ANALOG COMPUTER MODELS OF FISH POPULATIONS 



By Ralph P. Silliman, Fishery Biologist (Research) 

 Bureau of Commercial Fisheries Biological Laboratory, Seattle, Wash. 98102 



ABSTRACT 



A modern analog computer, together with an X-Y 

 plotter,' provides a means of constructing useful models 

 of commercially exploited fish populations. The model 

 combined conventional exponential fishing and natural 

 mortality rates with a Gompertz curve of growth in 

 weight. By combination of these rates and curve into 

 a single differential equation, survival curves for suc- 

 cessive year classes of fish were generated by the com- 

 puter and plotted by the plotter. Weights for all year 

 classes present in each season were summed graphi- 

 cally. Recruitment was determined from a stock- 

 recruitment curve, set into a function generator of the 

 computer. Yields for each season were calculated by 

 multiplying stock weight by rate of exploitation and 

 were compared with actual yields to test the validity 

 of the models. 



The technique was demonstrated by use of empirical 

 and hypothetical data for the Atlantic cod (Gadus 

 morhua). It is generally applicable to fisheries for 

 which good measures of total catch, growth rate, 

 natural and fishing mortality rates, and stock-recruit- 

 ment relation are available. 



It is important to use reasonable values of biological 

 variables in constructing the models because it was 

 not possible to demonstrate beyond doubt that the set 

 of parameters for any given model provides a unique 

 solution. 



Compared with other techniques, the analog-graphic 

 approach offers low cost of equipment, moderate com- 

 putation speed, ready accessibility of equipment, and 

 good visibility of results during computation. It is 

 limited in accuracy (two or three digits) and in scaling 

 requirements. 



Fishery biologists have devoted much effort in 

 determining changes in fish populations as thej' 

 respond to varying degrees of fishing intensity. 

 Because stocks usually cannot be observed and 

 measured directly, it has been necessary to use data 

 of catch and fishing effort and biological data on 

 relatively small samples of the stocks. These rec- 

 ords, plus associated data on the environment, have 

 composed most of the working materials of the fish- 

 ery biologist. Limited to such materials, the fishery 

 biologist has been forced to proceed largely by infer- 

 ence. There has been no alternative. As work be- 

 came quantitative, inference came to mean statistical 

 or biometric inference, or a combination of both. 



One method of quantitative inference is that of 

 simulation or modeling. Using the best empirical 



Note. — .Approved for publication Nov. 23, 1965. 



' Trade names referred to in this publication do not imply endorsement 

 of commercial products. 



data and biological judgment available, the biologist 

 erects hypotheses concerning the additive and sub- 

 tractive processes affecting the stocks. The former 

 include recruitment, growth, and immigration; the 

 latter, fishing mortality, natural mortality, and emi- 

 gration. To test the validity of the hypotheses, 

 characteristics of the models based on the hypotheses 

 can be compared with what is knowTi of the real 

 populations. Population models are used for the 

 same purpose as models in ship or power-dam design: 

 experiments are easier, quicker, and cheaper with the 

 model than with the full-scale object. Any tool that 

 will help the biologist in these processes should be 

 valuable. This report describes such a tool in the 

 form of an analog computer technique. 



Application of the analog computer as described 

 herein has not, to the best of my knowledge, been 

 made previously. Originality is not claimed, how- 

 ever, for the technique of simulation in general or in 



FISHERY bulletin: VOLUME 66, NO. 1 



31 



