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<br />Squawfish Population Viability Analysis --July 1993 <br /> <br />Page 17 <br /> <br />0 0 0 0 0 0 3 mL3 3 <br />mL7 mL9 <br />8 <br />j 0 0 0 0 0 0 0 0 <br />0 J 0 0 0 0 0 0 0 <br />0 0 j 0 0 0 0 0 0 <br />0 0 0 j 0 0 0 0 0 <br />0 0 0 0 J 0 0 0 0 <br />0 0 0 0 0 j 0 0 0 <br />0 0 0 0 0 0 .81 0 0 <br />0 0 0 0 0 0 0 .81 0 <br />0 0 0 0 0 0 0 0 .81 <br /> <br />Lx is the length of an x-year-old fish, which is established based on <br />regressions of adult growth rate performed above. It is assumed that this <br />Leslie Matrix yields a growth rate of 1.00. Only certain combinations of <br />the two unknowns, j and m, can produce this. The best way to determine <br />this parameter trade off is through the relationship for the net reproductive <br />rate, which must also be equal to 1.00. <br /> <br />00 <br /> <br />R = L 1 m = 1.00 <br />x=l x x <br /> <br />where Ix is the survivorship to age x. After some algebra, this relationship <br />reduces to <br /> <br />6 00 (x-7) 3 <br />R = 1.00 = j m L .81 (460+ 15(x-7)) <br />x=7 <br /> <br />which gives an implicit solution for m in terms of j, or vice versa. Some <br />possible combinations of j and m are <br /> <br />J m <br />.1 1.24597e-3 <br />.2 1.94683e-5 <br />.3 1.70915e-6 <br />.4 3.04193e-7 <br />.5 7.97423e-8 <br />