FISHERY BULLETIN: VOL. 76, NO. 1 



^2 ,i8Mi ^ ^-6M2 '"^^^^^2 (l_^ln/e2-6M2) = ;,^ (^g^^ Equation (21)). 



(1-mi) ln/22+6M2 



Solve for M2 by iteration. 

 Next, Equation (12) can be written as 



gl8% = g-6M2g-6(Fi+A72)g-6M3g-6(F2+A/3) = g-(6Fi + 12A/2)g-(6F2+12M3) 



O5 



(l-mi)(l-m2)m3 



= fe2e-(6F2+12M3) = ^^ 



The natural logarithm of ^4 



ln/j4 = -(6F2+12M3)+ln/e2 (18) 



which can be solved for F2 as follows: 

 -6F2 = ln/e4+12M3-lnfe2 



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Since e-«^2e-6(Fi+M2) = ^-(6Fi.i2iW2) = /j^, 



Equation (11) can be written 



(l-^,)a-m2) ^""^ = ^^^""^ ^ (l-e-<^-2-3>) = ,3 (20) 



and since g-^<^2+'W3) = ^-6F2-12A/3+6M3 ^ g-6(F2+i2M3H6M3 = ginfe4-infe2+6M3 (from Equation (18)) 



and (from Equation (19)) 



rin/j4-ln/e2+12M3"| 

 F2 ~ L 6 J _ -(Infe4-Infe2+12M3) 



Fo+Mo " rin/e4-ln/e2+12M3l ~ -(ln/?4-ln/22+12M3)+6M3 



-L § — -J^^3 



ln/e4-ln/22+12M3 ln/24-ln/e2+12M3 



ln/e4-ln/z2+12M3-6M3 ~ ln/e4-ln/22+6M3 



then Equation (20) becomes 



§. ln/e4-ln/f2+12M3 



jz ^3 rei8^i = /?2e-^^3 , u ^ u a^, (l-ei"''4-infc2+6M3) ^ f^ (text Equation (23)). 



(l-mi)(l-m2) ^ ln/e4-ln/22+6M3 / j v m 



Since e-^6^'i^i2M2) = /^^ and e-(«^2+i2iW3) = ^ 



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