will be represented by a straight line. Figure 1 shows in this fashion 

 the numerical values used in this paper. It will be seen at once that 

 in both periods the numbers of fish over age two decline at a constant 

 rate^/, while those of ages one and two years do not. It was assumed 

 that the one- and two-year-olds are not fully available to the fishery, 

 and the line was fitted to the other ages by inspection. The lines shovm 

 indicate an annual decline in logarithm of .22!^ for the first period and 

 .700 for the second. These may be translated into mortality rates (a) 

 by the following formulations ; 



Let 3]_ and So be the relative stocks of any tvro successive ages. 



Then S2 = S-l - aS]_ = S]_(l-a) 



and 1 - a = — z 

 Si 



taking logs log (1-a) = log $2 - log 3^ 



or log (1-a) = -(log 32-log 3]_) = -(annual decline in log) 



Substituting numerical values given above, and letting subscripts refer 

 to the two periods, we have: 



log (1-a-, ) = -.225 1-a-, = .60 a-[_ = I-.60 = .UO 

 log (l-a2) = -.700 l-a2 » .20 32 = 1-.20 = .80 



In other words, the total mortality, or rate of disappearance, as indicated 

 by the age compositions of the stocks, was I4.O percent for the first, and 

 80 percent for the second, period. 



SEPARATING FIS'JING MORTALITY FROi! NATURAL MORTALITY 



The total mortalities determined above may be broken down into fishing 

 mortality and natural mortality if the latter is assumed to be the same 

 for the two periods. In the absence of any evidence of a change in the 

 rate of natural mortality, this assumption was made, and the method noted 

 below was adopted. 



This depends upon the fact that, v.-ith the same natural mortality (n) 

 for two periods, a given pair of total mortalities (a-,, a ) combined with 

 a given ratio between the two fishing mortalities (m-, , 0.2; is associated 

 with a certain ratio betvreen the amounts of effort (I-^, I2) expended per 

 year during the two periods. The procedure is to determine what ratio 



(R * rlf ) between the two fishing mortalities gives the known ratio between 



__ 



-The regular decrease in numbers of the fish in each age class for the 



earlier period is a result of the method of age analysis employed, 



rather than a natural phenomenon. 



178 



