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COMPUTING LESLIE MATRIX Example After one year, we have only 250 fishes left. And then 125 have...

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Advance Math

COMPUTING LESLIE MATRIX

Example After one year, we have only 250fishes left. And then 125 have reached theirreproduction rate. If we set f3 = 8, then weare back to n = (1000, 0, 0): We seethat n1 = (0, 250, 0), n2 =(0, 0, 125), n3 = (1000, 0, 0)

Exercise Write down the Leslie matrix for theprevious example and calculate for various choices ofn the population vectorsni. What do you observe?

Exercise Showthat you can find some n such thatn+ = Ln =n. If n = (a,b, c) then

n+ = (8c, 0. 25a, 0.5b). Then (a, b, c) =(8c, 0. 25a, 0. 5b) determines aunique stable distribution n amongst theage groups. n itself is unique up to afactor.

Exercise Nowchange f3 = 8 to numbers smaller as well aslarger than 8, say 6 and 10. Thencalculate again for various choices of nthe population vectors ni.Can you still find some n suchthat n+ = n?

Answer & Explanation Solved by verified expert
3.5 Ratings (606 Votes)
Consider the Leslie matrix is given byIn this example andNow consider the initial population is out of which 250 isleft after one year and only 125    See Answer
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