Chapter 5.7, Problem 83E

To determine

(a)

To find:

Using the matrix equation, the total number of female owls for each of the next 5 yr,

suppose there are currently 3000 female northern spotted owls made up of 690 juveniles, 210 sub adults, and 2100 adults.

To determine

(b)

To conclude:

About the long-term fate of the northern spotted owl.

Using advanced techniques from linear algebra, we can show that in the long run,

$\left[\begin{array}{c}{j}_{n+1}\\ s_{n+1}\\ a_{n+1}\end{array}\right]\approx 0.98359\left[\begin{array}{c}{j}_n\\ s_n\\ a_n\end{array}\right]$.

To determine

(c)

To rework:

Part (a) under the new assumption.

In the model, the main impediment to the survival of the northern spotted owl is the number 0.18 in the second row of the $3\times 3$ matrix. This number is low for two reasons.

• The first year of life is precarious for most animals living in the wild.

• Juvenile owls must eventually leave the nest and establish their own territory. If much of the forest near their original home has been cleared, then they are vulnerable to predators while searching for a new home.

Suppose that, thanks to better forest management, the number 0.18 can be increased to 0.3.