GENERAL APPLICATION OF THE 

 TECHNIQUE 



Application of tho analog computer technique 

 described in this report requires estimation of a 

 series of constants or parameters. It also requires 

 a number of approximations and some appraisal of 

 their uniqueness. These two topics will be dis- 

 cussed in this section. 



PRELIMINARY ESTIMATES OF PARAMETERS 



An extensive literature is available on the estima- 

 tion of parameters of fish populations under exploi- 

 tation. Tlie most thoroughgoing summaries and 

 descriptions known to me are given in Beverton and 

 Holt (1957) and Ricker (1958). Treatment here is 

 limited to the specific constants, variables, and rela- 

 tions which must be estimated for simulations by 

 analog computer as described above. They will be 

 considered in descending order of the degree of 

 certainty witli which they are likely to be known. 



1. Annual yield. For most commercial fisheries 

 this figure is likely to be known rather precisely. 

 Since the original data come from wcighouts at the 

 time the fish are first sold, their accuracy has been 

 watched clo.sely by both fishermen and fish buyers. 

 If possible, catches should be segregated according 

 to biological stock units. 



2. Growth in weight. Lengths or weights at 

 specific ages are among the most commonly gathered 

 fishery data. If data are in lengths, they must be 

 converted to weights through a length-weight curve. 

 The length-weight relation is fairly stable as com- 

 pared with other parameters and can be determined 

 from a relatively small number of samples covering 

 the size range of the fisii in question. The Gompertz 

 growth curve can be fitted to the empirical data 

 directly on the analog computer simply by adjusting 

 potentiometer settings for G and g until a good fit is 

 obtained. 



3. Instantaneous fishing mortality rate, F. This 

 rate may be difficult to estimate with accuracy. If 

 empirical estimates are lacking, however, it may be 

 possible to produce an "educated guess" through 

 general knowledge of the history of the fishery, its 

 changes in yield, the size of the current fishery, .... 

 This value can V)e adjusted during simulation. 



Once a value of /'' is availal)le for one jjcriod, tlie 

 %'alues for other periods can be estimated if fishing 

 intensity is known. Data on the number and size 

 of units in the fleet are usually a\ailal)le. These 

 figures must be multiplied by an estimate of time in 



operation to obtain the value of fishing effort, /. 

 Once a series of values of / is on hand, together with 

 F and / for a "base period," values of F for all 

 periods can be calculated from the relation F = qf, 

 where 7 is a constant to be determined from the 

 base-period data. 



4. Instantaneous natural mortality rate, ^T. Esti- 

 mates of M may be availalilo from tagging or bio- 

 logical data, or an assumed value may be selected 

 for the initial trial. If an assumed value must be 

 used, guidance can often lie obtained from the 

 growth characteristics of the fish (Beverton and 

 Holt, 1959; Beverton, 1903). For fish in the com- 

 mercially available stock, values of .1/ are often low, 

 in the vicinity of 0.1 to 0.3. Frequently, reasonable 

 approximations can lie obtained by considering M 

 to be constant during the study period, for all ages 

 of fish. 



5. Stock-recruitment relation. Of the items re- 

 quired for simulation, this one is usually the most 

 difficult to obtain. If data are available on age com- 

 position, it may be possible to estimate the abun- 

 dance of the youngest (or youngest important) year 

 class in the commercially available stock. A series 

 of such estimates can then be related to the estimated 

 size of the spawning stock Ir years earlier, as was done 

 by Clark and Marr (1955). The resulting scatter 

 diagram may reveal a pattern that can form the 

 basis for one or more recruitment curves. It is 

 significant that only the portion of the curve cover- 

 ing the stock sizes encountered can affect the out- 

 come of the simulation. 



SUCCESSIVE APPROXIMATIONS AND 

 UNIQUENESS 



Once the preliminary estimates of the parameters 

 arc assembled, simulation trials can begin. Because 

 all the work is visible on tlie computer chart as it 

 proceeds, it is often possible to see in what direction 

 the parameters must be changed to produce a better 

 fit of calculated to actual catches. Experimentation 

 is readily accomplished, since all parameters may be 

 changed simply by resetting potentiometers (either 

 coefficient potentiometers or the several small ones 

 in the Diode Function Generator). For trials in the 

 applications above, each trial for 26 or 27 fishing 

 seasons consumed about one-half day. This work 

 included preparation of the chart and all other neces- 

 sary oi)erations leading to a plot of annual popula- 

 tions and yields. It is thus possible to accomplish 

 several trials within a reasonable period of time. 



42 



U.S. FISH -VN'D WILDLIFE SERVICE 



