complicate the problem of management (Stew- 

 art and Pontecorvo, 1970). 



For a first approximation we may visualize 

 the fisheries management apparatus as re- 

 quiring several aggregate yield functions as 

 operational concepts. The plurality is neces- 

 sary because our concepts of aggregate yield 

 are ambiguous: it may be a regional concept, 

 a concept associated with a particular level 

 of the food chain, a concept that involves a 

 set of stocks that are either economically or 

 ecologically consistent in some way, etc. The 

 ambiguities involved derive from the inade- 

 quacy of biological knowledge of aggregate 

 yield, what the economists might call macro 

 biological ocean processes, and also from the 

 open access common property status of the 

 stocks. This latter situation permits each 

 nation state to define its output goals in terms 

 of its own tastes (exploitation of alternative 

 species) and then to proceed to bargain for 

 its share in purely nationalistic terms. 



In the absence of adequate goals at the 

 level of aggregate yield, fishery administrators 

 are left dealing with partial equilibrium 

 systems, i.e., yield functions for particular 

 species, a circumstance which makes them 

 particularly vulnerable to pressure from eco- 

 nomic interests, fluctuations in the stocks and 

 the interaction between the two. 



Population Dynamics 



The population models developed by the 

 biologists are basically consistent with economic 

 models. Difficulties in the process of data col- 

 lection, statistical problems in fitting functions, 

 and the development of accurate forecasts are 

 all familiar ground. The question of the ade- 

 quacy and the cost of basic data does require 

 further comment. The observation of wild 

 populations is a time-consuming and costly 

 process. The fishermen are close observers of 

 the behavior of these populations and the com- 

 mercial catch is therefore an important data 

 source. Several types of bias may be involved 

 in using catch data, the most obvious being 

 that the data are restricted largely to what the 

 fishermen want to catch when they want to 

 catch it. 



Perhaps more important, however, are 

 certain problems inherent in the structure of the 



biological models. Biologists distinguish a 

 number of types of biological models, among 

 which are the logistic and the dynamic pool- 

 type. 



The logistic model results in a parabolic 

 yield cui-ve with a well-defined maximum, 

 and this has been utilized by many economists. 

 The maximum point on the yield curve repre- 

 sents the maximum sustainable yield."* At 

 this point the stock is roughly half as abundant 

 as in its initial state or maximum size. Two 

 assumptions of interest to economists lie be- 

 hind this model, the first "that the rate of 

 increase in the stock responds immediately 

 to changes in population density; second, 

 that the rate of natural increase at a given 

 weight of stock is independent of its age (or 

 size) composition." 



Naturally the adequacy of the assumptions 

 and the intrusion of exogenous forces affect 

 the adequacy of the model. But the matter 

 of greatest concern to the economist lies in 

 the first assumption. If there is not, as the 

 biological evaluation of this type of model 

 suggests there is not, an instantaneous ad- 

 justment between changes in population 

 density and population rate of growth the 

 economist for one becomes immediately inter- 

 ested in the time dimension of the adjustment 

 mechanism and the lag function that may be 

 utilized to describe it." Unless we limit our- 

 selves to consideration of long run equilibrium 

 solutions the integration of the biological 

 yield function into an economic system will 

 require the specification of the lag function. 

 For many purposes, particularly exposition, 

 it may be adequate to define the biological 

 system in terms of equilibrium points. How- 

 ever, if, as appears to be the case, the time 

 lags are significant, i.e., if they are of such 

 duration as to influence economic variables 

 (price, fishing effort, entry and exit), then 



'" Holt, (1962 p. 141-142), has suggested that this 

 particular function may be flat topped which "simply 

 means that the biological facts are not very relevant 

 to determining- where fishing becomes stabilized over 

 quite a range of variations in the situation." See 

 alsoGulland (1968). 



" Prof. G. Paulik has pointed out to me that the 

 time lags involved are a function of the species to 

 which the model is applied. In general tropical species 

 fit the first assumption fairly well but those in temperate 

 zones show much slower time rates of adjustment. 



14 



