further its percentage availability in previous years, and so arrive 

 at a nvimerical evaluation of its relative strength at commercial age* 

 Indeed, trial computations have practically proved the feasibility of 

 this calculationo 



Natural mortalityo ~ In computations so far undertaken we have as- 

 sume d~~thi~"probRbility that mortality from natural causes is constant. 

 This greatly simplifies the calculation of catch mortality. However, 

 this assumption should be examined critically and perhaps revised if it 

 is discovered that predators (other than man), and therefore predation, 

 has increased or decreased to an important extent in any two periods 

 under consideration.2/ 



Also the probability of death from natural causes may vary with 

 age, and the formulations may need appropriate revision. These eventu- 

 alities cannot be appraised until a series of age-distributions, properly 

 representing the sardine stock, become available. 



Catch mortality . - While remaining aware of the possible necessity 

 for revising the assumption of constant natural mortality, it is con- 

 venient to employ this assumption to simplify the computation of catch 

 mortality. Given two periods, in one of which the intensity of fishing 

 was greater than in the other, there is a unique combination of differ- 

 ing catch-mortalities in the first and second periods and of constant 

 natural mortality for both periods that will account for the total mor- 

 talities and the total catches in the two periods, respectively. The 

 mathematical formulation must take into consideration that the natural 

 and catch causes for death are operating simultaneously and, therefore, 

 complete with each other for the lives of the fish. It also involves 

 consideration of whether an increase in fishing intensity, i.e. the em- 

 ployment of more effort or gear, brings in competition between fishing 

 units. That is difficult of appraisal for the sardine fishery because 

 addition of boats may as easily produce an effect the opposite of compe- 

 tition, i.e. cooperation, through extending the scouting area and com- 

 municating information on the location of schools. The effect of coop- 

 eration has been neglected in the computations so far contemplated. 

 It should be taken into account, and probably will be, as soon as a 

 method of measuring it can be devised. 



"Tf It may be possible in such a case to regard the sardine as having 

 a number of predators, including man, and base the formulation on the 

 effects of the simultaneous probabilities of death from the several 

 categories of predation. The mathematics would be complicated and prob- 

 ably require data on more than two seasons, especially if a multiple 

 correlation method were employed, but should be feasible, given an ade- 

 quate quantity of data of reasonable reliability. 



15 



