BANDICOOTS

 

 

The Southern Brown Bandicoot (Isoodoon obesulus)

 

In parts of NSW the Brown Bandicoot is considered to be endangered.  The bandicoot lives for about 3 years and is sexually mature at 3 to 4 months. Bandicoots usually breed from winter through to the end of summer, and have a 12 day gestation period so a female bandicoot can produce 2-3 litters per year. Litters contain up to 6 young which become independent in 60 to 70 days. Survival rates are very low with less than half of any one litter surviving however the fecundity rates are high which gives the population a good chance of recovery.  The fecundity rate is the number of female offspring per female per year.

 

Assume that in one national park the population of the Southern Brown Bandicoot is estimated at 100 of which roughly half are female.  The ranger has done some careful data collection and obtained the following information.

 

Population

 

Age(x)  (at end of year)

Number (Nx) of females

1

20

2

18

3

12

 

Fecundity rates (Fx)

 

Age (x)

Fecundity rate (Fx)

1

0.5

2

2.0

3

0.8

 

Survival Rates

 

Age (x)

Survival Rate (Sx)

1

0.3

2

0.45

 

 

The ranger is wondering whether the population can survive without any intervention and asks your group for some help.

 

Notes on Leslie Matrices

 

A Leslie Matrix can be used to calculate the expected population in future years. In these notes Fx is the fecundity rate for a female of age x, Sx is the survival rate for a bandicoot of age x, and Nx is the number of females of age x.  The Leslie matrix L for the bandicoots is made up as follows.

 

 

The initial total female population is N1 + N2 + N3, and the initial female population vector is:

 

 

To calculate the total female population after one year, you compute the new population vector P1 and then sum its entries, where

 

.

 

Let Px be the population vector after x years. Then

 

.

 

 

 

Developed by Susan Worsley.

 

 

 

http://www.maths.uq.edu.au