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?
