And similarly for the second period: 



(VII) S_ = 2.3U ^ 3.98(.0O - .13) = 5.76 billions 



(VII) Si - ^-76 ^^'hkUdO - .13) ^ 6.9? billions 



In other words, the estimated annual recruitrtient to age one during 

 the second period was about two and a third times what it was in the first 

 period. 



EFFECT OF ERRORS IN ORIGINAL DATA 



As stated earlier, the numerical values used in the foregoing compu- 

 tations have been obtained by approximations, and may be considerably 

 in error. It is, therefore, desirable to knovj- what effect errors in the 

 various original data have on the final results. 



The curves in figure 2 indicate the values of natural and fishing 

 mortality which v/ill be obtaijied virith values of effort ratio and total 

 mortality centering- about those used in the foregoing computations. It 

 v;ill be noted that the effect of a given deviation is always greatest 

 on natural mortality, and least on fishing mortality, in the second period. 

 This is favorable to the practical application of the computations, since 

 the rate of natural mortality, in itself, is of relatively minor importance 

 in settling questions relating to the coraraercial fishery. On the other 

 hand, rate of fishing mortality under current conditions (second period) 

 of exploitation is of the greatest interest, since it leads to the esti- 

 mation of the size of the stock of pilchards from which the commercial 

 fishery must take its catch. 



Considering the relative seriousness of various types of errors, 

 it is apparent from figure 2 that errors .in computation of total mortality 

 are more serious than those in the effort ratio. For instance, the value 

 of the effort ratio used in our computations was U.O. PYom figure. 2 

 it may be seen that, using total mortalities of ,U0 the first period and 

 .80 the second period, a change in effort ratio from k-0 to 3.?, a decrease 

 of 12.5 percent, would cause an increase in the computed fishing mortality 

 for the second period of only 1.9 percent (from .77 to .785). However, 

 retaining the effort ratio of l|.0 and changing the total mortality for 

 the first period from .UO to .35, again a decrease of 12.5 percent^ would 

 result in an increase in fishing mortality for the second period of 2.6 

 percent (from .77 to .79). In other words, a given percentage error in 

 total mortality wbuld produce about l.U tiraeis the effect ou confuted fish- 

 ing mortality as the same percentage error in effort ratio (for the ex- 

 ample given). 



In general it may be said that fairly large errors in effort ratio 

 would not seriously affect the results of the computations, provided that 



177 



