growth rate, fishing and natural mortality, and 

 stock-rpcriiitment relation can be obtained. 



8. The problem of uni([ueness was studied from 

 simulations in which F and .V were varied over a 

 range of values. The failure of results to prove 

 uniqueness brings out the importance of using 

 reasonable values of parameters. 



9. As compared with other techniques, the analog- 

 graphic approach described here offers low initial cost 

 of equipment, moderate computation speed, ready 

 accessibility of equipment, and good visibility of 

 results during computation. It has limitations in 

 accuracy (two or three digits) and in requirements 

 for scaling variables. 



ACKNOWLEDGMENTS 



Suggestions from my se\eral re\ie\vers were freely 

 followed in revising the text. Reviews were fur- 

 nished by Vaughn C. Anthony, Raymond J. H. 

 Beverton, Anthony C. Burd, Paul H. Eschmeyer, 

 Re>Tiold A. Fredin. David J. Garrod, John A. 

 Gulland, Richard C. Hennemuth, Ralph Hile, 

 George Hirschhorn, Peter A. Larkin, Garth I. 

 Murphy, and William E. Ricker. Paul E. Huber, 

 of Electronic Associates, Inc., kindly reviewed the 

 sections on analog computation. .lohn L. McHugh 

 provided guidance during final revision of the 

 manuscript. 



LITERATURE CITED 



ASHI.KY, J. ROBEKT. 



lOCi:-!. Introduction to analog computation. John Wiley 

 and Sons, Inc., New York, 294 pp. 



Bar.wov, Feodor I. 



1918. K voprosu o biologicheskii osnovaniyakh rybnogo 



khozyaistva (On the question of the biological basis of 



fisheries). Moscow, Izv. Xauch. Is.sled. Ikhtiol. Inst., 



Izv. Otd. Rybovod. Xauch. -promysl. Issled. 1(1): 81- 



128. In Russian. 

 Beverton, R.wmond J. H. 



1903. Maturation, growth and mortality of clupeid and 



engraulid stocks in relation to fishing. Cons. Perma. 



Int. Explor. Mer, Rapp. Proe.-Verb. Reun. 154; 44-67. 

 Beverton, R.wmond J. H., and V. M. Hodder. 



1962. Report on working group of scientists on fishery 



.assessment in relation to regulation problems. Int. 



Comm. Northwest Atl. Fish., .\nnu. Proc. 11 (suppl.): 



1-81. 

 Beverton, R.wmond J. H., and S. J. Holt. 



1957. On the dynamics of exploited fish populations. 



Great Brit. Min. Agr. Fish. Food, Fish. Invest, ser. 



2, 19: 1-533. 

 1959. A review of the lifespans and mortality rates of 



fish in nature, and their relation to growth and other 

 physiological characteristics. Ciba Found. CoUoquia 

 on Ageing, 5: 142-180. Little, Brown and Co., Bcston. 

 BiGELow, Henry B., and Willi.\m C. Schroeder. 



1953. Fishes of the Gulf of Maine. U.S. Fish Wildl. 

 Serv., Fish. Bull. 53: viii + pp. 1-.577. 

 Cl.^rk, Fr.\nces N. 



1928. The weight-length relationship of the California 

 sardine {Sardina cacrutea) at San Pedro. Calif. Div. 

 Fish Game, Fish Bull. 12, 59 pp. 

 Cl.\rk, Frances N., and John C. Marr. 



1955. Popul.ation dynamics of the Pacific sardine. In 

 Progress Report, 1 July 1953 to 31 March 1955: 

 11-48. Calif. Dep. Fish Game, Mar. Res. Comm., 

 Calif. Coop. Oceanic Fish. Invest. 

 Doi, Takeyuki. 



1957. An analogue computer for analyzing the properties 

 of marine resources and pretlicting catches. Joint 

 Sci. Meet., Int. Comm. Northwest .\tl. Fish., Int. 

 Counc. Explor. Sea, Food .\gr. Organ. UX, Lisbon, 

 Doc. P. 12. 14 pp. 

 1962. The predator-prey and competitive relationships 

 among fishes caught in waters adjacent to Japan. 

 Bull. Tokai Regional Fish. Lab. 32: 49-118 (Fish. Res. 

 Bd. Can., Transl. Ser. 461). 

 Garfinkel, David, and Richard Sack. 



1964. Digital computer simulation of an ecological 

 system, based on a modified mass law. Ecology 45 

 (3): 502-507. 

 Graham, Michael. 



1935. Modern theory of exploiting a fishery, and appli- 

 cations to the North Sea trawling. J. Cons. 10 (3) : 

 264-274. 

 Holt, S. J., J. .A. Gulland, C. Taylor, and S. Kurita. 



1959. A standard terminology and notation for fishery 

 dynamics. J. Cons. 24(2): 239-242. 



International North Pacific Flsheries Commission. 



1962. The exploitation, scientific investigation and man- 

 agement of salmon (genus Oncorhynchiis) stocks on the 

 Pacific Coast of the United States in relation to the 

 abstention provisions of the Xorth Pacific Fi-sheries 

 Convention. 6. Supplementary information on salmon 

 stocks of the United States: Return escapement 

 relationships: salmon. Int. N. Pac. Fish. Comm., 

 Bull. 10: 67-72. 



Larkin, P. A., and A. S. Hourston. 



1964. A model for simulation of the population biology 

 of Pacific salmon. J. Fish. Res. Bd. Can. 21(5): 

 1245-1265. 



Larkin, P. A., and W. E. Ricker. 



1964. Further information on sustained j-ields from 

 fluctuating environments. J. Fish, Res. Bd. Can. 

 21(1): 1-7. 



Marc.alef, Ramon 



1962. Simplified physical models of populations of organ- 

 isms. Mem. Real Acad. Cien. Art., Bare. 34(5): 1-66. 



Odum, Howard T. 



1960. Biological potential and analogue circuits for the 

 ecosystem. Amer. Sci. 48(1): 1-8. 



ANALOG COMPUTER MODELS OF FISH POPUL.ATIONS 



45 



