2 Problem 3 2 from Textbook (page 80) Consider an age structured discrete time population dynamics model with evolution model (3 7) We assume that pj 1 Rp, 82 1 11 BN 1 BN 1 12 where R 1 N 1 0 p Rp 13 R 1 p 1 for all jn 1 A steady state solution is a population distribution that does not change in time, that is p Rp (3) This equation says that p is an eigenvector of the Leslie matrix R with eigenvalue 1 Show that the limiting ( ) , ) 1 j 1 (4) guarantees the existence of a steady state population (Hint Recall that an eigenvector can be scaled arbitrarily, so you can assume that p 1 Using the identity (3), you can explicitly construct the steady state )

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2. Problem 3.2 from Textbook (page 80). Consider an age-structured discrete time population dynamics model with evolution model (3.7) We assume that pj+1 =

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2. Problem 3.2 from Textbook (page 80). Consider an age-structured discrete time population dynamics model with evolution model (3.7) We assume that pj+1 = Rp, 82 1-11 BN-1 BN 1-12 where R = 1-N-1 0 p" Rp"-13 = R-1 p

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