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
0 0 f3
0. 25 0 0
0 0. 5 0
MIT 21F Spanish I - IV (OCW)
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Write down the Leslie matrix for the previous example and calculate for various
choices of n the population vectors ni.What do you observe?
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.
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?
Assume that this is the Spanish Section and NOT the Marine Biology/Algebra section.
Post this question in the Biology section. You might get an answer there. You might.