potentiometers at needed values of "F" and shifting 

 from one to tlie other. 



PROCEDURE OF SIMULATION 



Simulation of populations and yields by a com- 

 bination analog-graphic approach required develop- 

 ment of a standardized procedure. A chart was 

 prepared for the plotter, with appropriately scaled 

 coordinates for time (X-axis) and stock (Y-axis). 

 Vertical lines on this chart marked the points for 

 changes in mortality rates or recruitment relation. 



Because the commercial stock in any fishing season 

 is made vip of survivors from individual year classes 

 of various ages, that stock cannot be started "full 

 blown," with all year classes present. I therefore 

 started with a stock size such that the rate of exploi- 

 tation (E) estimated to be in effect would produce a 

 catch [Yir) eciual to the real catch for the first fishing- 

 season, or the mean catch for the first two fishing- 

 seasons of the study period. This stock was then 

 built up by starting year classes at times 1, 2, 3, . . . 

 n years before the beginning of the period ; n repre- 

 sents the number of years for a year class to pass 

 through the fishery. During this "prestuily" ])eriod, 

 the mortality rates in effect at the beginning of the 

 study period were assumed to be in effect. Each 

 rth curve begins at the value of R,r (assumed the 

 same for each year class) required to produce the 



1 = n 



specified initial value of total stock Pto=^^P n- 



i=l 



This value of 7?„, can be quickly determined by a 

 few computer trials. P, for each year class is gen- 

 erated until it declines to a small arbitrary value 

 close to zero, but only the portion extending into the 

 study period is plotted. 



The initial and subsequent values of P,o are cal- 

 culated by graphically summing the heights P„ of 

 the 7th survival curves for each fishing^ season, by 

 means of a pair of dividers. Once the initial value 

 of Pio has been obtained, the calculation is self- 

 sustaining. From the recruitment curves, values of 

 Ru^i corresponding to P,o t, years before are obtained. 

 Ry,i is generated as a function of P ,„ in the Diode 

 Function Generator (fig. 2) by the simple device of 

 setting the P,o potentiometer so that the plotter "F 

 value" corresponds to the P,„ value for the particular 

 year in question. 7?^( is then plotted by attaching 

 the Y input to the Ry, point in the computer circuit. 

 Any empirical or theoretical curve relating recruit- 



ment to spawning stock can be set into the Diode 

 Function Generator, which, with an input Xi, pro- 

 duces an output in the form of a curve //=/(xi), 

 composed of 10 straight segments. 



SiU'vival curves as described above can be gen- 

 erated for each year class entering the fishery during 

 the study period. As in the case of the initial season 

 just described, heights P„ of the individual survival 

 curves for each year are summed graphically, and a 

 mark made representing the total commercial stock, 



P,o=VP,,. The "P,„ set" potentiometer is ad- 



1=0 



justed to bring the "I'-value" of the plotter into 

 conformance with the total stock value P^. The 

 catch is calculated by setting potentiometer "E" 



(Fig. 2) at the value E = - 



jl_e-(F+.w]_ The 



catch or yield value proceeds from the simple rela- 

 tion Yu- = EP,o. It is plotted by attaching the "Y 

 input" of the plotter at the point F„ in the computer. 

 After plotting of Y^ the process for P„j (above) is 

 repeated, and the cycle recommenced. 



In outline, then, the process of simulating popula- 

 tion and yield is as follows: 



1. Set the initial value of Y,^ at the size of the 

 actual catch for the initial year or two of the 

 study period. 



i = n 



2. Determine initial P,„— Z^Pn from the rela- 



i=o 



tion P,„ = \\/E. 



3. By computer trial, find value R„i such that 



i = n 



^ P„ = initial P,„. 



1=0 



4. Generate n curves of Ph, where n is the num- 

 ber of years required for P,i to decline from 

 Rwi to an arbitrary small value near zero. 

 Start at 1, 2, 3, ... n years before the begin- 

 ning of the study period. 



5. By Diode Function Generator evaluate Rwt 

 for each season from P,„ for season U years 

 before. Generate curves P,j starting at 

 Pit = Rwi for each fishing season. 



6. For each fishing season, graphically deter- 



i = n 



mine P,„=%Pti. Calculate \\ = EP,„. 



ANALOG COMPUTER MODELS OF FISH POPULATIONS 



39 



