fp 



the two amounts of effort (^y^ «> U)* Natural mortality (n) is pu.t in terms 



of R, a-[_ and ap as follows : 1 



a, = m-, + n - m-,n 



(Ricker, p. 60, 1st paragraph) 

 a2 = mp + n - mpn 



But, by definition: R = !iir and mp ?= Pto, 



Substituting in the second equation above v/e have: ^2 ~ ^i + n - Rra,n 

 Multiplying the first equation by R: Ra-j^ => Rm]_ + Rn - Bm-^n 

 Subtracting from the last equation the one above it; 



Ra-, - ap = Rn - n = n(R - 1) 



Rai - a? , > 

 and n = ^^_ ^ < (I) 



fp 

 Now -^ must be gotten in terms of R, n, a]_ and a2 as follows : 



Starting again with: a]_ = ra-|_ + n - m^^n 



and transposing: a-j^ - n = m^^ - inj_n =_ra-,(l - n) 



a - n 



Dividing by (1 - n) : m, =^-i (II) 



-■- 1 - n 



Also, by definition: mp = Rm-j^ (III) 



f„ log (1 - mp) , ^ 



Finally: T^ ■ log (1 - m^j (I^) 



This last formula was developed by Ricker for fisheries of Type I, 

 However, as shown by Schaefer (19l;3), it may be used equally well for fish- 

 eries of Type II. 



Starting with a value of R of 2.U and substituting our previously 

 determined values of a^^ (.UO) and ap (.80), 2 j^ay be computed from the 

 above equations as follows ; 1 



rr^ 2.U(.U0) - .80 _ , 

 (I) n = 2.1; - 1 '^^^^^ 



(II) ra^ :, 1 _ .111^3 •^'^^^ 

 (III) ra2 = 2.1;(.3226) = .77U2 



rr.r^ £2 log (1 - ■77U2) 



(^^) f •- log (1 - .3226) ' ^'^^ 



174 



