+ 10 



Figure 2. — Analog computer circuit for generation of P, and W. Standard symbols for computing elements, scaling excluded. 



By integrating this expression, the computer gen- 

 erates P, as a function of {t—tr) for any given values 

 of /?^, g, G, F, and M. The circuit diagram, which 

 includes conventional symbols for the computing 

 elements, is shown within the broken line enclosures 

 of figure 2. The elements outside the broken lines 

 are used in the combination of analog and graphical 

 computation employed to sum the weights of year 

 classes for each season and to determine subsequent 

 recruitment. Their nature and use are described 

 later. 



As examples of analog computation, growth and 

 survival curves from the plotter are shown in figures 

 3 and 4. The data are hypothetical except for the 

 growth constants, which have been derived from 

 data for the California sardine. 



Data of growth in weight were obtained by com- 

 bining a curve of growth in length with a weight- 

 length relation. A table of length-at-age was given 

 in Phillips (1948) and a weight-length relation in 

 Clark (1928). Fitting of the Gompertz relation to 



these data (fig. 3) was readily accomplished by suc- 

 cessive trials, with appropriate adjustment of the 

 potentiometers for G and g. The fitted curve fol- 

 lowed expression (2b), with ?iv = 93 g., G = 0.825, 

 g = 0.44.5, and ^ = 2 years. 



Starting with a hypothetical 1,000 fish, 7?,^ = 93 kg. 

 when uv = 93 g. The upper curve (fig. 4) shows how, 

 with no fishing mortality and low natural mortality, 

 P, may increase for a year or two before mortality 

 overcomes growth. In the two lower curves the 

 effect of adding a substantial fishing mortality may 

 be seen. Application of an increase in fishing mor- 

 tality at t — tr = 2 resulted in the lower branched 

 curve. This change is readily made on the analog 

 computer by placing the machine in the "hold" 

 mode. The potentiometer for "F" is then reset, the 

 machine returned to "operate" mode and the com- 

 putation resumed. The ability to change quickly 

 the vital rates during a computation is one of the 

 advantages of the analog machine. It may be done 

 even more conveniently by presetting a number of 



ANALOG COMPUTER MODELS OF FISH POPULATIONS 



37 



