the field of fisheries. Familiar applications outside 

 the field of biology include aircraft and spacecraft 

 design, ballistic studies for militarj- services, and 

 management of systems such as power-generating 

 pools and nuclear reactors. Among biologists, the 

 ecologists especially lia\e made use of simulation. 

 Notable examples include the simulation of ecologi- 

 cal systems by tligital computer (Clarfinkel ami Sack, 

 1964) and by analog devices (Odum, 1960 and Mar- 

 galef, 1962). In fisheries there have been three 

 general types of simulation: analytical, digital, and 

 analog. 



Analytical simulation i.s the oldest and best known. 

 It is so well known that an extensive review is sui)er- 

 fluous here. In it the biologist analytically deter- 

 mines the nature of the mathematical relations 

 controlling population structure and jjopulation 

 response to exploitation. He then constructs mathe- 

 matical models which predict what will occur under 

 certain assumed conditions of the fishery and the 

 environment. Most of the classical contributions 

 to fishery dynamics are of this type. They include 

 tlie work of such authors as Baranov (1918), Rus.sell 

 (,1931), Thompson and Bell (1934), Graham (1935), 

 Schaefer (1954), Beverton and Holt (1957), and 

 Ricker (1958). During the history of the analytical 

 techni(iue the complexitj- and sophistication of the 

 formulations have generally increased; the work of 

 Beverton and Holt unc[ucstionably represents the 

 highest development in this respect to date. 



Some of the above authors have also used digital 

 simulation. Thompson and Bell (1934) arithmeti- 

 calh- constructed tables to simulate the catch and 

 catch per unit of effort of the Pacific halibut under 

 constant recruitment and certain assumed rates of 

 growth and mortalitj*. They demonstrated a 

 remarkable correspondence between the values pre- 

 dicted by this method and the observed values for 

 certain periods and areas. Ricker (1958) made 

 somewhat similar calculations based on analytical 

 functions and introduced the additional concept of 

 relation between stock size and rate of recruitment. 

 He expressed catches in terms of "equilibrium 

 yields" which would be obtained when the additive 

 processes affecting the populations just balanced the 

 subtractive ones. An outstanding example of digital 

 simulation of a fish stock is found in Larkin and 

 Hourston (1964). 



To my knowledge, onlj' Doi (1957, 1962) has pro- 

 jjosed api)lication of the analog computer to fishery 

 dj'namics. He set forth mathematical formulations 



and computer block diagrams and made applications 

 to Japanese fisheries. His formulas are similar to 

 those used here, in general, but differ in detail. He 

 also adapted the Volterra equations to analog treat- 

 ment of predatory and competitive relations among 

 lish populations. 



With some notable exceptions (Ricker, 1958; 

 Larkin and Hourston, 1964; Larkin and Ricker, 

 19()4; International North Pacific Fislieries Com- 

 mission, 1962), fishery-simulation attempts to date 

 have dealt with eciuilibrium population conditions. 

 This restriction is understandable in view of the 

 mathematical complexities introduced by varying 

 rates. Such an approach does, however, lead to 

 models which are somewhat unreal compared with 

 their counterparts in nature. For instance the 

 number of recruits annually entering the stocks 

 varies widely. This problem has been treated by 

 considering recruitment constant for short periods 

 (apparently close to the truth for some Pacific hali- 

 but stocks during various 8- to lO-j'car periods be- 

 tween 1918 and 1933) or circumvented by expressing 

 results in terms of "yield per recruit." Likewise, 

 fishing mortality varies with fishing intensity. Any 

 realistic simulation of fished populations over con- 

 siderable periods reciuires .^^ome provision for changes 

 in recruitment and other vital rates, as can be accom- 

 plished on the analog computer. The importance 

 of this problem was recognized by Schaefer and 

 Beverton (1963) who wrote: 



". . . . the characteristics of the recruitment to marine 

 fish populations — its degree of fluctuation, its relation to 

 stock size and the influence on it of changing environ- 

 mental conditions — are the key to the interpretation and 

 prediction of the long-term dynamics of a fi.sliery . . ." 



antl : 



".\ctual fisheries are, however, .seldom in steady 

 states ..." 



The remainder of this report is devoted to a 

 description of the plan of attack (Piatt, 1964 — strong 

 inference) used in the analog computer approach. 

 Briefly outlined, this plan is as follows: 



1. Formulation of vital rates in a manner suit- 

 able for analog solution, thus .setting up a 

 hj^pothesis. 



2. Simulation of populations and yields over the 

 pcM'iod for which observational data are 

 available. 



3. Comparison of simulated and observed yields, 

 testing the hypothesis. 



32 



U.S. FISH .\ND WILDLIFE SERVICE 



