A population starts with 100 members of age zero Assume that

A population starts with 100 members of age zero. Assume that each member of age 0 produces 1 offspring and that 2/3 survive to age 1. All members of age 1 produce three offspring and then die.

a) Find the corresponding Leslie Matrix Model.

b) Find the dominant eigenvalue of the leslie matrix and its corresponding eigenvector.

c) Describe the stable age distribution and the asymptotic behavior of the population.

Solution

a)

for 0 you have 1/3

and for 1 you have 2/3

b)

eigen values : 2/3 * 1   + 1/3 * 0 = 2/3

c)

behavior the population is uniform distributionj