RAFAIL: STUDY OF FISH POPULATION BY CAPTURE DATA 



where R' k - M* xx is the mean of available values. 

 All the above relations are correct except the 

 relation N^ = catch/F*. which is an approxima- 

 tion of N k0 = catch/F A '  a* . Ifthe computations 

 show that the calculated (R - M)-values are close 

 to each other, then the approximate expression 

 for Nko is satisfactory to obtain accurate estimates 

 for q k . Significantly different (R - M)-values may 

 also lead to accurate estimates for q k . However, it 

 may be necessary to use A' k to estimate a* to ob- 

 tain improved estimates for A/* -values_to arrive 

 at a better estimate for A' k and (R - M)- 

 values. The rest of the computations for period I 

 are: 



K 



n 



N k0 



= CIF' 



exp(Ai) A k Rk - M k A k 



1 2.32 x 10" 3 1,087,070 1.56503 0.44789 0.45021 0.44818 



2 6.96 x 10" 3 1,696,408 1.55869 0.44378 0.45072 0.44354 



3 4.64 x 10~ 3 . 2,644,181 0.4505 xx 0.44586 



According to Equation (5.4) we get 



A? = 0.1967277, A '? = 0.2008653, 



A 'i= 0.1987911 

 <$>A' = 0.04(0.393455-0.399656) 

 = 0.04(-0.0062) = -0.000248 

 M'/\<l>f\ = -0.000248/500 = -0.496 x 10" 6 



q k = (2.320-0.496)10~ 6 = 1.824 x 10" 6 . 



According to Equation (5.8) we can calculate &A ' 

 by another way as 



<t>A' 



= -0.08(0.4505)(13.92-2.32-4.64)(10 3 ) 



+ 0.04(96.88-5.38-21. 53X10 6 ) 

 = (-0.2508 + 0. 0028)(10" 3 ) = -0.248(10- 3 ) 



That is, the two methods gave the same results. 



B) Surveys 2, 3, and 4 



\og e (C/f)' k = 0.0009 

 <t>f = -500 

 q k = -0.0009/- 500 = 1.8 x 10" 6 . 



.'.<t>A'/\<i>f\ = 0.000191/500 = 0.382 x lO" 6 

 q k = (1.8 + 0.382H0- 6 

 = 2.182 x 10-6. 



The arithmetic mean for q k from the four surveys is 



(1.824 + 2. 182)(10- 6 )/2 = 4.006 x 10" 6 /2 



= 2.003 x 10" 6 . 



Equation (6.3) can be used to estimate q k in one 

 step as 



Qk 



-0.00116 + 0.00090 -0.000248 + 0.000191 

 -1,000 1,000 



0.002060 0.000057 0.002003 



1,000 1,000 

 2.003 x 10" 6 . 



1,000 



Period I has four sampling surveys and only two 

 estimates for q can be obtained as the data of only 

 three successive surveys are used to get a single 

 g-estimate as explained above. 



Computations for Period III 



\og e {Clf)' k = -0.03012 



tf = 1/2(40,000-10,000) = 15,000 



-0.03012 onnQ v in _ 6 



g* = 15,000 =2QQ8x 106 - 



The following computations are obtained ac- 

 cording to the last estimate of catchability 



K N k0 = CIF k (R' k -M k \ 



a; 



ak 



= C/Fjflk 



1 5,592,318 0.00214 -0.08322 0.9595 5,828,366 



2 5,172,012 -0.00788 -0.04306 0.9786 5,285,113 



3 4,929,531 -0.00290 xx -0.02298 0.9887 4,985,871 



The following estimates are obtained by above 

 steps 



R' k - M' k ™ = 0.44782 



A 2 = 0.44242, A^ = 

 A4 = 0.44062 

 4>A' = 0.04(0.3946628 

 = 0.000191 



0.44422, 



0.3898815) 



Above estimates show a recognizable variability 

 for the first estimated (R' k - M' k \ parameters; so 

 the calculations are proceeded to obtain the next 

 (R' k - M' k ) 2 -estimates which are in fact highly 

 accurate if compared with the original values in 

 Table 2. 



Using the so-called the less accurate A[ -esti- 

 mates to calculate <}>A'; we get 



567 



