
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 oneyearold 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
01 q 0 300
12 0.5 2 180
23 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?