In a fishery, a certain species of fish can be divided into three age groups, each one year long. The Leslie matrix for the female portion of the population is given by L =

⎛

⎝

0 3 36 1

3 0 0 0 1 2 0

⎞

⎠.

Show that, without harvesting, the fish population would double each year.

Describe the long-term behavior of the system if the following policies are applied:

(a) harvest 50% from each age class;

(b) harvest the youngest fish only, using a sustainable policy;

(c) harvest 50% of the youngest fish;

(d) harvest 50% of the whole population from the youngest class only;

(e) harvest 50% of the oldest fish.