Leslie matrix

A certain colony of bats has a life span of less than 3 years. Suppose that the females are divided into three age groups: those under age 1, those of age 1, and those of
age 2. Suppose further that the proportion of newborn females that survives until age 1 is q and that the proportion of one-year-old females that survives until age 2
is .5. Assume also that females under age 1 do not give birth, those of age 1 have, on average, 2 female offspring, and those of age 2 have, on average, 1 female offspring.
Suppose there are initially 300 females of age less than 1, 180 of age 1, and 130 of age 2.

(a)Write a Leslie matrix A for this colony of bats.

Age rate Birth Population
0-1 q 0 300
1-2 0.5 2 180
2-3 0 1 130

Leslie matrix
0 2 1 300
0.5 0 0 180
0 0.5 0 130

Is this correct?



(b) If q = .8, what will happen to the population in 50
years?