HENRY: NATURAL AND FISHING MORTALITIES OF CHINOOK SALMON 

 £3 



d^ =— orOs = (l-ml)^-l«''^le-«^2e-6(^l+^^2) (l-m2)e-«^'^3 g-6(^VM3),„3 from Equation (5). (12) 



9e =~ or 4 = (i-mi)c-i«'^^ie-6-^2e-6(^i+'^^2) ( 1-^2)6 «^^3e-6(^2-^^3) (i_;„3)e-6^^4 



TV. 



i^3 



F3+M4 



(l_e-6(^3+^4)) from Equation (6). (13) 



^4 



6, =ir^ ore, = (l-mi)e-i«'^^ie-6'^^2e-«(^'i-'^^2) (l-m2)e-^'^'3 



Nq 



g-6(F2+^/3^(l_;„3)e-6A^4e-6(f'3+'"4) from Equation (7). (14) 



Then for m, = m (fixed) {0i<mi<l){6^<m2<l){0r,<m3<l), text Equations (17) to (19), by rearranging 

 Equation (8) and taking natural logarithms we obtain 



-l/lSlnfj.V Ml (text Equation (20)). 

 \mi/ 



Then Equation (10) can be rewritten as 



^ISMj ^ g-6M2^-6(Fi+iV/2) = g-6A72-6Fi-6M2 = ^-{6F-^ + 12M 2) = /^ _ 



^3 



(l-mi)m2 

 The natural logarithm of /?2 



ln/e2 = -(6F1 + I2.W2) (15) 



which can be solved for F^ as follows: 



-6F1 = ln/e2+12M2 



ln/e2+12M2 

 Fi = g (text Equation (22)). (16) 



Equation (9) can be written 



and since e-«(^i+^^2) = ^-6Fi-i2.W2+6a/2 = ^-(6Fi^i2M2)+6M2 = ^infe2+6M2 (from Equation (15)) 



and (from Equation (16)) 



ln/e2+12A/2 

 i^i _ 6 _ -(lnfe2+12Af2) ^ Infe2+12M2 ^ ln/g2+12M2 



F1+M2 " ln/?2+12M2 ~ -(ln/?2+12M2)+6M2 ln/?2+12M2-6M2 ln/e2+6M2 



6 "'^^ 



then Equation (17) becomes 



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