SECT. 4] FISHERY DYNAMICS THEIR ANALYSIS AND INTERPRETATION 479 



With respect to the second assumption, although certain factors, such as 

 fecundity and perhaps mortality in many cases, are approximately proportional 

 to total biomass, growth is highly age-specific ; thus the age-structure of the 

 population, as well as its total biomass, must enter to some degree into its 

 potential for increase. 



It is to be noted that if the model is applied to data for steady states only, 

 these assumptions are not necessary. In this case the age-structure of the 

 population is uniquely determined by its biomass. Also, since in the steady 

 state the population during any year is, on the average, of the same size and 

 age-structure as during any subsequent year, the effect of time lag on recruit- 

 ment, etc. is eliminated. Actual fisheries are, however, seldom in steady states, 

 so we must deal with transient states, in which these effects appear. 



It is important in this connection to note that the changes in fishing effort 

 in many commercial fisheries are often gradual, so that the displacement from 

 steady state is not large. Furthermore, some kinds of fishes, and other organ- 

 isms, especially those of the tropics, such as peneid shrimp and yellowfin 

 tuna, enter the catchable stock very young, mature very early, and have a very 

 short life-span. For such species, the time lag between spawning and recruit- 

 ment is small, and effects of changes in size composition due to changes in 

 fishing effort are less important than for organisms of greater life-span. At the 

 other extreme there are fisheries based exclusively on the mature phase of 

 populations in which maturity does not occur until a relatively high age is 

 reached. A case in point is the Norwegian Lofoten fishery for mature arctic 

 cod, which are not recruited to the fishery until they are eight or nine years of 

 age, on the average. 



The rate of natural increase is determined not only by the magnitude and 

 age-structure of the population, but also by many environmental factors. 

 Variation in these will cause departures from the rate of increase that would 

 occur under average environmental conditions. In applying the model to the 

 data from the fishery, we assume that the effects of variable environmental 

 factors on recruitment, survival, and growth are random, or at least that they 

 are not correlated with population changes due to changes in fishing effort, so 

 that they may be averaged out. In other words, we assume that the mathe- 

 matical expectation of e in equation (21) is zero. 



Variations in the fishes 1 environment may also affect their behaviour so as to 

 make them more or less accessible to capture. It is. again, implicitly assumed in 

 the application that these effects are random, or at least uncorrelated with 

 changes in fishing effort, so that the mathematical expectation of the constant 

 c remains the same for different levels of fishing effort (and population size). 



4. Concluding Remarks 



As was mentioned at the beginning of this chapter, the fact that the two 

 approaches to the analysis and prediction of fishery dynamics have evolved 



