all other parameters were held constant. 

 Curves of calculated values (fig. 7), bracketing 

 those used in the third trial above, are revealing. 

 For this particular set of combinations, only one 

 other than the third approaches its "goodness of 

 fit." The combination of F = 0.35 with ,V = 0.2.5 

 produced about as good a fit as the combination of 



the third trial; r was slightly higher, and 5',r/)V was 

 slightly lower. The difference in F of 0.05, however, 

 is well within what might be considered reasonable 

 error in a rough approximation. 



Obviously, curves of the type in figure 7 cannot 

 "prove" the uniqueness of fit obtained with any 

 particular combination of parameters. Since F, M, 

 and the shape and height of the recruitment curve 

 can be continuously varied, the number of possible 

 combinations is infinite. Every effort should be 

 made, therefore, to use reasonable values of bio- 

 logical parameters. Thus we know that F, M, and 

 the recruitment curve are sound because biologists 

 generally recognize that fish stocks are affected by 

 fishing, natural mortahty, and recruitment. The 

 question of "reasonal)le values" is more difficult, 

 but the range of possibilities may be narrowed by 

 use of empirical data as indicated under'Treliminary 

 Estimates of Parameters." 



COMPARISON WITH OTHER TECHNIQUES 



By appropriate transformations of the formulas, 

 any of the calculations reported above can be per- 

 formed on either conventional desk calculators or 

 electronic digital computers. It is pertinent, there- 

 fore, to consider the relative advantages and dis- 

 advantages of analog computation as compared with 

 other techniques. 



1. Initial cost of equipment. — The analog com- 

 puter and plotter equipped as I used them cost 

 about $8,000. This figure is substantially more than 

 a good desk calculator ($1,000 to $2,000) but not 

 over one-tenth the cost of comparable digital equip- 



1.0 



+ .5 



-.5 - 



< 

 1.4- 



^ 



\ II, F HELD CONSTANT, 

 \ M VARIED 



1, M HEL_D CONSTANT, 

 F VARIED 



> 



Figure 7. — Effect of varying F or jV/ in simulation trials 

 with cod. The value r is the coefficient of correlation 

 between calculated catches (?„) and actual catches (V'„). 

 Since r is affected only by Z, and not the ratio of its com- 

 ponents F and M, it has only one value for each pair of 

 combinations. The fraction ?«,/)'«, represents the ratio of 

 the mean calculated catch (vio) to the mean actual catch 

 (Tu,). Vertical line of dashes indicates combination of 

 values used in third cod simulation trial. 



ANALOG COMPUTER MODELS OF FISH POPULATIONS 



43 



