ment. It is, of course, possible to perform work on 

 digital machines under contract or rental arrange- 

 ments at no initial cost. This arrangement is also 

 possible for analog machines. 



2. Time required for computation. — For the total 

 operation as outlined above, limited tests indicated 

 analog-graphic computation to be about four times 

 as fast as desk calculation. With digital computers, 

 the calculation time is a matter of minutes. If time 

 required for preparation of data for computer cal- 

 culation, programming the computer, and exchange 

 of data with the computer center are considered, 

 however, total time may well ajiproach that for the 

 analog method. 



3. Visihilitij of ivork during computation. — In the 

 analog-graphic method, stock size, recruitment rate, 

 and yield are all visible in graphic form as the 

 computation proceeds. This advantage is impor- 

 tant to the biologist, since it quickly reveals absurd 

 results, or permits him to end a computation that 

 is leading away from reality. Work is invisible 

 during digital computation, and the final "readout" 

 is usually in the form of a table that may have to 

 be plotted for study. 



4. Scale adjustment. — Quantities generated within 

 an analog computer must be kept within the voltage 

 limits of the machine. This limitation leads to a 

 considerable amount of "fussing" to achieve proper 

 scaling of the variables. This problem is only minor 

 in digital calculation and therefore represents a 

 comparative disadvantage for the analog computer. 

 Fortunately, once scaling has been adopted for a 

 given formula, it can usually be used with only one 

 or two changes when shifting to a new set of empirical 

 data for the same formula. 



"). Accuracy of results. — Because of the nature of 

 components in an analog computer, the final results 

 are usually accurate only to two or three significant 

 digits. At the present stage of development of 

 fishery science, the empirical data available are not 

 such as to justify carrying more fligits. In fact, 

 two-digit accuracy in fishery predictions would be 

 considered more than satisfactory by most fishery 

 administrators. Thus, the accuracy limitations of 

 the analog machine as compared with digital com- 

 putation do not at present represent a serious 

 disadvantage. 



6. Summary comparison of methods. — From the 

 above brief listing, the analog technique is seen to 

 have advantages in comparatively low initial cost 

 of equipment, moderately rapid computation rate, 



and visibility of results. It has limitations in accu- 

 racy and in scaling requirements and is slower than 

 a digital comijuter. Decision as to which techni(|ue 

 to use must depend on the situation of the individ- 

 ual investigator. Factors liearing on the decision 

 include the salaries of persons doing various parts of 

 the work, the accessibility of the research station 

 to a digital computer, anrl the types of emiiirical 

 data availalile. 



UTILITY OF THE TECHNIQUE 



In this report I have described what may be a 

 useful working tool for the fishery biologist. The 

 example of application given demonstrated the types 

 of l)asic data neeiled and the way in which they 

 could be adjusted to improve "goodness of fit" of 

 calculated to actual catches. As with any tech- 

 niciue, its utility can be asses.sed only by those 

 making use of it. 



Where extensive biological data are available, 

 simulation is valuable in determining the effects of 

 interaction among the varying mortality, growth, 

 and recruitment rates. The accuracy with which 

 actual catches can be rei)roduced should serve as a 

 check on the validity of the sampling, analysis, 

 and interpretation involved in the derivation of 

 popvilation parameters. 



SUMMARY 



1. The objective of this study was to develop :m 

 analog-computer simulation techni(iue for niodoling 

 exploited fish jiopulations. 



2. The mathematical formula for survival of a 

 year class expressed the effect of fishing and natural 

 mortality rates and incorporated a Oompertz curve 

 of growth. 



3. Survival curves for successive year classes were 

 generated on an analog computer through use of 

 the differential form of the survival formula. A 

 combined analog-graphic technique summed the 

 weights of survivors in each season to give the weight 

 of the fishable stock. 



4. Yield was calculated by applying the rate of 

 exploitation to the fishable stock. 



5. Properly lagged recruitment was determined 

 from the stock weight tluough a stock-recruitment 

 curve. 



6. Mechanics of the technique were demonstrated 

 by application to the Atlantic cod. 



7. This technique may be applied to any fishery 

 for which good measures or estimates of catch, 



44 



U.S. FISH .\ND WTLDUKE SKUVICE 



