Assume that a certain species, say fish, reproduces only during the third year and then dies. Assume that we have an initial population of n0 n 1000, 0, 0, that is of 1000 newborns, and no other fishes. Assume that during the first year, 25% survived and then 50% of those make it to reproduction age. The Leslie matrix for this situation is L 0 0 f3 0. 25 0 0 0 0. 5 0 Example

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Qstn. Write down the Leslie matrix for the previous example and calculate for various choices of n the population vectors ni.What do you observe? Qstn. Show that you can find some n such that n Ln n. If n a, b, c then n 8c, 0. 25a, 0. 5b. Then a, b, c 8c, 0. 25a, 0. 5b determines a unique stable distribution n amongst the age groups. n itself is unique up to a factor. Qstn. Now change f3 8 to numbers smaller as well as larger than 8, say 6 and 10.Then calculate again for various choices of n the population vectors ni.Can you still find some n such that n n?

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